Bayesian Statistical Methods
This course, for graduate students, provides an introduction to Bayesian statistics, with a focus on both practical application of Bayesian regression methods to data as well as philosophical background on statistical inference and interpretation of statistical analyses. Topics include Bayes's theorem and tools for applying it, including quadratic approximations, and Hamiltonian Monte Carlo sampling. Advanced methods include mixture models, multilevel regression methods, models incorporating ordinary differential equations, and critical evaluation of statistical models and modeling analyses.
I divide the semester into three parts:
Introduction to Bayes's Theorem and its Applications:
The first part of the course introduces the basic concepts of Bayesian statistics, using simplified approximations to calculate difficult equations. This section will focus on linear regression methods.
Monte Carlo Methods:
Next, we study Monte Carlo methods, which help us solve more difficult problems that our earlier approximations are not powerful enough for. This section will introduce statistical models of discrete data (counts, categories, etc.), and generalized linear models.
For the final part of the semester, we will explore modeling advanced methods, such as mixture models, multilevel models, and statistical models that incorporate ordinary differential equations. We will also study advanced ways of thinking about statistical modeling, such as information theory and model comparison using information criteria, working with messy data, and comparing models based on scientific principles to purely statistical models.
Course web site
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