This is an announcement of the Statistics departmental seminar. Coffee and refreshment will be served at 3:15pm.
Speaker: Aaron Smith, Tutte Institute for Mathematics and Computing
Time: 3:15-4:30pm on Thursday, Jan 30, 2014.
Location: Sidney Smith Hall, Room 1074
Title: Efficiency Bounds and Concentration Inequalities for Adaptive Samplers
Markov chain Monte Carlo (MCMC) is a ubiquitous tool for estimating integrals over complicated probability distributions. In practice, the performance of MCMC algorithms depends heavily on a large number of tuning parameters that can be difficult to select. This problem is sometimes solved by using “adaptive” MCMC methods to learn parameters on the fly. Although these methods are popular, very little is known about the properties of estimates that they produce. In this talk, I present new finite-time error bounds and concentration inequalities for a popular class of adaptive algorithms, the equi-energy (EE) sampler. These ideas are also used to provide the first proofs that the EE sampler can be more efficient than its non-adaptive competitors.
Speaker: Shan Jiang, PhD, Bank of Montreal
Date: Friday, January 31, 2014
Registration and Network: 5:00pm – 5:45 pm
Presentation: 5:45pm – 6:15pm
Dinner Together in Asian Legend: 6:15pm-8:00pm
Registration: Please send an email to seminar.sora@gmail.com with your affiliation. You will receive a confirmation letter if there is a seat available.
Location
University of Toronto, HS614, 155 College Street
Speaker: Phil Chalmers, York University
Department of Psychology
Title: Mixed effects models for item response data
Abstract: A special selection of item response theory (IRT) models can be understood as generalized mixed-effects models (GLMM), and as such can be estimated using existent software packages such as lme4 in R or PROC NLMIXED in SAS. The benefits of estimating IRT models using GLMM methodology is the ability to include additional fixed and random effect variables to help explain the rich properties a test may posses. However, although a GLMM approach can be used for some IRT models, it is not flexible enough to include more common models seen in educational and psychological testing literature. This talk will explore a newer estimation framework designed to be flexible to user specifications, accurate in the presence of multiple random effect covariates, and allow a much larger number of useful IRT models to be utilized in item analysis work. The GLMM approach to modelling IRT data will be contrasted with the proposed estimation framework, and analysis of simulated and empirical data will be presented.
Suggested Readings:
De Boeck, P. D., et al. (2011). The Estimation of Item Response Models with the lmer Function from the lme4 Package in R . Journal of Statistical
Software, 39, 1-28.
**CANCELLED DUE TO WEATHER**
The seminar will be rescheduled soon
SHAPE CONSTRAINED
REGRESSION USING
GAUSSIAN PROCESS
PROJECTIONS
Lizhen Lin, Duke University
Shape constrained regression analysis has applications
in dose-response modeling, environmental risk
assessment, disease screening and many other areas.
Incorporating the shape constraints can improve
estimation efficiency and avoid implausible results.
In this talk, I will talk about nonparametric methods for
estimating shape constrained (mainly monotone
constrained) regression functions. I will focus on a novel
Bayesian method from our recent work for estimating
monotone curves and surfaces using Gaussian process
projections. Inference is based on projecting posterior
samples from the Gaussian process.
Theory is developed on continuity of the projection and
rates of contraction. Our approach leads to simple
computation with good performance in finite samples.
The projection approach can be applied in other
constrained function estimation problems including in
multivariate settings.
Speaker: Dr. Augustine Wong, York University
Department of Mathematics and Statistics
Title: Overview of Likelihood-Based Inference
Abstract: Obtaining a confidence region or a performing significance test of a parameter based on the likelihood function is commonly used in statistics. Professor Pek in last year’s presentation introduced two likelihood-based methods: Wald method (based on the maximum likelihood estimate of the parameter) and Wilks method (likelihood ratio method). In this talk, the accuracy of these two methods is examined. When the parameter of interest is a scalar parameter, a special way of combining the Wald method and the Wilks method is proposed. This proposed method gives extremely accurate inference results even when the sample size is extremely small.
Suggested Readings:
1. Barndorff-Nielsen, O.E., & Cox, D.R. (1994). Inference and Asymptotics. Chapman & Hall.
2. Bedard, M., Fraser, D.A.S., & Wong, A. (2007). Higher accuracy for Bayesian and frequentist inference: large sample theory for small sample likelihood . Statistical Science 22, 301-321.
3. Doganaksoy, N. & Schmee, J. (1993). Comparisons of approximate confidence intervals for distributions used in life-data analysis . Technometrics 35, 175-184.
4. Fraser, D.A.S., 1990. Tail probabilities from observed likelihoods. Biometrika 77, 65-76.
5. Fraser, D.A.S., Reid, N. & Wu, J. (1999). A simple general formula for tail probabilities for frequentist and Bayesian inference . Biometrika 86, 249-264.
6. Reid, N. (1988). Saddlepoint methods and statistical inference. Statistical Science 3, 213-238.
7. Reid, N. (1996). Higher order asymptotics and likelihood: a review and annotated bibliography . Canadian Journal of Statistics 24, 141-166.
8. Wong, A. & Wu, J. (2000). Practical use of small sample asymptotics for distributions used in life-data analysis . Technometrics 42, 149-155.
9. Wong, A. & Wu, J., (2001). Approximate inference for the factor loading of a simple factor analysis model . Scandinavian Journal of Statistics 28, 407-414.
(Note: 1, 4, 5, 6, 7 are background material, 2 is to related to Bayesian, and the rest are specific applications.)