Created
March 3, 2023 16:29
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#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 | |
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