Department of Statistics

Prerequisite: Stat 205 / Math 218

Topics in the theory of continuous time stochastic processes, including

local martingales, semi-martingales, stochastic integration, Ito's formula, Girsanov's formula,

Levy processes, diffusion processes, SDEs, Markov processes, semigroups, generators, martingale problems,

additive functionals, local time, excursions.

Participants will prepare overviews of material from various sources and develop class presentations

and course notes with guidance from the instructor.

Sources:

Pitman-Yor:  Guide to BM and related stochastic processes

Revuz-Yor: Continuous martingales and Brownian motion

Kallenberg: Foundations of Modern Probability

Rogers-Williams: Diffusions, Markov Processes and Martingales

This class explores parallels between human cognition and ideas in probability and statistics, with an emphasis on statistical machine learning. Minds and machines face similar computational problems, meaning that we can develop new hypotheses about human cognition by seeing how those problems are solved in statistics and find new challenges for machine learning by studying human cognition. Probabilistic models of cognition have recently become very popular in cognitive science, and the class will explore the implications of current research in areas such as causal learning, categorization, approximate inference, probabilistic grammars, and probabilistic logic, working through a new book on these topics.

Assessment: Students will write weekly notes on the reading, give presentations, and complete an independent research project related to computational modeling of human cognition.

Prerequisites: Basic familiarity with ideas from probability and statistics as used in machine learning. An undergraduate course in these areas is sufficient and Computer Science 281A/Statistics 241A is excellent preparation.