BayesTutorial

A collection of notebooks and scripts demonstrating various conceptual aspects of Bayesian inference.

CohensCongressExample notebook

Picks up on an example which points to a possible misinterpretation when transforming natural language into statements about probability, especially applied to statistical hypothesis testing. Goes on to discuss the probability that a research finding is true given a significant hypothesis test (positive predictive value, PPV). Exemplifies how this probability depends on the base rate of research hypotheses being true and the power of the test.

GaussInference notebook

Some examples of Bayesian inference with simple Gaussian models:

• estimating a mean from a single, one-dimensional data point (demonstrates how estimates depend on prior and likelihood)
• inferring two hidden causes from a single, one-dimensional data point (demonstrates two-dimensional Gaussians, relationship between prior and likelihood, how estimated causes depend on assumed prior correlations and model)

estimating_a_mean script

Demo showing Bayesian estimation of a two-dimensional mean as data points arrive sequentially. Can demonstrate:

• narrowing of posterior for more data points
• that posterior will include true mean most of the time (calibrated)
• that posterior will not include true mean most of the time (uncalibrated)
• that posterior is influenced by prior, but data overwrites that influence