STATS 225: Bayesian Analysis
Lecture 3: Markov chain Monte Carlo
Babak Shahbaba
Department of Statistics, UCI
Background
We saw previously that in certain situations, the posterior
distribution has a closed form (e.g., when the prior is
conjugate), and t
STATS 225: Bayesian Analysis
Lecture 1: Introduction
Babak Shahbaba
Department of Statistics, UCI
Why Bayesian?
Statistics methods are mainly inspired by applied scientic
problems.
The overall goal of statistical analysis is to provide a robust
framewor
STATS 225: Bayesian Analysis
Lecture 5: More on MCMC
Babak Shahbaba
Department of Statistics, UCI
Convergence diagnosis
When using MCMC methods for sampling, it is important to
make sure that the chain has converged to its target
distribution. That is, i
STATS 225: Bayesian Analysis
Lecture 10: More ecient MCMC methods
Babak Shahbaba
Department of Statistics, UCI
Background
Simple Metropolis algorithm and Gibbs sampler explore the
posterior distribution using a random walk.
While this strategy might wor
STATS 225: Bayesian Analysis
Lecture 10: Nonparametic Bayesian
Dirichlet process mixture models
Babak Shahbaba
Department of Statistics, UCI
Dirichlet process mixture models
In this lecture, we are going to introduce Dirichlet process
mixture models.
Th
STATS 225: Bayesian Analysis
Lecture 7: Linear and generalized linear models
Babak Shahbaba
Department of Statistics, UCI
Bayesian Linear regression models
Consider the following ordinary liner regression model:
y |x, , 2 N(x, 2 In )
y is a column vecto
STATS 225: Bayesian Analysis
Lecture 8: More on model evaluation
Babak Shahbaba
Department of Statistics, UCI
Decision theory
In the Bayesian paradigm, hypothesis testing and model
evaluation are special cases of decision problems. In fact many
topics su
STATS 225: Bayesian Analysis
Lecture 6: Hierarchical Bayesian models
Babak Shahbaba
Department of Statistics, UCI
Reminder: Exchangeability
We discussed exchangeability before.
Informally, a set of observations y = (y1 , ., yn ) are
exchangeable if in c