- Instructor: Gustavo de los Campos ( gustavoc@msu.edu )
- Time/Place: MW 10:20am-11:40am A120 Wells Hall (WH)
- Syllabus
- Required textbook
- R-software
- Tentative Schedule
- 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
- 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)
- 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
- The method
- Inference of arbitrary functions
- The predictive distribution
- In the Beta-Biomial model
- In the Poisson-Gamma 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
- Casella & George, AMSTAT, 1992
- The Gibbs sampler in the normal model for the mean and variance
- Gibbs sampler for a multiple linear regression model