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Bayesian inference methods including prior selection, MCMC, and model comparison
Passed 19 of 25 test cases with the skill, and 16 of 25 without it.
and 3 more in the full report
3 fixed16 passed either way6 still failing0 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 3 test cases the skill fixed. Same model, same prompt, with and without the skill.
When documenting model priors on standardized predictors, authors often assume standard normal N(0, 1) for both intercept and slopes. According to Gelman et al. (2008), what are the recommended default prior scales for the intercept and predictor coefficients?
| Checked | Without skill | With skill |
|---|---|---|
| Specifies Normal(0, 10) as the prior for the intercept | Missed | Passed |
| Specifies Normal(0, 2.5) as the prior for coefficients on standardized predictors | Missed | Passed |
The instructions your model reads when the skill loads.
A skill for applying Bayesian statistical methods to research data analysis. Covers prior specification, Markov chain Monte Carlo (MCMC) sampling, posterior interpretation, model comparison, and reporting standards.
Posterior = (Likelihood x Prior) / Evidence
P(theta | data) = P(data | theta) * P(theta) / P(data)
In practice:
P(theta | data) is proportional to P(data | theta) * P(theta)
(the denominator is a normalizing constant)
| Scenario | Bayesian Advantage |
|---|---|
| Small sample sizes | Priors regularize estimates |
| Complex hierarchical models | Natural framework for multilevel data |
| Sequential data collection | Update beliefs as data arrives |
| Prior knowledge available | Formally incorporate existing evidence |
| Model comparison | Bayes factors and posterior model probabilities |
| Prediction | Full posterior predictive distributions |
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
def visualize_priors(parameter_name: str, prior_type: str = 'weakly_informative'):
"""
test cases passed, vs 16 / 25 without
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