STA 831
Probability & Statistical Models

Here is the latest semester STA 831 Web Site for registered students

Synopsis: This course is concerned with foundational and core theory, modelling, and computational topics in probability and statistics:

  • Multivariate distribution theory, simulation and applied probability models in statistics.
  • Applied stochastic processes- examples of Markov processes arising in Bayesian analysis and statistical models, including linear and nonlinear Markov processes, stationarity, relation to MCMC.
  • Monte Carlo integration and simulation methods: direct, convolution/compositional, accept/reject, importance sampling, weighting and sequential methods.
  • Markov Chain Monte Carlo methods: Gibbs sampling and Metropolis Hastings-- ideas, examples and detailed theory.
  • Theory of Markov processes: ergodicity, irreducibility, convergence, eigentheory, reversibility. Markov chains on continuous, multivariate state-spaces.
  • Examples using latent variable & hidden Markov model arising in Bayesian analysis & MCMC methods.
  • Graphical models: concepts, theory and examples of directed and undirected graphs. Roles in probability modelling and in MCMC.
  • Other theoretical topics relevant for computational Bayesian analysis, as time permits: EM algorithm, entropic tilting, variational Bayes.
Core goals include those of (a) developing facility for theoretical manipulations of multivariate distributions (mastery of linear algebra and multivariate calculus) in statistical models; (b) mastery of theory and implementation of key methods of simulation of multivariate distributions, including Markov chain Monte Carlo methods, and accompanying theory of convergence of MCMC methods as well as practicalities; (c) familiarisation with theory and exploration of multivariate structure in graphical modelling and Markov process models; (d) exposure to other theoretical topics in multivariate distribution theory (divergence, exponential families, etc), and many theoretical and applied examples.

The course is leavened throughout with theoretical and technical examples, as well as with examples drawing on data from areas such as finance, genetics, neuroscience, genomics and climatology.

Prerequisites: STA 831 is a fast-paced 1st year Statistical Science PhD core course. Background in core mathematical statistics, Bayesian and non-Bayesian inference, applied modelling in statistics and computation is defined by prerequisite courses STA 702, 721 and 732 (concurrent registration in 732 is pre-approved).

All students must have expertise and facility in computing and applied statistics (including from prerequisites STA 702 and 721). Regular use of Matlab will be routine in in-class and homework examples. The course does not teach computing in Matlab; students must be or become proficient prior to start of class, or program all from scratch in python, R or other.

Registration: This course is primarily for 1st-year PhD students in Statistical Science. Advanced graduate students in the Master's in Statistical Science program, and then students in other graduate programs, may/can be admitted to register subject to instructor permission and seats available.

Graduate credit units: 3

Assessment:

  • ~10 weekly homework assignments.
  • One midterm exam.
  • One final exam.
  • Regular class participation and engagement.

Texts & Reading: Copious, detailed course notes from instructor and supplementary materials provided.

Code & Data: Students will be expected to develop computational algorithms and exploratory modelling exercises with minimal supervision. Copious support code (Matlab) and many instructor examples will be provided, with much explored in-class and through homework.

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