Statistical Modeling and Bayesian inference

Author

Neil Ernst

Published

February 5, 2026

One approach building inferential analyses is to use a frequentist, hypothesis testing approach where you examine the long-run probability of the data-generating mechanisms to assess how likely the results are under a null hypothesis.

The alternative is to set some limits on what you feel is likely to be true a priori, model the data generating process statistically, i.e. with a probability distribution, and then run Bayes’s theorem \(P(A|B) = (P(B|A) * P(A))/P(B)\) over the data collected. This produces the posterior probability of the parameters of interest, allowing for inferences to be drawn.

We will start with some motivation from McElreath: https://speakerdeck.com/rmcelreath/l01-statistical-rethinking-winter-2019 and associated videos

Learning Outcomes

  • Apply Bayesian inference to software problems
  • Relate statistical sampling problems to numerical analysis problems (e.g., as discussed in detail in CSC 349a).
  • Apply statistical probability distributions to model software problems.
  • Appreciate the rationale for causal graphs and causal language.
Topic Readings Exercises
Basic Statistical Inference from a Bayesian Perspective
Causal Modeling
Probability Distributions and Priors

Required Readings

Optional Readings and Activities

Exercises

  • Make sure you can get the sample tutorial notebook to run in its entirety.