Flexible Models: Nonparametric
and Semiparametric Methods
Koop, Chapter 10
The Idea
Always have a likelihood function that is in
some sense parametric
But can relax various features e.g.
NLRM:
Rela
Modeling Covariance Matrices in
Terms of Standard Deviations
and Correlations
Barnard, McCulloch & Meng (2000)
Rousseeuw & Molenberghs (1994)
The Central Idea
A Particular Matrix Decomposition
Example
Bayesian Statistics & Econometrics
Fall 2009
Assignment #1 Due 10/2/09
Problems. Please prepare written answers to the following problems:
(1) (12 points) Find an example in any field of a published a
Bayesian Statistics & Econometrics
Fall 2009
Assignment #2 Due 10/14/09
Problems. Please prepare written answers and (where appropriate) MATLAB output for
whichever of the following problems are inclu
Bayesian Statistics & Econometrics
Fall 2009
Assignment #3 Due 10/21/09
Problems. Please prepare written answers and (where appropriate) MATLAB output for
whichever of the following problems are inclu
Bayesian Statistics & Econometrics
Fall 2009
Assignment #4 Due 10/30/09
Problems. Please prepare written answers and (where appropriate) MATLAB output for the
following problems:
(1) (6 points) Metrop
Bayesian Statistics & Econometrics
Fall 2009
Assignment #5 Due 11/11/09
Problems. Please prepare written answers and (where appropriate) MATLAB output for the
following problems:
(1) (8 points) Hetero
Qualitative and Limited
Dependent Variable Models
Koop, Chapter 9
Strategy
Qualitative or limited dependent variable
makes NLRM not directly applicable
Normality not a reasonable assumption for
depe
Introduction to Time Series
Koop, Chapter 8
Strategy and Background
Already covered AR(p) models in chapter 6
Develop state space models here
Is one way of doing time series
Bayesian approaches to
Linear Regression Model with
Panel Data
Koop, Chapter 7
Panel Data
(also called Longitudinal Data)
Multiple observations for each unit
E.g., T observations on each of N units
Types of Models
Pooled
A Bayesian Perspective
on p-Values
Frequentist Approach
Available data is sample from a larger real or
imagined population
Focus is on estimators
Criteria: unbiased, efficient, etc.
Many results o
Linear Regression Model with
a Single Explanatory Variable
Koop, chapter 2
Regression Set Up
Likelihood Function
Rewrite Sum in Likelihood
New Likelihood Expression
Normal-Gamma Form
Gamma Distributio
Linear Regression Model with
Many Variables
Koop, chapter 3
Regression Set Up
Error Distribution
Likelihood Function
Rewrite Sum in Likelihood
Derivation of Rewritten Sum
Error in Book - Likelihood
Ga
Posterior Simulation I
Geweke, Chapter 4
Start Through Section 4.2
The Paradigm
Key Questions
for a Posterior Simulator
Does it converge?
Need a Theorem
If so, is it efficient?
Versus alternatives
Nonlinear Regression Model
Koop, Chapter 5
Metropolis-Hastings algorithm
Can be used as a step within Gibbs Sampler
Gelfand-Dey
Method to compute marginal likelihoods
Posterior predictive p-value
Posterior Simulation II
Geweke, Chapter 4
Section 4.3 to End
The Paradigm
Key Questions
for a Posterior Simulator
Does it converge?
Need a Theorem
If so, is it efficient?
Versus alternatives
Gibbs
Linear Regression Model with
General Error Covariance Matrix
Koop, Chapter 6
New Assumptions
General Error Covariance Matrix
Transformed Model
Transformation: Math
Independent Normal Gamma
Set Up
Like
Bayesian Statistics & Econometrics
Fall 2009
Assignment #5 Due 11/30/09
Problems. Please prepare written answers and (where appropriate) MATLAB output for the
following problems:
(1) (4 points) Probit