Using data (and judgment if desired), Bayesian Linear Regression generates joint and marginal probability distributions over quantities of interest and applies those probability distributions to prediction. To ensure proper application and interpretation of linear regression, whether Bayesian or classical, the course develops Bayesian linear regression in depth, omitting no steps. In addition to assessing underlying data, the Bayesian linear conjugate system developed enables analytical answers that are straightforward, perceptive, blazingly quick, simple to implement, and produce results. They are an archetype for more intricate Bayesian systems, presaging what to anticipate. We pay attention to "big data" and "small data," the latter more characteristic of real world Decision Analysis. Serial data gathering is illustrated, and classical is shown to be a special case of Bayes. All course examples are solved using R or Excel; there is little emphasis on simulation. Students work examples, do projects, and explain findings. Matrix algebra and continuous probability are highly recommended.
3 units · Letter or Credit/No Credit
Using data (and judgment if desired), Bayesian Linear Regression generates joint and marginal probability distributions over quantities of interest and applies those probability distributions to prediction. To ensure proper application and interpretation of linear regression, whether Bayesian or classical, the course develops Bayesian linear regression in depth, omitting no steps. In addition to assessing underlying data, the Bayesian linear conjugate system developed enables analytical answers that are straightforward, perceptive, blazingly quick, simple to implement, and produce results. They are an archetype for more intricate Bayesian systems, presaging what to anticipate. We pay attention to "big data" and "small data," the latter more characteristic of real world Decision Analysis. Serial data gathering is illustrated, and classical is shown to be a special case of Bayes. All course examples are solved using R or Excel; there is little emphasis on simulation. Students work examples, do projects, and explain findings. Matrix algebra and continuous probability are highly recommended.
Offered in Winter 2027 at Stanford University.