pokie-score 0.1.4.dev0

Implemenation of the Pokie from Sharief et al. 2025

Pokie: Posterior over k Inference Estimation

Pokie is a Python package for evaluating the calibration and accuracy of posterior distributions through a sample-based, likelihood-free method. It enables Bayesian model comparison in simulation-based settings where the true posterior is unknown and standard metrics fail.

How Pokie Works

1. Select a Ground Truth

• Pick a truth sample $y^*_{j} \sim p(y | x^*, \mathcal{M}^*)$

2. Draw Posterior Samples

• Draw N samples ${ y_{i,j} }_{i=1}^N \sim p(y | x^*, \mathcal{M})$

3. Repeat for Lr Random Regions:

• Sample a random center $c_{j,\ell} \in \mathbb{R}^q$
• Select a random posterior sample to define a radius: $r_{j,\ell} = | c_{j,\ell} - y_{i,j} |$
• Define a region $\mathcal{R}{j,\ell}$ as the hypersphere around $c_{j,\ell}$ with radius $r_{j,\ell}$

4. Count Points

• Count how many posterior samples fall into the region: $n = \sum_i \mathbf{1}[y_{i,j} \in \mathcal{R}_{j,\ell}]$
• Check if the ground-truth sample falls inside: $k = \mathbf{1}[y^*j \in \mathcal{R}_{j,\ell}]$

5. Update Score

if k == 1:
    score += (n + 1) / (N + 2)
else:
    score += (N - n + 1) / (N + 2)

6. Final Pokie Score: $P_{\text{Pokie}}(\mathcal{M}) = \frac{\texttt{score}}{L \cdot L_r}$

Interpretation

• Well-calibrated posterior → Pokie score → ≈ 2/3
• Misaligned posterior → Pokie score → ≈ 1/2

Example Usage

import torch
from pokie import pokie

# Ground truth parameters (T samples in q-dim)
truth = torch.randn(T, q)

# Posterior samples from M models (M, T, S, q)
posterior = torch.randn(M, T, S, q)

# Run Pokie
score = pokie(truth, posterior, num_runs=100)
print(score)  # Pokie scores for each model

Developing

If you're a developer then:

git clone [e-mail]:SammyS15/Pokie.git
cd Pokie
git checkout -b my-new-branch
pip install -e .

But make an issue first so we can discuss implementation ideas.