Chapter 5: Bayesian Statistical Inference

This chapter develops the fundamentals of Bayesian statistical inference, and finishes with some examples of computing statistics in this manner.

Coin Toss Odds Ratio

Malmquist Bias Example

Eddington-Malmquist & Lutz-Kelker Biases

Log-likelihood for Gaussian Distribution

Posterior for Gaussian Distribution

Gaussian/Gaussian distribution

Gaussian Distribution with Gaussian Errors

Gaussian Distribution with Gaussian Errors

Binomial Posterior

Log-likelihood for Cauchy Distribution

Posterior for Cauchy Distribution

Log-likelihood for Uniform Distribution

Log-likelihood for Gaussian plus linear background

Unbinned Poisson Data

Binned Regression: Poisson vs Gaussian

Poisson Statistics with arbitrarily small bins

Plot the posterior of mu vs g1 with outliers

Plot the Outlier Probability

Odds Ratio for Cauchy vs Gaussian

Selection of Histogram bin size

Distribution Representation Comparison

MCMC for the Cauchy distribution

Histogram for Double-gaussian model test

MCMC Model Comparison

Gaussian Distribution with Gaussian Errors

Finding a signal in a background