DiceProblem.fsx

//http://allendowney.github.io/ThinkBayes2/chap03.html#the-dice-problem

#r "nuget: FSharp.Stats, 0.4.12-preview.1"
open FSharp.Stats
open FSharp.Stats.Distributions

let normalise (dist: Map<'a, float>) =
    let totalProbability = dist |> Map.toSeq |> Seq.sumBy snd
    dist |> Map.map (fun k v -> v / totalProbability)
let updatePosteriorDist (likelihoods: Map<'a, float>) (priorDist: Map<'a, float>) =
    priorDist
    |> Map.map (fun k v ->
        match (likelihoods.TryFind k) with
        | Some l -> v * l
        | None -> v)
    |> normalise
 
let priorDiceDist = EmpiricalDistribution.createNominal () ([ 6; 8; 12 ])

let updateDice data priorDist =
    let likelihood =
        priorDist
        |> Map.toSeq
        |> Seq.map (fun (k, v) -> k, (if data > k then 0. else 1. / (float k)))
        |> Map.ofSeq
    updatePosteriorDist likelihood priorDist
    
updateDice 7 priorDiceDist