Infer.NET user guide : Fun

Two coins in Fun

(See file Samples\Fun\Coins\Coins.fs.)

Suppose you toss two coins, observe that not both of them are heads, and would like to infer the posterior probability of each of them being heads. To do so using Infer.NET Fun you start by writing a model as follows:

open MicrosoftResearch.Infer.Fun.FSharp.Syntax

let coins () =
    let c1 = random (Bernoulli(0.5))
    let c2 = random (Bernoulli(0.5))
    let bothHeads = c1 && c2
    observe (bothHeads = false)
    c1, c2, bothHeads

The model uses two special functions defined in MicrosoftResearch.Infer.Fun.FSharp.Syntax: the function random returns a random sample from a given distribution and the function observe marks the execution as failed if the condition is not satisfied. The goal of the inference is to produce the distribution of the output variables of the model across all executions in which no observation fails. Sampling from a model is as simple as calling the function:

printf "Sample: %O\n" (coins ())

To perform inference the quoted version of the function is given to the function inferFun3 which returns a triple of distributions, one for each return value of

open MicrosoftResearch.Infer.Fun.FSharp.Inference
open MicrosoftResearch.Infer.Distributions

let (c1D, c2D, bothD)
    : IDistribution<bool> * IDistribution<bool> * IDistribution<bool>
    = infer <@ coins @> ()

printf "coins distribution \n%O\n%O\n%O\n" c1D c2D bothD
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