Dept of Statistical Sciences 2017-2018 Special Topics 6 week Courses

Note: these courses are offered as 6-week courses:

STA4502H: Topics in Stochastic Processes
Jeffrey Rosenthal

S – 2nd half
Feb 28 – Apr 4

This course will focus on convergence rates and other mathematical properties of Markov chains on both discrete and general state spaces.
Specific methods to be covered will include coupling, minorization conditions, spectral analysis, and more.  Applications will be made to card shuffling and to MCMC algorithms.

STA4505H: Applied Stochastic Control: High Frequency & Algorithmic Trading
Sebastian Jaimungal
S-Jan 9 – April 3
Note: STA 4505 (ad-hoc) Tuesdays from 6pm -9pm in Stewart Bldg 409

With the availability of high frequency financial data, new areas of research in stochastic modeling and stochastic control have opened up. This 6 week course will introduce students to the basic concepts, questions and methods that arise in this domain. We will begin by looking at several features seen in intra-day financial data, and examine how to build simple machine learning based models to describe the behaviour of the data. Next, we will investigate some of the typical algorithmic trading strategies employed in industry ranging from Bollinger bands, momentum and mean-reversion strategies, pairs trading, and statistical arbitrage. We will then develop stochastic optimal control problems for algorithmic trading and show how to solve them using the principles of dynamic programming leading to Hamilton-Jacobi-Bellman equations. Finally, we will look at reinforcement learning approaches to algorithmic trading. Students will also have a chance to work with historical limit order book data, develop Monte Carlo simulations and gain a working knowledge of the models and methods.

STAT4509H: Insurance Risk Models 1
Andrei Badescu

F-1st half term
Sept 13 – Oct 18

The aim of this course is to provide an introduction to advanced insurance risk theory. This course covers frequency and severity models, aggregate losses and compound distributions. In the first part of the course we mainly focus on the analysis of Cox distributions, Mixed Erlang distributions and Phase-type distributions. On the second part we introduce the continuous time ruin model and focus on some of the ruin related risk measures under various frequency and severity distributions. Certain model extensions are presented and related to the Stochastic Claim Reserving area.

STA 4514H: Spatial Statistics
Dan Simpson

F-1st half term
Jan 8 – Feb 12

This is an advanced course in models and methods for spatial data, with an emphasis on data which are not normally distributed. The course will cover different types of random spatial processes and how to incorporate them into mixed effects models for normal and non-Normal data, with maximum likelihood and Bayesian inference used for the two types of data respectively. Spatial point processes, where there are random locations rather than measurements at fixed locations, will be dealt with extensively. Following the course, students will be able to undertake a variety of analyses on spatially dependent data, understand which methods are appropriate for various research questions, and interpret and convey results in the light of the original questions posed.

STA 4515H: Multiple Hypothesis testing and its Applications
Lei Sun

F-2nd half term
Sept 26 – Nov 30

A central issue in many current large-scale scientific studies is how to assess statistical significance while taking into account the inherent multiple hypothesis testing issue.  This graduate course will provide an in-depth understanding of the topic in the context of data science with a focus on statistical `omics’. We start with an insightful revisit of single hypothesis testing, the building block of multiple hypothesis testing.  We then study the fundamental elements of multiple hypothesis testing, including the control of family-wise error rate and false discovery rate.  We will also touch upon various more advanced topics such as data integration, selective inference and fallacy of p-values.  The course will provide both analytical arguments and empirical evidence. Students are evaluated based on class participation and one final research report on a suggested or self-selected project related to multiple hypothesis testing.

STA4516H: NEW! Nonstandard Analysis and Applications to Statistics and Probability
Daniel Roy

F-1st half term
Sept 11 – Oct 16

Basic concepts in nonstandard analysis, including infinitesimal and infinite numbers, and descriptions of basic concepts like continuity and integration in terms of these notions. Advanced topics, including Loeb measure theory. Applications to stochastic processes and statistics.

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