Simple plant growth models

In this example, we use Bristlecone to fit a suite of classical non‑linear plant‑growth models to data from a controlled growth experiment.

Paine et al. (2012) identify seven widely used functional forms for modelling plant biomass through time. These models differ in their assumptions about asymptotes, growth rates, and curvature, and are a natural testbed for demonstrating Bristlecone’s model‑expression system and optimisation workflow.

We implement the dM/dt forms of all seven models using Bristlecone’s declarative syntax, then fit them to the Holcus unshaded growth dataset from Paine et al. (2012) using Nelder–Mead optimisation.

First, we open Bristlecone core libraries.

Defining the models

For units of measure, we can choose to use built-in F# units from the FSharp.Data.UnitSystems.SI.UnitSymbols namespace, or declare our own. Similarly, time-based units (days, months, years) are available in the Bristlecone.Time module. Here, we use the time units from Bristlecone, and declare grams as a new unit type.

[<Measure>] type gram

let mass = state<gram> "mass"

For the growth functions, there are five different parameters across the seven models, which we declare. To declare parameters, a reasonable starting bound and a constraint are required. Often, parameters will be declared as Positive, but can also be NoConstraints for unconstrained. Parameter constraints are handled automatically by the optimisers, such that the Nelder-Mead algorithm will run in a transformed (unbounded) parameter space.

Each model is expressed in its differential form (dM/dt), which Bristlecone integrates automatically when fitting continuous‑time systems.

The parameter r represents different biological processes across the seven models (absolute growth rate, proportional growth rate, curvature parameter, etc.), so we define rAbs and r separately to avoid conflating meanings.

module GrowthFunctions =

    // Parameters
    let K = parameter "K" Positive 20.0<gram> 40.0<gram> // upper asymptote
    let β = parameter "β" Positive 0.1 2.0
    let L = parameter "L" Positive 20.0<gram> 40.0<gram> // lower asymptote

    // The meaning of r changes between models, so define it seperately
    let rAbs = parameter "r_abs" Positive 1.1<gram/day> 1.2<gram/day>
    let r = parameter "r" Positive 0.01</day> 2.00</day>

    // 7x typical model forms (ODEs)
    let linear = P rAbs
    let exponential = P r * This<gram>
    let powerLaw = P r * This<gram> ** P β
    let monomolecular = P r * (P K - This<gram>)
    let logistic = P r * This<gram> * (Constant 1. - This / P K)
    let logisticFour = P r * (This<gram> - P L) * ((P K - This) / (P K - P L))
    let gompertz = P r * This<gram> * Logarithm (P K / This)

    // Scaffold into a list of plausable hypotheses:        
    let hypotheses =
        let mkModel ode = Model.empty |> Model.addRateEquation mass ode
        [
            "linear", mkModel linear |> Model.estimateParameter rAbs
            "exponential", mkModel exponential |> Model.estimateParameter r
            "power", mkModel powerLaw |> Model.estimateParameter r |> Model.estimateParameter β
            "monomolecular", mkModel monomolecular |> Model.estimateParameter r |> Model.estimateParameter K
            "logistic (3-par)", mkModel logistic |> Model.estimateParameter r |> Model.estimateParameter K
            "logistic (4-par)", mkModel logisticFour |> Model.estimateParameter r |> Model.estimateParameter K |> Model.estimateParameter L
            "gompertz", mkModel gompertz |> Model.estimateParameter r |> Model.estimateParameter K
        ]

Load the dataset

Here, to keep the example simple we have defined the data in code, but otherwise you may load data in as you see fit.

Bristlecone expects time‑series to be provided in Bristlecone's TimeSeries type. For ecological datasets recorded in modern calendar time, the helper TimeSeries.fromNeoObservations converts (value, DateTime) pairs into a typed time‑series that Bristlecone can align with the model’s time units.

Lastly, Bristlecone expects a Map of TimeSeries for use in the fit function.

let baseDay = System.DateTime(2000, 01, 01)
let data =
    [
        mass.Code, TimeSeries.fromNeoObservations [
        0.05, baseDay.AddDays 14
        0.33, baseDay.AddDays 35
        2.43, baseDay.AddDays 70
        3.63, baseDay.AddDays 98
        5.81, baseDay.AddDays 133
        7.28, baseDay.AddDays 161
        5.87, baseDay.AddDays 189
        ]
    ]
    |> Map.ofList

Model-fitting

All seven growth models are naturally expressed as ODEs, so we use a continuous‑time estimation engine. The call to Bristlecone.forDailyModel ensures that the engine interprets the model in daily units, matching the temporal resolution of the dataset.

We use a simple Nelder–Mead optimiser, as the models are simple with only between one and three parameters. If we wanted increased robustness to local optima, we could choose to run a swarm-based Nelder-Mead instead.

Plant‑growth data typically exhibit heteroscedasticity: measurement error increases with biomass. We therefore use a Gaussian likelihood with an exponential variance function, parameterised by σ0 and σ1.

We specify no conditioning. Here, we know that plant biomass was effectively zero at time zero, so we do not need to condition the time-zero value; it is known. The model fitting will therefore run from the first time-point in the data onwards.

Then, we can just run all of the hypotheses.

Each model is compiled before fitting. Compilation resolves the symbolic model expression into an executable system of equations and prepares the likelihood function for evaluation.

module Settings =
    let engine =
        Bristlecone.mkContinuous ()
        |> Bristlecone.forDailyModel
        |> Bristlecone.withCustomOptimisation (Optimisation.Amoeba.single Optimisation.Amoeba.Solver.Default)
        |> Bristlecone.withConditioning Conditioning.NoConditioning
        |> Bristlecone.withSeed 200000

    let endCond = Optimisation.EndConditions.whenNoBestValueImprovement 100<iteration>

let sigmaBase = parameter "σ0[x]" Positive 0.01<gram> 0.5<gram>
let sigmaGrowth = parameter "σ1[x]" Positive 0.01</gram> 0.5</gram>
let variance = ModelLibrary.NegLogLikelihood.Variance.exponential sigmaBase sigmaGrowth

let results =
    GrowthFunctions.hypotheses
    |> List.map (fun h ->
            let hy =
                snd h
                |> Model.useLikelihoodFunction (ModelLibrary.NegLogLikelihood.NormalWithVariance (Require.state mass) variance)
                |> Model.compile
            fst h, Bristlecone.fit Settings.engine Settings.endCond data hy
    )

The plot below overlays the observed biomass with the fitted trajectories from each model, allowing visual comparison of model performance.

Graphing.fitPlot results
|> Plotly.NET.GenericChart.toChartHTML

Model selection

Because this example uses a non‑Bayesian fitting approach (maximum likelihood with Nelder–Mead optimisation), we can compare competing growth models using constrained Akaike’s Information Criterion (AICc).

AIC provides a balance between goodness‑of‑fit and model complexity, and the corresponding Akaike weights give the relative support for each model in the candidate set.

let weights = ModelSelection.Akaike.akaikeWeights (results |> Seq.map snd)

For more complex analyses involving multiple subjects, multiple hypotheses, or replicate fits, see the Model Selection documentation for the ResultSet‑based workflow.

The resultant weights are:

weights 
|> Seq.zip (results |> Seq.map fst)
|> Seq.map(fun (m,(r,w)) ->
    sprintf "| %s | -logL: %f | AICc: %f | Weight: %f |" m r.Likelihood w.AICc w.Weight
    )
|> String.concat "\n"

"| linear | -logL: 0.329993 | AICc: 18.659986 | Weight: 0.000006 |
| exponential | -logL: 12.874793 | AICc: 43.749586 | Weight: 0.000000 |
| power | -logL: -5.599349 | AICc: 36.801302 | Weight: 0.000000 |
| monomolecular | -logL: 0.329993 | AICc: 48.659986 | Weight: 0.000000 |
| logistic (3-par) | -logL: 5.349318 | AICc: 58.698637 | Weight: 0.000000 |
| logistic (4-par) | -logL: 4.494261 | AICc: Infinity | Weight: 0.000000 |
| gompertz | -logL: -26.620829 | AICc: -5.241659 | Weight: 0.999994 |"

The output indicates that the best‑supported model is the gompertz growth model, with approximately 99% support.

The reason that the gompertz is identified as the best model, despite the fit not looking as good by eye as the three-parameter logistic form, is because the likelihood function with exponential variance penalises errors at larger biomasses less heavily.

We can estimate the implied sigma for each observation, for example for the gompertz fit:

let sigmaAt (expected: float<gram>) =
    let s0 = (snd results.[6]).Parameters.Get sigmaBase
    let s1 = (snd results.[6]).Parameters.Get sigmaGrowth
    s0 * exp (s1 * expected)

let diagnostics =
    (snd results.[6]).Series
    |> Map.find mass.Code
    |> fun ts -> ts.Values
    |> Seq.map (fun d ->
        let fitted = d.Fit
        let observed = d.Obs
        let sigma = sigmaAt (fitted * 1.<gram/ModelSystem.state>)
        sprintf "Fit = %f, Obs = %f, sigma = %f" fitted observed sigma
    )
    |> Seq.toList

diagnostics

["Fit = 0.515472, Obs = 0.330000, sigma = 0.000000";
 "Fit = 2.430000, Obs = 2.430000, sigma = 0.000000";
 "Fit = 3.629969, Obs = 3.630000, sigma = 0.000025";
 "Fit = 4.280808, Obs = 5.810000, sigma = 0.962549";
 "Fit = 4.474745, Obs = 7.280000, sigma = 22.391603";
 "Fit = 4.549555, Obs = 5.870000, sigma = 75.382107"]

The sigma values are very tight for the first three time points for the gompertz fit, as shown above. Other models fail to predict the earlier biomasses with such closeness, so are heavily penalised as a result.

Model fit quality / uncertainty

For maximum‑likelihood fits, Bristlecone supports profile‑likelihood confidence intervals for individual parameters. Profile likelihoods are robust to non‑linearity and asymmetry in the likelihood surface, making them preferable to approximate Hessian‑based intervals for ecological models.

Below is an example of how to compute a profile likelihood for the parameters of a fitted model.

let likelihoodProfile =
    results
    |> Seq.take 1 // just run the first only in this example
    |> Seq.map(fun (name,r) ->

        // Lookup the original hypothesis model using its name:
        let h =
            GrowthFunctions.hypotheses |> Seq.find (fun s -> fst s = name)
            |> snd
            |> Model.useLikelihoodFunction (ModelLibrary.NegLogLikelihood.NormalWithVariance (Require.state mass) variance)
            |> Model.compile

        // Run a profile likelihood around the Maximum Likelihood Estimate:
        let l = 
            Bristlecone.Confidence.ProfileLikelihood.profile
                Bristlecone.fit
                Settings.engine
                data
                h
                100<iteration>
                r
        name, l )
    |> Seq.toList

The likelihood profile returns a 68% and 95% interval for each parameter. We can inspect them like so:

likelihoodProfile.Head
|> snd
|> Seq.map(fun kv -> sprintf "[%s] 95 CI %f - %f (estimate = %f)" kv.Key.Value kv.Value.``95%``.Lower kv.Value.``95%``.Upper kv.Value.Estimate )

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module Bristlecone from Bristlecone

--------------------
namespace Bristlecone

module Language from Bristlecone
<summary> An F# Domain Specific Language (DSL) for scripting with Bristlecone. </summary>

module Time from Bristlecone

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val Measure: sId: MeasureId<'u> -> ModelExpression<'u>

--------------------
type MeasureAttribute = inherit Attribute new: unit -> MeasureAttribute

--------------------
new: unit -> MeasureAttribute

[<Measure>] type gram

val mass: StateId<gram>

val state: name: string -> StateId<'u>

val K: IncludedParameter<gram>

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val parameter: code: string -> con: Parameter.Constraint<'u> -> lower: float<'u> -> upper: float<'u> -> IncludedParameter<'u>
<summary> Define an estimatable parameter for a Bristlecone model. </summary>

--------------------
[<Measure>] type parameter

val Positive: Parameter.Constraint<'u>

val β: IncludedParameter<1>

val L: IncludedParameter<gram>

val rAbs: IncludedParameter<gram/day>

[<Measure>] type day

val r: IncludedParameter</day>

val linear: ModelExpression<gram/day>

val P: name: IncludedParameter<'u> -> ModelExpression<'u>

val exponential: ModelExpression<gram/day>

val This<'u> : ModelExpression<'u>

val powerLaw: ModelExpression<gram/day>

val monomolecular: ModelExpression<gram/day>

val logistic: ModelExpression<gram/day>

val Constant: x: float<'u> -> ModelExpression<'u>

val logisticFour: ModelExpression<gram/day>

val gompertz: ModelExpression<gram/day>

val Logarithm: expr: ModelExpression<1> -> ModelExpression<1>
<summary> The natural logarithm of an expression. </summary>

val hypotheses: (string * ModelBuilder.ModelBuilder<day>) list

val mkModel: ode: ModelExpression<'u> -> ModelBuilder.ModelBuilder<gram/'u>

val ode: ModelExpression<'u>

module Model from Bristlecone.Language
<summary> Terms for scaffolding a model system for use with Bristlecone. </summary>

val empty<'time> : ModelBuilder.ModelBuilder<'time>

val addRateEquation: name: StateId<'state> -> expr: ModelExpression<'state/'time> -> mb: ModelBuilder.ModelBuilder<'time> -> ModelBuilder.ModelBuilder<'time>

val estimateParameter: p: IncludedParameter<'u> -> builder: ModelBuilder.ModelBuilder<'time> -> ModelBuilder.ModelBuilder<'time>

val baseDay: System.DateTime

namespace System

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[<Struct>] type DateTime = new: date: DateOnly * time: TimeOnly -> unit + 16 overloads member Add: value: TimeSpan -> DateTime member AddDays: value: float -> DateTime member AddHours: value: float -> DateTime member AddMicroseconds: value: float -> DateTime member AddMilliseconds: value: float -> DateTime member AddMinutes: value: float -> DateTime member AddMonths: months: int -> DateTime member AddSeconds: value: float -> DateTime member AddTicks: value: int64 -> DateTime ...
<summary>Represents an instant in time, typically expressed as a date and time of day.</summary>

--------------------
System.DateTime ()
   (+0 other overloads)
System.DateTime(ticks: int64) : System.DateTime
   (+0 other overloads)
System.DateTime(date: System.DateOnly, time: System.TimeOnly) : System.DateTime
   (+0 other overloads)
System.DateTime(ticks: int64, kind: System.DateTimeKind) : System.DateTime
   (+0 other overloads)
System.DateTime(date: System.DateOnly, time: System.TimeOnly, kind: System.DateTimeKind) : System.DateTime
   (+0 other overloads)
System.DateTime(year: int, month: int, day: int) : System.DateTime
   (+0 other overloads)
System.DateTime(year: int, month: int, day: int, calendar: System.Globalization.Calendar) : System.DateTime
   (+0 other overloads)
System.DateTime(year: int, month: int, day: int, hour: int, minute: int, second: int) : System.DateTime
   (+0 other overloads)
System.DateTime(year: int, month: int, day: int, hour: int, minute: int, second: int, kind: System.DateTimeKind) : System.DateTime
   (+0 other overloads)
System.DateTime(year: int, month: int, day: int, hour: int, minute: int, second: int, calendar: System.Globalization.Calendar) : System.DateTime
   (+0 other overloads)

val data: Map<ShortCode.ShortCode,TimeSeries.TimeSeries<float,System.DateTime,int<year>,System.TimeSpan>>

property StateId.Code: ShortCode.ShortCode with get

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module TimeSeries from Bristlecone.Time
<summary>Contains functions and types to create and manipulate `TimeSeries` values, which represent observations ordered in time.</summary>

--------------------
type TimeSeries<'T,'date,'timeunit,'timespan> = TimeSeries.TimeSeries<'T,'date,'timeunit,'timespan>

val fromNeoObservations: dataset: TimeSeries.Observation<'a,System.DateTime> seq -> TimeSeries.TimeSeries<'a,System.DateTime,int<year>,System.TimeSpan>
<summary>Create a time-series where time is represented by standard (modern) calendars and dates and times through the built-in .NET DateTime type.</summary>
<param name="dataset">A sequence of observations, which consist of data and dates / times</param>
<typeparam name="'a">The type of the data in the series</typeparam>
<returns>A time-series of DateTime observations ordered oldest to newest.</returns>

System.DateTime.AddDays(value: float) : System.DateTime

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module Map from Bristlecone

--------------------
module Map from Microsoft.FSharp.Collections

--------------------
type Map<'Key,'Value (requires comparison)> = interface IReadOnlyDictionary<'Key,'Value> interface IReadOnlyCollection<KeyValuePair<'Key,'Value>> interface IEnumerable interface IStructuralEquatable interface IComparable interface IEnumerable<KeyValuePair<'Key,'Value>> interface ICollection<KeyValuePair<'Key,'Value>> interface IDictionary<'Key,'Value> new: elements: ('Key * 'Value) seq -> Map<'Key,'Value> member Add: key: 'Key * value: 'Value -> Map<'Key,'Value> ...

--------------------
new: elements: ('Key * 'Value) seq -> Map<'Key,'Value>

val ofList: elements: ('Key * 'T) list -> Map<'Key,'T> (requires comparison)

val engine: EstimationEngine.EstimationEngine<System.DateTime,System.TimeSpan,day,1>

val mkContinuous: unit -> EstimationEngine.EstimationEngine<System.DateTime,System.TimeSpan,year,'u>
<summary>A basic estimation engine for ordinary differential equations, using a Nelder-Mead optimiser.</summary>

val forDailyModel: engine: EstimationEngine.EstimationEngine<'a,'b,'u,'v> -> EstimationEngine.EstimationEngine<System.DateTime,System.TimeSpan,day,'v>

val withCustomOptimisation: optim: EstimationEngine.Optimisation.Optimiser -> engine: EstimationEngine.EstimationEngine<'a,'b,'u,'v> -> EstimationEngine.EstimationEngine<'a,'b,'u,'v>

namespace Bristlecone.Optimisation

module Amoeba from Bristlecone.Optimisation
<summary> Nelder Mead implementation Adapted from original at: https://github.com/mathias-brandewinder/Amoeba </summary>

val single: settings: Optimisation.Amoeba.Solver.Settings -> EstimationEngine.Optimisation.Optimiser
<summary> Optimise an objective function using a single downhill Nelder Mead simplex. </summary>

module Solver from Bristlecone.Optimisation.Amoeba
<summary> Nelder–Mead downhill simplex </summary>

val Default: Optimisation.Amoeba.Solver.Settings

val withConditioning: c: Conditioning.Conditioning<'u> -> engine: EstimationEngine.EstimationEngine<'a,'b,'v,'u> -> EstimationEngine.EstimationEngine<'a,'b,'v,'u>
<summary> Choose how the start point is chosen when solving the model system </summary>

module Conditioning from Bristlecone

union case Conditioning.Conditioning.NoConditioning: Conditioning.Conditioning<'u>

val withSeed: seed: int -> engine: EstimationEngine.EstimationEngine<'a,'b,'u,'v> -> EstimationEngine.EstimationEngine<'a,'b,'u,'v>
<summary> Use a mersenne twister random number generator with a specific seed. </summary>

val endCond: EstimationEngine.EndCondition

module EndConditions from Bristlecone.Optimisation
<summary>Composable end conditions to specify when optimisation routines should end.</summary>

val whenNoBestValueImprovement: window: int<iteration> -> results: EstimationEngine.Solution list -> iteration: int<iteration> -> EstimationEngine.OptimStopReason
<summary> Given a list of solutions, which are ordered most recent first, returns `true` if there are at least `window` recent results, and the change within the recent results is no more than `tolerance`. </summary>

[<Measure>] type iteration

val sigmaBase: IncludedParameter<gram>

val sigmaGrowth: IncludedParameter</gram>

val variance: ModelLibrary.NegLogLikelihood.Variance.VarianceFunction<gram,gram>

namespace Bristlecone.ModelLibrary

module NegLogLikelihood from Bristlecone.ModelLibrary
<summary>Negative log likelihood (-logL) functions to represent a variety of distributions and data types.</summary>
<namespacedoc><summary>Pre-built model parts for use in Bristlecone</summary></namespacedoc>

module Variance from Bristlecone.ModelLibrary.NegLogLikelihood
<summary>Functions representing how variance is handled within likelihood functions.</summary>

val exponential: sigma0: IncludedParameter<'u> -> sigma1: IncludedParameter<'v> -> ModelLibrary.NegLogLikelihood.Variance.VarianceFunction<'u,/'v>
<summary> Variance is exponential to the expected value (σ = σ0 * exp(σ1 * x)), where sigma1 is the baseline variance and sigma2 is the rate of growth in variance per units of expx. </summary>

val results: (string * ModelSystem.EstimationResult<System.DateTime,int<year>,System.TimeSpan>) list

module GrowthFunctions from Plant-growth

Multiple items
module List from Bristlecone

--------------------
module List from Microsoft.FSharp.Collections

--------------------
type List<'T> = | op_Nil | op_ColonColon of Head: 'T * Tail: 'T list interface IReadOnlyList<'T> interface IReadOnlyCollection<'T> interface IEnumerable interface IEnumerable<'T> member GetReverseIndex: rank: int * offset: int -> int member GetSlice: startIndex: int option * endIndex: int option -> 'T list static member Cons: head: 'T * tail: 'T list -> 'T list member Head: 'T with get member IsEmpty: bool with get member Item: index: int -> 'T with get ...

val map: mapping: ('T -> 'U) -> list: 'T list -> 'U list

val h: string * ModelBuilder.ModelBuilder<day>

val hy: ModelSystem.ModelSystem<day>

val snd: tuple: ('T1 * 'T2) -> 'T2

val useLikelihoodFunction: likelihoodFn: ModelSystem.Likelihood<ModelSystem.state> -> builder: ModelBuilder.ModelBuilder<'u> -> ModelBuilder.ModelBuilder<'u>

val NormalWithVariance: obs: Require.ObsForLikelihood<'u> -> varianceFn: ModelLibrary.NegLogLikelihood.Variance.VarianceFunction<'u,'u> -> ModelSystem.Likelihood<'v>

module Require from Bristlecone.Language

val state: s: StateId<'u> -> Require.ObsForLikelihood<'u>

val compile: (ModelBuilder.ModelBuilder<'u> -> ModelSystem.ModelSystem<'u>)

val fst: tuple: ('T1 * 'T2) -> 'T1

val fit: engine: EstimationEngine.EstimationEngine<'a,'b,'modelTimeUnit,'u> -> endCondition: EstimationEngine.EndCondition -> timeSeriesData: CodedMap<TimeSeries<float<'u>,'a,'c,'b>> -> model: ModelSystem.ModelSystem<'modelTimeUnit> -> ModelSystem.EstimationResult<'a,'c,'b> (requires comparison and comparison)
<summary>Fit a time-series model to data.</summary>
<param name="engine">An estimation engine configured and tested for the given model.</param>
<param name="endCondition">The condition at which optimisation should cease.</param>
<param name="timeSeriesData">Time-series dataset that contains a series for each equation in the model system.</param>
<param name="model">A model system of equations, likelihood function, estimatible parameters, and optional measures.</param>
<returns>The result of the model-fitting procedure. If an error occurs, throws an exception.</returns>

module Settings from Plant-growth

namespace Plotly

namespace Plotly.NET

val fitPlot: r: (string * ModelSystem.EstimationResult<System.DateTime,int<year>,System.TimeSpan>) seq -> GenericChart.GenericChart

val r: (string * ModelSystem.EstimationResult<System.DateTime,int<year>,System.TimeSpan>) seq

Multiple items
val string: value: 'T -> string

--------------------
type string = System.String

module ModelSystem from Bristlecone
<summary> Represents an ordinary differential equation model system and its likelihood as an objective function that may be optimised. </summary>

type EstimationResult<'date,'timeunit,'timespan> = { ResultId: Guid Likelihood: float<-logL> Parameters: ParameterPool Series: CodedMap<FitSeries<'date,'timeunit,'timespan>> Trace: Trace list InternalDynamics: CodedMap<float<state> array> option Metadata: List<string * string> }
<summary> An estimated model fit for a time-series model. </summary>

Multiple items
val int: value: 'T -> int (requires member op_Explicit)

--------------------
type int = int32

--------------------
type int<'Measure> = int

[<Measure>] type year

Multiple items
[<Struct>] type TimeSpan = new: hours: int * minutes: int * seconds: int -> unit + 4 overloads member Add: ts: TimeSpan -> TimeSpan member CompareTo: value: obj -> int + 1 overload member Divide: divisor: float -> TimeSpan + 1 overload member Duration: unit -> TimeSpan member Equals: value: obj -> bool + 2 overloads member GetHashCode: unit -> int member Multiply: factor: float -> TimeSpan member Negate: unit -> TimeSpan member Subtract: ts: TimeSpan -> TimeSpan ...
<summary>Represents a time interval.</summary>

--------------------
System.TimeSpan ()
System.TimeSpan(ticks: int64) : System.TimeSpan
System.TimeSpan(hours: int, minutes: int, seconds: int) : System.TimeSpan
System.TimeSpan(days: int, hours: int, minutes: int, seconds: int) : System.TimeSpan
System.TimeSpan(days: int, hours: int, minutes: int, seconds: int, milliseconds: int) : System.TimeSpan
System.TimeSpan(days: int, hours: int, minutes: int, seconds: int, milliseconds: int, microseconds: int) : System.TimeSpan

Multiple items
val seq: sequence: 'T seq -> 'T seq

--------------------
type 'T seq = System.Collections.Generic.IEnumerable<'T>

val variables: (ShortCode.ShortCode * (ShortCode.ShortCode * (string * ModelSystem.FitSeries<System.DateTime,int<year>,System.TimeSpan>)) seq) seq

Multiple items
module Seq from Bristlecone

--------------------
module Seq from Microsoft.FSharp.Collections

val collect: mapping: ('T -> #('U seq)) -> source: 'T seq -> 'U seq

val name: string

val res: ModelSystem.EstimationResult<System.DateTime,int<year>,System.TimeSpan>

ModelSystem.EstimationResult.Series: CodedMap<ModelSystem.FitSeries<System.DateTime,int<year>,System.TimeSpan>>

val map: mapping: ('T -> 'U) -> source: 'T seq -> 'U seq

val kv: System.Collections.Generic.KeyValuePair<ShortCode.ShortCode,ModelSystem.FitSeries<System.DateTime,int<year>,System.TimeSpan>>

property System.Collections.Generic.KeyValuePair.Key: ShortCode.ShortCode with get
<summary>Gets the key in the key/value pair.</summary>
<returns>A <typeparamref name="TKey" /> that is the key of the <see cref="T:System.Collections.Generic.KeyValuePair`2" />.</returns>

property System.Collections.Generic.KeyValuePair.Value: ModelSystem.FitSeries<System.DateTime,int<year>,System.TimeSpan> with get
<summary>Gets the value in the key/value pair.</summary>
<returns>A <typeparamref name="TValue" /> that is the value of the <see cref="T:System.Collections.Generic.KeyValuePair`2" />.</returns>

val groupBy: projection: ('T -> 'Key) -> source: 'T seq -> ('Key * 'T seq) seq (requires equality)

val charts: GenericChart.GenericChart seq

val varCode: ShortCode.ShortCode

val modelFits: (ShortCode.ShortCode * (string * ModelSystem.FitSeries<System.DateTime,int<year>,System.TimeSpan>)) seq

val obsLine: GenericChart.GenericChart

val head: source: 'T seq -> 'T

val toObservations: series: TimeSeries.TimeSeries<'a,'b,'c,'d> -> ('a * 'b) seq
<summary>Turn a time series into a sequence of observations</summary>
<param name="series">A time-series</param>
<typeparam name="'a">The underlying data type</typeparam>
<typeparam name="'b">The date/time representation</typeparam>
<returns></returns>

val d: ModelSystem.FitValue

val v: System.DateTime

ModelSystem.FitValue.Obs: float<ModelSystem.state>

val toList: source: 'T seq -> 'T list

val l: (System.DateTime * float<ModelSystem.state>) list

type Chart = static member AnnotatedHeatmap: zData: #('a1 seq) seq * annotationText: #(string seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a3 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a3 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?XGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a4 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?YGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a5 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a5 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZSmooth: SmoothAlg * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?ReverseYAxis: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible and 'a5 :> IConvertible) + 1 overload static member Area: x: #IConvertible seq * y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillPattern: Pattern * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Bar: values: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Keys: 'a1 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiKeys: 'a1 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerPatternShape: PatternShape seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPattern: Pattern * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Base: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiWidth: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member BoxPlot: [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a0 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a0 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a1 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a1 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?WhiskerWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?BoxPoints: BoxPoints * [<Optional; DefaultParameterValue ((null :> obj))>] ?BoxMean: BoxMean * [<Optional; DefaultParameterValue ((null :> obj))>] ?Jitter: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?PointPos: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Outline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Notched: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?NotchWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?QuartileMethod: QuartileMethod * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a0 :> IConvertible and 'a1 :> IConvertible and 'a2 :> IConvertible) + 2 overloads static member Bubble: x: #IConvertible seq * y: #IConvertible seq * sizes: int seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Candlestick: ``open`` : #IConvertible seq * high: #IConvertible seq * low: #IConvertible seq * close: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a4 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a5 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a5 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?IncreasingColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Increasing: FinanceMarker * [<Optional; DefaultParameterValue ((null :> obj))>] ?DecreasingColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Decreasing: FinanceMarker * [<Optional; DefaultParameterValue ((null :> obj))>] ?WhiskerWidth: float * [<Optional; DefaultParameterValue ((true :> obj))>] ?ShowXAxisRangeSlider: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a4 :> IConvertible and 'a5 :> IConvertible) + 2 overloads static member Column: values: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Keys: 'a1 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiKeys: 'a1 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerPatternShape: PatternShape seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPattern: Pattern * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Base: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiWidth: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member Contour: zData: #('a1 seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a2 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a3 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a3 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineSmoothing: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLine: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursColoring: ContourColoring * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursOperation: ConstraintOperation * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursType: ContourType * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowContourLabels: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLabelFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?Contours: Contours * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?NContours: int * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible) static member Funnel: x: #IConvertible seq * y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Offset: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextInfo: TextInfo * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLineStyle: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorFillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLine: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?Connector: FunnelConnector * [<Optional; DefaultParameterValue ((null :> obj))>] ?InsideTextFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutsideTextFont: Font * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) static member Heatmap: zData: #('a1 seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiX: 'a2 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: 'a3 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiY: 'a3 seq seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?XGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?YGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZSmooth: SmoothAlg * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?ReverseYAxis: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a2 :> IConvertible and 'a3 :> IConvertible and 'a4 :> IConvertible) + 1 overload ...

static member Chart.Point: xy: (#System.IConvertible * #System.IConvertible) seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
static member Chart.Point: x: #System.IConvertible seq * y: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)

val lines: GenericChart.GenericChart seq

val modelName: string

val fit: ModelSystem.FitSeries<System.DateTime,int<year>,System.TimeSpan>

ModelSystem.FitValue.Fit: float<ModelSystem.state>

val x: string

val s: (System.DateTime * string * float<ModelSystem.state>) seq

val x: System.DateTime

val y: float<ModelSystem.state>

val l: (System.DateTime * float<ModelSystem.state>) seq list

static member Chart.Line: xy: (#System.IConvertible * #System.IConvertible) seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'c * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'c seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: StyleParam.DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: StyleParam.Fill * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPattern: TraceObjects.Pattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'c :> System.IConvertible)
static member Chart.Line: x: #System.IConvertible seq * y: #System.IConvertible seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: StyleParam.Colorscale * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: StyleParam.DrawingStyle * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: StyleParam.Fill * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillPattern: TraceObjects.Pattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> System.IConvertible)

property List.Head: (System.DateTime * float<ModelSystem.state>) seq with get

val append: source1: 'T seq -> source2: 'T seq -> 'T seq

static member Chart.combine: gCharts: GenericChart.GenericChart seq -> GenericChart.GenericChart

static member Chart.withTitle: title: Title -> (GenericChart.GenericChart -> GenericChart.GenericChart)
static member Chart.withTitle: title: string * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleFont: Font -> (GenericChart.GenericChart -> GenericChart.GenericChart)

property ShortCode.ShortCode.Value: string with get

static member Chart.Grid: [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SubPlots: (StyleParam.LinearAxisId * StyleParam.LinearAxisId) array array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XAxes: StyleParam.LinearAxisId array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YAxes: StyleParam.LinearAxisId array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RowOrder: StyleParam.LayoutGridRowOrder * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Pattern: StyleParam.LayoutGridPattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XGap: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YGap: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: LayoutObjects.Domain * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XSide: StyleParam.LayoutGridXSide * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YSide: StyleParam.LayoutGridYSide -> (#('a1 seq) -> GenericChart.GenericChart) (requires 'a1 :> GenericChart.GenericChart seq)
static member Chart.Grid: nRows: int * nCols: int * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?SubPlots: (StyleParam.LinearAxisId * StyleParam.LinearAxisId) array array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XAxes: StyleParam.LinearAxisId array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YAxes: StyleParam.LinearAxisId array * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?RowOrder: StyleParam.LayoutGridRowOrder * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Pattern: StyleParam.LayoutGridPattern * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XGap: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YGap: float * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Domain: LayoutObjects.Domain * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?XSide: StyleParam.LayoutGridXSide * [<System.Runtime.InteropServices.Optional; System.Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?YSide: StyleParam.LayoutGridYSide -> (#(GenericChart.GenericChart seq) -> GenericChart.GenericChart)

module Graphing from Plant-growth

val fitPlot: r: (string * ModelSystem.EstimationResult<System.DateTime,int<year>,System.TimeSpan>) seq -> Plotly.NET.GenericChart.GenericChart

module GenericChart from Plotly.NET
<summary> Module to represent a GenericChart </summary>

val toChartHTML: gChart: Plotly.NET.GenericChart.GenericChart -> string

val weights: (ModelSystem.EstimationResult<System.DateTime,int<year>,System.TimeSpan> * ModelSelection.Akaike.AkaikeWeight) seq

module ModelSelection from Bristlecone
<summary>Contains tools for conducting Model Selection across individual subjects and hypotheses.</summary>

module Akaike from Bristlecone.ModelSelection
<summary>Functions for conducting Akaike Information Criterion (AIC).</summary>

val akaikeWeights: models: ModelSystem.EstimationResult<'date,'timeunit,'timespan> seq -> (ModelSystem.EstimationResult<'date,'timeunit,'timespan> * ModelSelection.Akaike.AkaikeWeight) seq
<summary>Akaike weights for a sequence of `EstimationResult`s.</summary>
<param name="models">The input model results</param>
<returns>An (EstimationResult * float) sequence of estimation results paired to their Akaike weights.</returns>
<exception name="ArgumentException">Occurs when there are no observations within an estimation result.</exception>

val zip: source1: 'T1 seq -> source2: 'T2 seq -> ('T1 * 'T2) seq

val m: string

val r: ModelSystem.EstimationResult<System.DateTime,int<year>,System.TimeSpan>

val w: ModelSelection.Akaike.AkaikeWeight

val sprintf: format: Printf.StringFormat<'T> -> 'T

ModelSystem.EstimationResult.Likelihood: float<-logL>

ModelSelection.Akaike.AkaikeWeight.AICc: float

ModelSelection.Akaike.AkaikeWeight.Weight: float

module String from Microsoft.FSharp.Core

val concat: sep: string -> strings: string seq -> string

val sigmaAt: expected: float<gram> -> float<gram>

val expected: float<gram>

Multiple items
val float: value: 'T -> float (requires member op_Explicit)

--------------------
type float = System.Double

--------------------
type float<'Measure> = float

val s0: float<gram>

val s1: float</gram>

val exp: value: 'T -> 'T (requires member Exp)

val diagnostics: string list

val find: key: 'Key -> table: Map<'Key,'T> -> 'T (requires comparison)

val ts: ModelSystem.FitSeries<System.DateTime,int<year>,System.TimeSpan>

property TimeSeries.TimeSeries.Values: ModelSystem.FitValue seq with get

val fitted: float<ModelSystem.state>

val observed: float<ModelSystem.state>

val sigma: float<gram>

[<Measure>] type state

val likelihoodProfile: (string * Map<ShortCode.ShortCode,Confidence.ConfidenceInterval>) list

val take: count: int -> source: 'T seq -> 'T seq

val h: ModelSystem.ModelSystem<day>

val find: predicate: ('T -> bool) -> source: 'T seq -> 'T

val s: string * ModelBuilder.ModelBuilder<day>

val l: Map<ShortCode.ShortCode,Confidence.ConfidenceInterval>

namespace Bristlecone.Confidence

module ProfileLikelihood from Bristlecone.Confidence
<summary>Given a maximum likelihood estimate (MLE), the profile likelihood method runs a Monte Carlo algorithm that samples around the MLE.</summary>
<remarks>The range for each parameter is discovered at 95% and 68% confidence based on a chi squared distribution.</remarks>

val profile: fit: (EstimationEngine.EstimationEngine<'a,'b,'u,'v> -> EstimationEngine.EndCondition -> 'c -> ModelSystem.ModelSystem<'modelTimeUnit> -> ModelSystem.EstimationResult<'d,'e,'f>) -> engine: EstimationEngine.EstimationEngine<'a,'b,'u,'v> -> subject: 'c -> hypothesis: ModelSystem.ModelSystem<'modelTimeUnit> -> n: int<iteration> -> result: ModelSystem.EstimationResult<'g,'h,'i> -> Map<ShortCode.ShortCode,Confidence.ConfidenceInterval>
<summary> The profile likelihood method samples the likelihood space around the Maximum Likelihood Estimate </summary>

property List.Head: string * Map<ShortCode.ShortCode,Confidence.ConfidenceInterval> with get

val kv: System.Collections.Generic.KeyValuePair<ShortCode.ShortCode,Confidence.ConfidenceInterval>

property System.Collections.Generic.KeyValuePair.Value: Confidence.ConfidenceInterval with get
<summary>Gets the value in the key/value pair.</summary>
<returns>A <typeparamref name="TValue" /> that is the value of the <see cref="T:System.Collections.Generic.KeyValuePair`2" />.</returns>

Confidence.ConfidenceInterval.Estimate: float