Think Bayes - Chapter 4 Exercise 4.1.fsx

(*
Exercise: In Major League Baseball, most players have a batting average between .200 and .330, which means that their probability of getting a hit is between 0.2 and 0.33.

Suppose a player appearing in their first game gets 3 hits out of 3 attempts. What is the posterior distribution for their probability of getting a hit?

https://colab.research.google.com/github/AllenDowney/ThinkBayes2/blob/master/notebooks/chap04.ipynb#scrollTo=LB4DESMrA0bs
*)
#r "nuget: FSharp.Stats, 0.4.12-preview.1"
#r "nuget: Plotly.NET"

open FSharp.Stats.Distributions
open Plotly.NET

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

let updateBinomPosterior (priorDist: Map<float, float>) (posteriorN: int) (posteriorK: int) =
    priorDist
    |> Map.map (fun p v -> Discrete.Binomial.PMF p posteriorN posteriorK * v)
    |> Empirical.normalize

let uniformPrior = Empirical.createNominal (linspace 0.1 0.4 101)

let posteriorAfter25 = updateBinomPosterior uniformPrior 100 25

let posteriorAfter25and33 = updateBinomPosterior posteriorAfter25 3 3

[ Chart.Line(posteriorAfter25 |> Map.toSeq, Name = "Probability of hit after 25/100")
  Chart.Line(posteriorAfter25and33 |> Map.toSeq, 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