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In this example, we use Bristlecone to fit non-linear models of plant growth to some data from a plant growth experiment.

In the paper How to fit nonlinear plant growth models and calculate growth rates: an update for ecologists, Paine et al (2012) explain that there are seven key functional forms that can be used to represent plant biomass growth over time.

Here, we write the dM/dt forms of the seven equations in the Bristlecone model expression system, then fit these using Nelder-Mead (amoeba) optimisation to some sample plant growth data. The data is the Holcus unshaded growth experiment data as shown in the figures of Paine et al (2012).

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 notNegative, 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.

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 formatted into Bristlecone's TimeSeries type. For neo-ecological data, the TimeSeries.fromNeoObservations function may be used to work in .NET DateTime space. In this case, we do this by defining a basal date to pin the time-series to, then pass the list of tuples of data value and date to the Bristlecone function.

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 [
        0.07, baseDay.AddDays 14
        0.44, baseDay.AddDays 35
        2.83, baseDay.AddDays 70
        4.47, baseDay.AddDays 98
        8.39, baseDay.AddDays 133
        9.00, baseDay.AddDays 161
        6.13, baseDay.AddDays 189
        ]
    ]
    |> Map.ofList

Model-fitting

We need to define some basic settings to run the model-fitting. The estimation engine represents a common fixed method used to fit a model. The engine specified below uses the default continuous-time engine (Bristlecone.mkContinuous) with some minor changes.

The engine needs to explicitly know about the temporal resolution of the models that will be applied. Here, we call Bristlecone.forDailyModel to make the engine suitable for use against daily-resolution models.

We specify to use the swarm-based Nelder-Mead algorithm for optimisation. This is more robust than a single simplex, as it runs ten simplex at five levels, dropping the worst results and resetting the starting bounds at each level until no improvements are made.

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.

For the -log likelihood function, we are applying a standard gaussian function from the built-in selection in the Bristlecone.ModelLibrary. However, for plant growth models we likely should be using a gaussian function with heteroscedacity, because the associated error may increase in magnitude as biomass increases. We also therefore need to declare the sigma parameter required by the gaussian function.

Then, we can just run all of the hypotheses.

module Settings =
    let engine =
        Bristlecone.mkContinuous ()
        |> Bristlecone.forDailyModel
        |> Bristlecone.withCustomOptimisation (Optimisation.Amoeba.swarm 5 10 Optimisation.Amoeba.Solver.Default)
        |> Bristlecone.withConditioning Conditioning.NoConditioning

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

let sigma = parameter "σ[x]" Positive 0.01<gram> 0.5<gram>

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

The resultant model fits are shown in the below graph.

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

No value returned by any evaluator

Model selection

As we are applying a non-bayesian model fitting approach in this example, we can apply Akaike weights to discren which is the most appropriate model representation to explain this data.

A weights function exists for simple lists of competing hypotheses for a single subject, which in this case is the single plant biomass time-series.

For more complex sets of results, use the results set functionality described in the model selection documentation; this takes into account the subjects, hypotheses, and one or more replicates for each.

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

The resultant weights are:

Model

MLE

AICc

Weight

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

No value returned by any evaluator

The output indicates that the best model is linear, with approximately 72% support (this may vary as the above table is auto-generated).

Model fit quality / uncertainty

...

let likelihoodProfile =
    [results.[0]]
    |> 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.Normal (Require.state mass) sigma)
            |> Model.compile

        // Run a profile likelihood around the Maximum Likelihood Estimate:
        let l = 
            Bristlecone.Confidence.ProfileLikelihood.profile
                Bristlecone.fit
                Settings.engine
                data
                h
                1000<iteration>
                r
        name, l )
    |> Seq.toList


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 results2 =
    GrowthFunctions.hypotheses
    |> List.map (fun h ->
            let variance = ModelLibrary.NegLogLikelihood.Variance.exponential sigmaBase sigmaGrowth
            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
    )
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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 -> 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
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>
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 swarm: levels: int -> amoebaAtLevel: int -> settings: Optimisation.Amoeba.Solver.Settings -> EstimationEngine.Optimisation.Optimiser
<summary> Optimisation heuristic that creates a swarm of amoeba (Nelder-Mead) solvers. The swarm proceeds for `numberOfLevels` levels, constraining the starting bounds at each level to the 80th percentile of the current set of best likelihoods. </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 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 sigma: IncludedParameter<gram>
val results: (string * ModelSystem.EstimationResult<System.DateTime,int<year>,System.TimeSpan>) list
module GrowthFunctions from Plant-growth
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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>
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>
val Normal: obs: Require.ObsForLikelihood<'u> -> sigma: IncludedParameter<'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
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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
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[<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
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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
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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 likelihoodProfile: (string * Map<ShortCode.ShortCode,Confidence.ConfidenceInterval>) list
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>
val sigmaBase: IncludedParameter<gram>
val sigmaGrowth: IncludedParameter</gram>
val results2: (string * ModelSystem.EstimationResult<System.DateTime,int<year>,System.TimeSpan>) list
val variance: ModelLibrary.NegLogLikelihood.Variance.VarianceFunction<gram,gram>
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 NormalWithVariance: obs: Require.ObsForLikelihood<'u> -> varianceFn: ModelLibrary.NegLogLikelihood.Variance.VarianceFunction<'u,'u> -> ModelSystem.Likelihood<'v>

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