/STT465

STT 465 : Bayesian Statistical Methods (MSU)

STT465: Bayesian Statistical Methods (MSU)

Homework

  • HW 1 (Due W Sept 14 in class).
  • HW 2: Problems 3.3, 3.7 and 3.9 from the book (due Wednesday, Sept 28th in class).
  • HW 3

Chapter 2. Belief, probability and exchangeability

  • Sections: 2.1-2.8, tpics covered:
  • Beliefs and properties of belief functions
  • Rules of probability
  • Total probability
  • Marginal probability
  • Bayes Rule
  • Probability functions as a way of describing beliefs
  • Independence
  • Conditional independence
  • Discrete RV (definition, pdf, probability of events, examples, includin Bernoulli, Binomial and Poisson)
  • Contionous RV (definition, CDF, pdf, examples: Normal)
  • Descriptors of Distributions: Expectation, Variance, quantiles.
  • Joint Marginal and Conditional Distributions (both for discrete and contionous)
  • The joint distribution of independent and IID RV
  • Exchangeability (definiton and example: Bernoulli)
  • Conditional independence (example: Bernoulli model)
  • De Finetty's Theorem (theorem and implications for building Bayesian models)

Chapter 3. One Parameter Models

  • For the Beta-Binomial and Poisson-Gamma models we will cover:
    • Sampling Model
    • Maximum Likelihood Estimation
    • Large sample distribution of MLE
    • Large sample Frequentist CI (computation and interpretation)
    • Prior
    • Posterior
    • Bayesian inference
      • Maximum a posteriori
      • Posterior mean
      • Bayesian Credibility Regions

Chapter 4. Monte Carlo Approximation

  • The method
  • Inference of arbitrary functions
  • The predictive distribution
    • In the Beta-Biomial model
    • In the Poisson-Gamma model

Chapter 5. The Normal Model

  • The normal distribution: parameters, and properties
  • Likelihood for nomal model
    • MLE estimate of the mean and variance
    • Bias and variance of the MLE estimates
  • Bayesian model for the mean with known variance
    • Likelihood
    • Normal prior for the mean
    • Posterior distribution for the mean
    • The Bayesian estimate as a compromise between the information provided by the likelihood (MLE estiamate) and that conveyed by the prior.
    • The normal model for the mean and variance
      • Likelihood
      • The Scaled-invers Chi-square
      • Joint prior distribution for the mean and variance
      • Joint posterior
      • Alternative sampling schemes

Chapter 6. The Gibbs Sampler