Lecture Notes

1 Bayesian Inference

1.1 Fundamentals of Bayesian Statistics (link to pdf, imgInvGa, imgGa)

Introduction to Bayesian inference and foundation of decision theory.

Assignment 1: (Text, Solution)

1.2 Review of Bayesian estimation  (link to pdf)

Introduction to the Bayesian linear regression model with natural conjugate prior.

Assignment 2: (Text, Solution)

2 Bayesian computation  

2.1 Introduction to Monte Carlo methods (link to pdf/code)

Posterior approximation, application to linear and nonlinear models

2.2 Filtering methods (link to pdf/code)

Introduction to filtering methods, univariate and multivariate SV models

Assignment 3: (Text, Solution)

3 Bayesian methods for regression models 

3.1 Introduction (link to pdfA/codeA, link to pdfB/codeB)

Introduction to Linear Regression Model (LRM) with spherical and non-spherical errors. Bayesian model comparison.

3.2 Multiple equation models (link to pdfC/codeC, link to pdfD/codeD)

LRM with Time-varying parameters and stochastic volatility. Multiple equation LRM  (SUR, VAR, Panel models) with different prior distributions will be presented.

Assignment 4: (Text)

4 Bayesian Nonparametric Methods

4.1 Introduction to Bayesian Nonparametrics (BNP) (link to pdf/code)

Mixture Models, Infinite Mixture Models, Dirichlet and Pitman-Yor process priors, BNP clustering, Chinese Restaurant Processes, Slice sampling and MCMC sampling for nonparametric models.

4.2 BNP VAR models (link to pdf/code)

Nonparametric mixtures for array and BNP-VAR models, Dependent Pitman-Yor process priors, Application of BNP-VAR models to economics.

Assignment 5: (Text)