ST 740: Bayesian Inference
Fall session, 2005
ST 740: Bayesian Inference
Bayesian Inference and Analysis
Fall session, 2005
Course Outline
1. The Bayesian Paradigm (Chapter 1)
2. Prior Information to Distribution (Chapter 3)
3. Decision Theory (Chapter 2)
4. Point Estimation (Chapter 4)
5. Tests and Credible Regions (Chapter 5)
6. Bayesian Calculations (Chapter 6)
ST 740 Lecture Slides, Fall 2005
7. Hierarchical and Empirical Bayes (Chap 10)
http://courses.ncsu.edu/st740/
Sujit Ghosh
http://www.sujitghosh.net/
Department of Statistics
North Carolina State University
Main reference for this course:
Robert, C. P. (2001). The Bayesian Choice,
Springer-Verlag, New York.
c
Sujit
K. Ghosh
c
Sujit
K. Ghosh
Slide 1
ST 740: Bayesian Inference
Fall session, 2005
ST 740: Bayesian Inference
• Statistics should be considered an
interpretation of natural phenomena, rather
than explanation
• Statistical inference is based on a probabilistic
modeling of the observed phenomenon
• In this course we consider decision-oriented
aspects of statistical inference
• This course also features the modern
computational aspects of Bayesian inference
and introduces the use of softwares like
WinBUGS and R
• This course ignores some important aspects of
statistical practice such as those related to
data collection
c
Sujit
K. Ghosh
Slide 3
Fall session, 2005
Notations
1. The Bayesian Paradigm
• The main purpose of statistical theory is to
derive from observations an inference about
the population
Slide 2
x ∼ f : x is distributed according to f
f (x|θ): conditional distribution of x given θ
π(θ): marginal distribution of θ
x1 , x2 , . . . , xn ∼ f (x|θ): x1 , x2 , . . . , xn is a
sample of size n from f (x|θ)
We shall often use the term density and
distribution interchangeably when writing
x∼f
Unless otherwise specified x or θ are vectors
Caution: Usual probabilistic convention that
random variables are represented by capital
letters and their realization by the corresponding
lower case letter is not followed in this course
c
Sujit
K. Ghosh
Slide 4