Advanced stochastic modelling and Monte Carlo strategies for implementing Bayesian inference with low-level, mid-level and high-level representations, for estimation and prediction in physically-based inverse problems.

Bayesian inference can be described as the mathematics of making up your mind. This paper covers contemporary Monte Carlo methods for performing computational inference for inverse problems, and tools for representation of unknowns. Aimed at students who will go on to analyze data from complex physical systems, or who would like to compute with states of knowledge.

Prerequisites:
None

Recommended:
ELEC445

This paper consists of 8 lectures and 8 workshops. There are 3 assignments.

Assesment:
Final Exam 70%, Assignments 30%

Important information about assessment for ELEC446

Course Coordinator:
Assoc Prof Colin Fox

After completing this paper students are expected to have achieved the following major learning objectives:

• build stochastic models over low-level, mid-level, and high-level representations
• know the basic methods of statistical inference in the Bayesian framework
• state a correct Markov chain Monte Carlo algorithm for a range of state spaces, and be able to prove distributional convergence of that algorithm
• know how to define and evaluate computational efficiency of a MCMC
• be able to solve inverse problems in simple PDEs, for linear forward maps, and in image reconstruction using a suitable MCMC, and be able to present resulting estimates and uncertainties in an accessible graphical form
• be able to count objects by implementing a high-level representation, and quantify uncertainty in number

Additional outcomes:
An overall goal is to broaden each student's horizons about the possibilities of computing with states of knowledge, and the interplay between knowledge and representation.

Topics:

• Expectations, univariate sampling
• MCMC basics
• Algorithmic efficiency
• Inverse diffusion problem
• Image reconstruction
• Linear-Gaussian problems
• Counting objects