Overview

Description

CALENDAR DESCRIPTION:

The Bayesian approach to statistics is an alternative and increasingly popular way of quantifying uncertainty in the presence of data. This course considers comparative statistical inference, prior distributions, Bayesian computation, and applications. Quantitative.

COURSE DETAILS:

Course Outline:

Part 1: Introduction to Bayesian Statistics

• Motivation for Bayesian Analysis
• Review of Likelihood-Based Inference
• Comparison of Likelihood-Based and Bayesian Inference
• Bayesian Analysis in a Nutshell

Part 2: Bayesian Inference for Simple Models

• Exchangeability and deFinetti’s Representation Theorem
• Informative Prior distributions
• Binomial Models
• Poisson Models
• Univariate Normal Models
• Summarizing Posterior Inference
• Noninformative and Weakly Informative Prior Distributions
• Scientific Application: Hardness Ratios in High-Energy Astrophysics

Part 3: Multiparameter Models

• Marginalization and Monte Carlo
• Normal Data with Noninformative and Conjugate Priors
• Scientific Application: Estimating the Speed of Light
• Multinomial Models
• Multivariate Normal Models
• Scientific Application: Analysis of a Bioassay Experiment

Part 4: Bayesian Computing

• Introduction to Bayesian Computing
• Rejection Sampling
• Importance Sampling
• Introduction to Markov Chain Monte Carlo
• Metropolis and Metropolis-Hastings Algorithms
• Gibbs Sampler
• Hybrid and Alternative Algorithms
• Scientific Application: Inference in High-Energy Astrophysics

Part 5 (time permitting):

• Bayesian Hierarchical Models
• Hyperpriors
• James-Stein Estimators and Shrinkage
• Scientific Application: Supernova Color Corrections

Grading

Materials

REQUIRED READING:

REQUIRED READING NOTES: