Admit or reject

Data

import Random
import TuringModels

using CSV
using DataFrames
using StatsFuns
using Turing

Random.seed!(1)

file_path = joinpath(TuringModels.project_root, "data", "UCBadmit.csv")
df = CSV.read(file_path, DataFrame; delim=';')

12×5 DataFrame
 Row │ dept     gender   admit  reject  applications
     │ String1  String7  Int64  Int64   Int64
─────┼───────────────────────────────────────────────
   1 │ A        male       512     313           825
   2 │ A        female      89      19           108
   3 │ B        male       353     207           560
   4 │ B        female      17       8            25
   5 │ C        male       120     205           325
   6 │ C        female     202     391           593
   7 │ D        male       138     279           417
   8 │ D        female     131     244           375
   9 │ E        male        53     138           191
  10 │ E        female      94     299           393
  11 │ F        male        22     351           373
  12 │ F        female      24     317           341

Model

@model function m_pois(admit, reject)
   α₁ ~ Normal(0,100)
   α₂ ~ Normal(0,100)

   for i ∈ 1:length(admit)
       λₐ = exp(α₁)
       λᵣ = exp(α₂)
       admit[i] ~ Poisson(λₐ)
       reject[i] ~ Poisson(λᵣ)
   end
end;

Output

chns = sample(m_pois(df.admit, df.reject), NUTS(), 1000)

Chains MCMC chain (1000×14×1 Array{Float64, 3}):

Iterations        = 501:1:1500
Number of chains  = 1
Samples per chain = 1000
Wall duration     = 4.3 seconds
Compute duration  = 4.3 seconds
parameters        = α₁, α₂
internals         = lp, n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error, tree_depth, numerical_error, step_size, nom_step_size

Summary Statistics
  parameters      mean       std   naive_se      mcse        ess      rhat   ess_per_sec
      Symbol   Float64   Float64    Float64   Float64    Float64   Float64       Float64

          α₁    4.9864    0.0250     0.0008    0.0008   765.8630    1.0005      178.2735
          α₂    5.4419    0.0184     0.0006    0.0007   876.9997    0.9993      204.1433

Quantiles
  parameters      2.5%     25.0%     50.0%     75.0%     97.5%
      Symbol   Float64   Float64   Float64   Float64   Float64

          α₁    4.9370    4.9705    4.9848    5.0032    5.0363
          α₂    5.4052    5.4302    5.4417    5.4542    5.4784

using StatsPlots

StatsPlots.plot(chns)

"/home/runner/work/TuringModels.jl/TuringModels.jl/__site/assets/models/admit-reject/code/output/chns.svg"

Original output

m_10_yyt_result = "
    mean   sd 5.5% 94.5% n_eff Rhat
 a1 4.99 0.02 4.95  5.02  2201    1
 a2 5.44 0.02 5.41  5.47  2468    1
";