# Statistics seminar

Title: Big Data Big Bias Small Surprise

Speaker: S. Ejaz Ahmed, Brock University

Date and time:
24 Mar 2014,
2:30pm -
3:30pm

Location: CLE C113

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In high-dimensional statistics settings where number of variables is greater than observations, or when number of variables are increasing with the sample size, many penalized regularization strategies were studied for simultaneous variable selection and post-estimation. However, a model may have sparse signals as well as with a number predictors with weak signals. In this scenario variable selection methods may not distinguish predictors with weak signals and sparse signals. The prediction based on a selected submodel may not be preferable in such cases. For this reason, we propose a high-dimensional shrinkage estimation strategy to improve the prediction performance of a submodel. Such a high-dimensional shrinkage estimator (HDSE) is constructed by shrinking a ridge estimator in the direction of a candidate submodel. We demonstrate that the proposed HDSE performs uniformly better than the ridge estimator. Interestingly, it improves the prediction performance of given candidate submodel generated from most existing variable selection methods. The relative performance of the proposed HDSE strategy is appraised by both simulation studies and the real data analysis.

Title: Zero-inflated Models in Practice

Speaker: Laurie Ainsworth, SFU

Date and time:
05 Mar 2014,
2:30pm -
3:30pm

Location: CLE C113

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Zero-inflated models have many applications in ecology. They can be used to model species habitat suitability, to identify resistance to disease, and to account for detection rates in occupancy studies. We will discuss a variety of mechanisms that produce zeros in ecological data and discuss several types of zero-inflated models in the context of ecological examples. For example, Williamson¹s Sapsucker is an endangered species inhabiting parts of Southern B.C.. Initial monitoring of this rare woodpecker indicated the need for zero-inflated models. Ongoing development of the monitoring program has raised several issues related to: estimation of detection rates, stratified sampling, and the use of dual frame sampling designs. On the other hand, studying the effect of shipping noise on marine mammals highlights the need for zero-inflated functional data analysis methods. In this talk, we will discuss a variety of ecological applications, from endangered species to water quality analysis, and identify needs for further zero-inflated model development.

Title: The projection median and its connection to multivariate ranks, medians and depth-weighted averages

Speaker: Alexandre Leblanc, University of Manitoba

Date and time:
17 Feb 2014,
2:30pm -
3:30pm

Location: CLE C113

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ABSTRACT: In this presentation, I will discuss the concepts of multivariate ranks, depth and outlyingness. I will also describe how multivariate medians can be defined as points of highest depth or multivariate rank, or lowest outlyingness. For estimating multivariate location, I will describe depth-weighted averages and the Stahel-Donoho estimator, which are robust sample averages with adaptive weights. As an alternative to these computationally intensive methods that are impractical in high dimensional problems, I will present the projection median introduced by Durocher & Kirkpatrick (2005, 2009). Recent results suggest that this estimator is an interesting alternative to the other better known robust methods of estimating multivariate location. This is based on joint work with S. Durocher and M. Skala (University of Manitoba, Computer Science).

Title: Methodology for analyzing at-sea dive behaviour of northern fur seals in the Bering Sea.

Speaker: Ruth Joy, SFU

Date and time:
13 Jan 2014,
2:30pm -
3:30pm

Location: CLE C113

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The population of northern fur seals (Callorhinus ursinus) in the Pribilof Islands, Alaska has declined dramatically during the past 35 years. Arresting the decline of the species requires an understanding of their foraging behaviour at sea and is particularly important for those adult females whose foraging success is also linked to pup survival. In this talk, I propose an augmented state space methodology for studying behavioural patterns using high resolution movement time series. I show how non-stationary time series models that describe systems for whom parameters evolve slowly over time relative to the state dynamics can be estimated at relevant time scales for behavioural inference. This framework allows us to relate the time-varying parameter estimates of an auto-regressive system model to the fur seal¹s at-sea behaviour. The at-sea behaviour states of eleven lactating female northern fur seals are then matched, spatially and temporally, to a set of environmental variables, some of which are averages that represented the oceanic conditions over a large spatial area. I propose to account for the mismatch of scale between seal behaviour and the spatial variables by applying an error-in-covariate Bayesian hierarchical model. Using this approach, I was able to link together northern fur seals that went to disparate regions of the eastern Bering Sea, with widely variable information about their underlying environmental fields. This application of a hierarchical model relates changes in identifiable behavioural states of the northern fur seal to changes in the Alaska commercial groundfish industry over diurnal (24-hour) foraging cycle. The methodology described in this talk is adaptable for analyzing any type of high-resolution movement data on marine predators, and will allow for the characterization of other at-sea behaviours or descriptors of pelagic habitat.

Title: The Pitman Estimator of the Cauchy Location and Scale Parameters

Speaker: Gabriela Cohen Freue, University of British Columbia

Date and time:
02 Dec 2013,
2:30pm -
3:30pm

Location: DSB C130

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Abstract: The Cauchy distribution arises in a variety of disciplines

including physics, geology, engineering, and finance. This talk focuses on

the estimation of the Cauchy location and scale parameters. Given the

invariance of the Cauchy family, it is natural to restrict attention to

the class of location and scale equivariant estimators. Since the Cauchy

distribution has infinite moments, the most natural estimators in this

class, the sample mean and standard deviation, are not useful. The

simplest alternative, the sample median and median absolute deviation, are

unbiased and consistent but inefficient. To improve on this aspect, in

this talk I will present the Pitman estimator of the location and scale

parameters of the Cauchy family. This estimator achieves minimum mean

squared error in the class of location and scale equivariant estimators.

While in general the Pitman estimator is intractable, we derive its closed

form for this family using elements from Complex Analysis. Results from a

simulation study will be presented to study and compare the performance of

the proposed estimator with that of other existing estimators, in

particular for small sample sizes.

Title: Estimating Geodesic Barycenters

Speaker: Bernie C. Till, UVic

Date and time:
25 Nov 2013,
2:30pm -
3:30pm

Location: DSB C130

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Subtitle: Application of Conformal Geometric Algebra to the Statistical

Analysis of Reach and Grasp

Abstract: The motion of a rigid body in 3-dimensional Euclidean space can be represented as the trajectory of a point in the non-Riemannian manifold of the the Lie group SE(3). Using an experiment in the cognitive psychology of motor action as a motivating application, this talk shows how to formulate the statistical analysis of such trajectories using Conformal Geometric Algebra in order to simplify calculations and allow conclusions to be drawn about the effect of cognitive state on the kinematics of reach-and-grasp movements.

Conformal Geometric Algebra is the Clifford algebra Cl(4,1), together with a particular geometric interpretation, which provides a unified, coordinate-free framework in which to represent not only the geometric primitives of Euclidean 3-space, but also the group elements of SE(3), as well as the elements of its Lie algebra.

Title: Imprinting Test for Disease-Associated SNPs Under Mixture Model

Speaker: Jiahua Chen, University of British Columbia

Date and time:
18 Nov 2013,
2:30pm -
3:30pm

Location: DSB C130

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Abstract: Genomic imprinting is a known aspect of the etiology of

schizophrenia, a serious and common neuropsychiatric disease. The

imprinting phenomenon depicts differential expression levels of the allele

depending on its parental origin. When the parental origin is unknown, the

expression level has a finite normal mixture distribution. In such

applications, a random sample of expression levels consists of three

subsamples according to the number of minor alleles an

individual possesses, of which one is the mixture and the other two are

homogeneous. This understanding leads to a likelihood ratio test (LRT) for

the presence of imprinting. Because of the nonregularity of the finite

mixture model, the classical asymptotic conclusions on likelihood-based

inference are not applicable. We show that the maximum likelihood

estimator of the mixing distribution remains consistent. More

interestingly, thanks to the homogeneous subsamples,

the LRT statistic has an elegant and rather distinct

$0.5\chi2_1+0.5\chi2_2$ null limiting distribution. Simulation studies

confirm that the limiting distribution provides precise approximations of

the finite sample distributions under various parameter settings. The LRT

is applied to expression data sets for the schizophrenia susceptibility

gene GABRB2. Our analyses provide evidence for imprinting for a number of

isoform expressions of its GABA_A receptor $\beta_2$ subunit protein

encoded by the GABRB2 gene.

Based on joint work with Shaoting Li, Jianhua Guo, Bing-Yi Jing,and Hong

Xue.

Title: Linking mind, brain, and behavior: Using Hierarchical Bayesian parameter estimation in a model-based fMRI study of decision maki

Speaker: Adam Krawitz, Department of Psychology, UVic

Date and time:
21 Oct 2013,
2:30pm -
3:30pm

Location: DSB C130

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Abstract: A challenge for computational cognitive neuroscience is to

understand the relationship between mental processes, neural activity, and

behavior. I will present a particular approach to this challenge using a

functional magnetic resonance imaging (fMRI) study of decision making

under uncertainty. Mathematical models of the cognitive processes

hypothesized to be used in performing the decision-making task are fit to

behavioral data using hierarchical Bayesian parameter estimation. The

model fits are then used to generate predicted timecourses for putative

mental processes. These predictions are then compared to the measured

timecourses of neural activity. In this way, participants¹ decisions are

related to their brain activity by way of a theoretically motivated and

formally specified model of cognition.