Bayes example

#r "nuget: FSharp.Stats, 0.4.12-preview.1"
#r "nuget: fsharp.data"
#r "nuget: Plotly.NET"

open FSharp.Data
open FSharp.Stats
open FSharp.Stats.Distributions
open Plotly.NET

let normalise (dist: seq<'a * float>) =
    let totalProbability = dist |> Seq.sumBy snd
    dist |> Seq.map (fun (k, v) -> k, v / totalProbability) |> Map.ofSeq

let updatePosteriorDist  (priorDist: Map<'a, float>) (likelihoods: Map<'a, float>) =
    priorDist
    |> Map.toSeq
    |> Seq.map (fun (k, v) ->
        match (likelihoods.TryFind k) with
        | Some l -> printfn "k: %f , V: %f, L: %f" k v l ; (k, v * l)
        | None -> printfn "None"; (k, v))
    |> normalise
    |> Map.toSeq


let linspace start stop count =
    [|start .. ((stop-start) / (count-1.)) .. stop|]

let uniformPrior = (linspace 0.1 0.4 101) |> Array.map (fun i -> i, 1.) |> normalise

let genLike prior n k = 
    prior
    |> Map.toSeq
    |> Seq.map (fun (p, v) -> p, (DiscreteDistribution.binomial p n).PMF k)
    |> Map.ofSeq

let priorAfter25 = updatePosteriorDist uniformPrior (genLike uniformPrior 100 25 )

let priorAfter28 = updatePosteriorDist uniformPrior (genLike uniformPrior 103 28 )

let priorAfter25and33 = updatePosteriorDist (priorAfter25 |> Map.ofSeq) (genLike uniformPrior 3 3 )

[
Chart.Line(priorAfter25, Name = "Probability of hit after 25/100");
Chart.Line(priorAfter28, Name = "Probability of hit after 28/103");
Chart.Line(priorAfter25and33, Name = "Probability of hit after 25/100 and then 3/3");
Chart.Line((uniformPrior |> Map.toSeq), Name = "Uniform Probability"); 
]
|> Chart.combine
|> Chart.withXAxisStyle ("Proportion of Hits")
|> Chart.withYAxisStyle ("Probability")
|> Chart.show