MonteCarlo (bristlecone) | bristlecone

bristlecone

MonteCarlo Module

Namespace: Bristlecone.Optimisation
Assembly: Bristlecone.dll

A module containing Monte Carlo Markov Chain (MCMC) methods for optimisation. An introduction to MCMC approaches is provided by [Reali, Priami, and Marchetti (2017)](https://doi.org/10.3389/fams.2017.00006)

Types and nested modules

Type/Module	Description
Filzbach	An adaptation of the Filzbach method (originally by Drew Purves)
MetropolisWithinGibbs
RandomWalk
SimulatedAnnealing	A meta-heuristic that approximates a global optimium by simulating slow cooling as a slow decrease in the probability of temporarily accepting worse solutions.
TuningMode
Frequency
TuneMethod

Functions and values

Function or value	Description
``Adaptive-Metropolis-withinGibbs`` Full Usage: ``Adaptive-Metropolis-withinGibbs`` Returns: `Optimiser<float>`	An adaptive Metropolis-within-Gibbs sampler that tunes the variance of each parameter according to the per-parameter acceptance rate. Reference: Bai Y (2009). “An Adaptive Directional Metropolis-within-Gibbs Algorithm.” Technical Report in Department of Statistics at the University of Toronto. Returns: `Optimiser<float>`
``Automatic(AdaptiveDiagnostics)`` Full Usage: ``Automatic(AdaptiveDiagnostics)`` Returns: `Optimiser<float>`	Implementation similar to that proposed by Yang and Rosenthal: "Automatically Tuned General-Purpose MCMC via New Adaptive Diagnostics" Reference: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.70.7198&rep=rep1&type=pdf Returns: `Optimiser<float>`
``Metropolis-withinGibbs`` Full Usage: ``Metropolis-withinGibbs`` Returns: `Optimiser<float>`	A non-adaptive Metropolis-within-gibbs Sampler. Each parameter is updated individually, unlike the random walk algorithm. Returns: `Optimiser<float>`
`adaptiveMetropolis weighting period` Full Usage: `adaptiveMetropolis weighting period` Parameters: weighting : `float` period : `Frequency` Returns: `Optimiser<float>`	A Markov Chain Monte Carlo (MCMC) sampling algorithm that continually adjusts the covariance matrix based on the recently-sampled posterior distribution. Proposed jumps are therefore tuned to the recent history of accepted jumps. weighting : `float` period : `Frequency` Returns: `Optimiser<float>`
`constrainJump initial jump scaleFactor c` Full Usage: `constrainJump initial jump scaleFactor c` Parameters: initial : `float` jump : `float` scaleFactor : `float` c : `Constraint` Returns: `float`	Jump in parameter space while reflecting constraints. initial : `float` jump : `float` scaleFactor : `float` c : `Constraint` Returns: `float`
`metropolisHastings' random writeOut endCondition propose tune f theta1 l1 d scale iteration` Full Usage: `metropolisHastings' random writeOut endCondition propose tune f theta1 l1 d scale iteration` Parameters: random : `Random` - `System.Random` to be used for drawing from a uniform distribution. writeOut : `LogEvent -> unit` - side-effect function for handling `LogEvent` items. endCondition : `(float * float[]) list -> int -> bool` - `EndCondition` that dictates when the MH algorithm ends. propose : `'a -> float[] -> float[]` - proposal `'scale -> 'theta -> 'theta` that generates a jump based on the scale value. tune : `int -> (float * float[]) list -> 'a -> 'a` - parameter of type `int -> (float * 'a) list -> 'b -> 'b`, where `int` is current iteration, f : `float[] -> float` - an objective function, `'a -> float`, to optimise. theta1 : `float[]` - initial position in parameter space of type `'a`. l1 : `float` - initial value of -log likelihood at theta1 in parameter space d : `(float * float[]) list` - history of the chain, of type `(float * 'a) list`. Passing a list here allows continuation of a previous analysis. scale : `'a` - a scale of type `'b`, which is compatible with the scale tuning function `tune` iteration : `int` - the current iteration number Returns: `(float * float[]) list * 'a` `(float * 'a) list * 'b` - A tuple containing a list of results, and the final scale used in the analysis. The `(float * 'a) list` represents a list of paired -log likelihood values with the proposed theta.	A recursive metropolis hastings algorithm that ends when `endCondition` returns true. random : `Random` `System.Random` to be used for drawing from a uniform distribution. writeOut : `LogEvent -> unit` side-effect function for handling `LogEvent` items. endCondition : `(float * float[]) list -> int -> bool` `EndCondition` that dictates when the MH algorithm ends. propose : `'a -> float[] -> float[]` proposal `'scale -> 'theta -> 'theta` that generates a jump based on the scale value. tune : `int -> (float * float[]) list -> 'a -> 'a` parameter of type `int -> (float * 'a) list -> 'b -> 'b`, where `int` is current iteration, f : `float[] -> float` an objective function, `'a -> float`, to optimise. theta1 : `float[]` initial position in parameter space of type `'a`. l1 : `float` initial value of -log likelihood at theta1 in parameter space d : `(float * float[]) list` history of the chain, of type `(float * 'a) list`. Passing a list here allows continuation of a previous analysis. scale : `'a` a scale of type `'b`, which is compatible with the scale tuning function `tune` iteration : `int` the current iteration number Returns: `(float * float[]) list * 'a` `(float * 'a) list * 'b` - A tuple containing a list of results, and the final scale used in the analysis. The `(float * 'a) list` represents a list of paired -log likelihood values with the proposed theta.
`randomWalk tuningSteps` Full Usage: `randomWalk tuningSteps` Parameters: tuningSteps : `TuneStep<float> seq` Returns: `Optimiser<float>`	A Markov Chain Monte Carlo (MCMC) sampling algorithm that randomly 'walks' through a n-dimensional posterior distribution of the parameter space. Specify `tuningSteps` to prime the jump size before random walk. tuningSteps : `TuneStep<float> seq` Returns: `Optimiser<float>`
`randomWalk' tuningSteps random writeOut n domain startPoint f` Full Usage: `randomWalk' tuningSteps random writeOut n domain startPoint f` Parameters: tuningSteps : `TuneStep<float> seq` random : `Random` writeOut : `WriteOut` n : `EndCondition<float>` domain : `Domain` startPoint : `Point<float> option` f : `float[] -> float` Returns: `Solution<float> list`	tuningSteps : `TuneStep<float> seq` random : `Random` writeOut : `WriteOut` n : `EndCondition<float>` domain : `Domain` startPoint : `Point<float> option` f : `float[] -> float` Returns: `Solution<float> list`
`toFn method interval` Full Usage: `toFn method interval` Parameters: method : `TuneMethod` interval : `int` Returns: `int -> (float * float[]) seq -> Matrix<float> * float -> Matrix<float> * float`	method : `TuneMethod` interval : `int` Returns: `int -> (float * float[]) seq -> Matrix<float> * float -> Matrix<float> * float`