Angara.Statistics

A collection of essential algorithms for Bayesian data constrained modelling. Includes Mersenne twister random number generator, common probability distributions, sampling statistics and quantiles, a kernel density estimator and a resumable Metropolis-Hastings MCMC sampler.

Example

Here is how you draw from normal distribution

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#r "Angara.Statistics.dll"
open Angara.Statistics

let generator = MT19937() // Mersenne twister with default seed
let distribution = Normal(37.0, 9.0)
draw generator distribution

See Probability distributions tutorial for more information.

Next snippet shows how to infer a parameter of a Poisson distribution data using MCMC sampler.

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let fake_data = [for _ in 1..1000 -> draw generator (Poisson 5.)]

open Angara.Filzbach
let log_likelihood (p:Parameters) =
    let lambda = p.GetValue("lambda")
    Seq.sumBy (fun d -> log_pdf (Poisson lambda) d) fake_data
let prior = Parameters.Empty.Add("lambda",LogUniform(0.001, 1000.0))
let posterior = Sampler.runmcmc(prior, log_likelihood, 1000, 100)
Sampler.print posterior

The last line of the above snippet prints credible intervals of the posterior distribution of the parameter:

Samples max log likelihood*prior = -2227.54, acceptance rate at sampling = 0.317
------------+------------+------------+------------+------------+------------+------------+------------+
       name |      lower |  lower 95% |  lower 68% |     median |  upper 68% |  upper 95% |      upper | isLog
------------+------------+------------+------------+------------+------------+------------+------------+
     lambda |      0.001 |    4.91295 |    4.94402 |    5.02152 |    5.10106 |    5.18737 |       1000 | true

See Filzbach tutorial for more information.

Samples & documentation

Documentation includes tutorials automatically generated from *.fsx files in the content folder. The API reference is automatically generated from Markdown comments in the library implementation.

• Tutorial contains a further explanation of this sample library.

• API Reference contains automatically generated documentation for all types, modules and functions in the library. This includes additional brief samples on using most of the functions.

Contributing and copyright

The project is hosted on GitHub where you can report issues, fork the project and submit pull requests. If you're adding a new public API, please also consider adding samples that can be turned into a documentation. You might also want to read the library design notes to understand how it works.

The library is available under Public Domain license, which allows modification and redistribution for both commercial and non-commercial purposes. For more information see the License file in the GitHub repository.

• Angara.Statistics
• Home page
• Get library via NuGet
• Source code on GitHub
• License
• Release notes
• Getting started
• Probability distributions tutorial
• Documentation
• Supported probabilty distributions
• API reference