| Seminars | |||
| 2010-11 seminars 2009-10 seminars 2008-09 seminars 2007-08 seminars 2006-07 seminars 2005-06 seminars Seminars 2012-2013Upcoming
Wednesday, June 5, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Andrea Gottlieb (San Jose State University) Title: A stickiness coefficient for longitudinal data Abstract: The stickiness coefficient, a novel summary statistic for time-course and longitudinal data will be introduced. The stickiness coefficient provides a simple, intuitive and informative measure that captures key information contained in time-course data. Under the assumption that the data are generated by the trajectories of a smooth underlying stochastic process, the stickiness coefficient summarizes the extent to which deviations from the mean trajectory tend to co-vary over time. The estimation scheme proposed will allow for estimation even in the case that the longitudinal data are sparsely observed at irregular times and may be corrupted by noise. The estimation procedure as well as consistency and convergence rates will be discussed. I will illustrate the resulting stickiness coefficient with several theoretical calculations as well as economic and health related data examples. Wednesday, September 28, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Alexandra Chronopoulou (PSTAT-UCSB) Title: Parameter Estimation for Fractional SDEs Abstract: We consider the parameter estimation problem for a multidimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H > 1/2, with non-linear random drift and diffusion coefficients. Due to the intractability of the likelihood function, we propose the maximizer of a partial likelihood as the estimator of the parameters of the model. We show how to compute this estimator using Malliavin calculus techniques and approximation results. We study the computational efficiency of our method and we provide rates of convergence for the approximation task. For a particular class of fractional SDEs, we establish consistency of the proposed estimator. We apply our methodology to the estimation of the parameters of the fractional Black-Scholes model using S&P 500 data. Wednesday, October 12, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Dimitris Fouskakis (National Technical University of Athens, currently visiting PSTAT-UCSB) Title: Power Intrinsic Variable Selection for Normal Models based on Zellner’s g-Prior Abstract: In order to express prior ignorance in Bayesian variable selection problems, proper prior distributions with large variances or non-informative improper distributions can be used. Bayes factors are well known for their sensitivity on prior variances, while, when using improper priors, Bayes factors cannot be determined because of the involvement of the unknown normalizing constants. This has urged the Bayesian community to develop various methodologies to overcome the problem of prior specification in model comparison and variable selection problems. An important part of this research is focused on the so-called objective model selection methods having their source on the intrinsic priors in order to provide an approximate proper Bayesian interpretation for intrinsic Bayes factors. These intrinsic priors use improper priors as a starting point and overcome the problem of indeterminacy of the Bayes factor since the same constant is involved in all marginal likelihoods. In this paper we develop the methodology of intrinsic priors when using proper priors as a starting point. Specifically we focus on normal linear models and we use initially the Normal-inverse gamma Zellner’s g-prior. We introduce the power intrinsic Zellner’s g-prior where we use the intrinsic prior methodology in order to define the joint prior distribution of the model parameters and the error variance. Moreover, by borrowing ideas from the power prior approach we avoid the use of a minimal training sample and the sensitivity of posterior results on the selection (and size) of this training sample in our intrinsic prior methodology. The methodology is illustrated on both simulated and real examples and sensitivity analysis reveals broad stability of our conclusions. Wednesday, October 26, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Georgios Fellouris (USC) Tittle: Decentralized sequential change detection Abstract: Consider a number of dispersed sensors which transmit their observations to a decision maker at some central location. At some unknown time, an event causes an abrupt change in the dynamics of all sensors. The classical change detection problem is to detect the time of the change as soon as possible, while avoiding a large number of false alarms, using the sequentially acquired sensor observations. However, in many applications, a limited communication bandwidth does not allow the implementation of the optimal centralized detection rule and calls for a decentralized formulation of the problem; that is, the decision maker has to detect the change under quantization constraints, as well as restrictions on the communication rate of the sensors. In this talk, we will review existing approaches to the decentralized change detection problem. We will then propose a novel approach, which turns out to be efficient both from a statistical and a practical point of view. More specifically, the proposed detection rule has strong asymptotic optimality properties, under both a discrete-time and a continuous-time setup, while requiring a minimal communication activity in the sensor network. Finally, we will illustrate with simulation experiments that the proposed scheme is much more efficient than existing decentralized detection rules. Monday October 31, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM [Note the unusual day of the week] Dr. David Draper (UC Santa Cruz) Title: Bayesian model specification: toward a Theory of Applied Statistics Abstract: The Bayesian approach to statistical inference, prediction and decision-making has a simple structure, with one equation for each of these three fundamental activities, and it can be shown to be based on a straightforward logical progression from principles to axioms to a foundational theorem with corollaries. However, this approach requires the user to specify two ingredients (usually called the prior and sampling distributions) for inference and prediction and two more ingredients (an action space and a utility function) for decision-making, and as a profession we lack the same kind of logical progression from principles to axioms to theorems that would constitute optimal specification of these four ingredients (by "optimal" here I mean "coming as close as possible to the goal of {conditioning only on true/false propositions that are rendered true by the context of the problem and the design of the data-gathering activity}"). Successfully developing such a logical progression would yield a Theory of Applied Statistics, which we need and do not yet have. In this talk I'll explore the extent to which four principles (Calibration, Modeling-As-Decision, Prediction, and Decision-Versus-Inference) constitute progress toward this goal. Wednesday, November 9, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Ruth Williams ( UCSD Math Dept) Tittle: Queueing up for enzymatic processing: correlations through coupled degradation Abstract: A major challenge for systems biology is to deduce the molecular interactions that underlie correlations observed between concentrations of different intracellular molecules. Although direct explanations such as coupled transcription or direct protein-protein interactions are often considered, potential indirect sources of coupling have received much less attention. Here we show how correlations can arise generically from a posttranslational coupling mechanism involving the processing of multiple protein species by a limited number of copies of a common enzyme. By observing a connection between a stochastic model and a multiclass queue, we obtain a closed form expression for the steady-state distribution of the numbers of molecules of each protein species. From analytic expressions for the moments and correlations associated with this distribution, we observe a striking phenomenon that we call correlation resonance: for small dilution rate, correlations peak near the balance-point where the total rate of influx of proteins into the system is equal to the maximum processing capacity of the enzymes. The talk will describe the theoretical developments and the results of related experiments. As time allows, a generalization to time-dependent distributions for enzymatic processing networks will be discussed. Based on joint work with Natalie Cookson, Tal Danino, Jeff Hasty, Will Mather, Octavio Mondragon-Palomino, Lev Tsimring. Wednesday, November 16, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Dar A. Roberts (Geography Department, UCSB) Tittle: A twenty-seven year history of land-cover change in Rondonia Brazil, derived from standardized mixture models and decision tree classifiers Abstract: I report on research results from the state of Rondônia, SW Brazil, a region that has undergone some of the most rapid and extensive forest clearing and subsequent pasture development, abandonment and regrowth in Brazil. I describe a general procedure, in which standardized methods for atmospheric correction, image normalization and spectral mixture analysis are used to decompose imagery. The imagery, acquired over most of the state, provides annual measures of surface composition changes between 1984 and 2010, thereby quantifying changes typically missing from more sparse temporal series. Spectral fractions for green vegetation, non-photosynthetic vegetation, soil and shade are fed into a decision tree classifier to produce maps of dominant land-cover classes, including mature forest, secondary forest, pasture, bare soil, water and burn scars. Time series analysis is used to reduce classification errors that result in disallowed transitions, such as a direct transition from pasture to mature forest. Additional corrections are applied to reduce misclassification between second growth forest and mature forest due to lighting geometry and confusion between old second growth and mature forest. Examples are provided showing spatial/temporal dynamics over most of the state. Transitions between mature forest, pasture and secondary forest are analyzed to evaluate the spatial extent and persistence of secondary forest and pasture. I demonstrate the utility of this data set for examining specific research questions with two examples, one analyzing how forest fragmentation impacts forest carbon content along forest edges, the other quantifying changes in carbon stocks using a “book keeping” approach. Wednesday, November 30, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Dick Startz (Economics Department, UCSB) Tittle: Instrumental Variable Estimation Under Weak Identification Monday, January 9, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Konstantinos Spiliopoulos (Brown University) Title: Recent results on systemic risk in large financial networks & more Abstract: The past several years have made clear the need to better understand the behavior of risk in large interconnected financial networks. Interconnections often make a system robust, but they can act as conduits for risk. In this talk, I will present recent results on modeling the dynamics of correlated default events in the financial market. An empirically motivated system of interacting point processes is introduced and we study how different types of risk, like contagion and exposure to systematic risk, compete and interact in large-scale systems. A law of large numbers for the loss from default is proven and used for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. Large deviation arguments are then used to identify the way that atypically large (i.e. ``rare'') default clusters are most likely to occur. The results give insights into how different sources of default correlation interact to generate typical and atypical portfolio losses. Time permitting, I will discuss briefly recent general results on large deviations and Monte-Carlo methods for multiple scale systems. Questions of interest include qualitative and quantitative descrpition of transitions probabilities between different equilibrium states of a given system. The results can potentially have applications in scientific disciplines such as chemistry and are also related to certain stochastic volatility models. Wednesday, January 11, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Tomoyuki Ichiba (PSTAT) Title: Planar Diffusions with rank-based characteristics Abstract: We construct a diffusion process with values in the plane and with rank-based drift/dispersive characteristics. We compute the transition probabilities of this process and the order statistics, discuss pathwise uniqueness and strength of related stochastic differential equations, and study its dynamics under a time-reversal. We also show that the planar diffusion can be represented in terms of one-dimensional diffusion with bang-bang drift driven by a standard Brownian motion, its local time accumulated at the origin, and an independent standard Brownian motion, in a form which can be construed as a two-dimensional analogue of the stochastic equation satisfied by the so-called skew Brownian motion. This is a joint work with E. Robert Fernholz, Ioannis Karatzas, and Vilmos Prokaj. Thursday, January 12, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Sergey Nadtochiy (Oxford Man Institute) Title: MARKET-BASED APPROACH TO MODELING DERIVATIVES PRICES ABSTRACT. Most classical models for derivatives prices focus on prescribing the time evolution of the underlying stochastic factors. The prices of derivatives are then computed, for example, via the risk-neutral expectations. As markets developed and many derivative contracts became liquidly traded, it appeared necessary, in order to avoid creating arbitrage opportunities and to fully exploit the information given by the market, to calibrate such models so that they reproduce the observed derivatives prices. However, the calibration results may vary significantly from day to day, implying that none of the calibrated models can be used to describe the future time evolution of the derivatives prices and, in particular, study the risks associated with them. The idea of the market-based approach is to model the derivatives prices directly, as the prices of generic financial assets. This approach allows to start a model from an arbitrary combination of derivatives prices currently observed in the market, without having to change (recalibrate) the model. In this presentation, I will outline the main problems associated with the construction of a market-based model and will present the general methodology which provides solutions to these problems. I will also give an overview of the existing constructions of the market-based models, starting with the famous Heath-Jarrow-Morton theory, and show how these results agree with the general method. Finally, I will illustrate the theory by constructing (both mathematically and numerically) a family of market-based models for the European call options of multiple strikes and maturities. Wednesday, January 18, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Yan Dolinsky (ETH Zurich) Title: Numerical Schemes for Stochastic Volatility Models Abstract: We present a tree based approximations for stochastic volatility models, such as the Stein and Stein model, Heston model etc. The importance of such numerical schemes follows from the wide use of stochastic volatility models among practitioners and the fact that for these models analytical solutions usually are not available. We show how to calculate efficiently options prices (European and American) with general type of payoffs such as Vanilla Options, Barrier Options, Lookback Options, Asian options etc. Our main tool is the weak convergence approach which allows to approximate diffusion processes by correlated random walks. Friday, January 20, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Gerard Brunick (PSTAT, UCSB) Title: Optimal Investment in the Presence of High-water Mark Fees Abstract: In this talk, we will consider the problem of optimal asset allocation for an agent who may invest in a money market fund, a stock, and a hedge fund. We model the risky assets as correlated geometric Brownian motions and we assume that our investor maximizes discounted CRRA utility from consumption on an infinite horizon. We further suppose that the investment in the hedge fund is subject to a proportional performance fee that is assessed each time the cumulative profit-to-date derived from the investment in the hedge fund eaches a new running maximum. We will see that this problem reduces to the optimal control of a reflected diffusion. We will examine the regularity of the associated Hamilton-Jacobi-Bellman equation and show the existence of optimal controls. Finally, we will examine some qualitative properties of the optimal investment strategy. Monday Jan 23, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Alexandra Chronopoulou (PSTAT, UCSB) Title: Stochastic volatility models with long-memory in discrete and continuous time Abstract: We consider a continuous time stochastic volatility model with long memory in which the stock price is described by a Geometric Brownian motion with volatility that follows a fractional Ornstein-Uhlenbeck process. In addition, we study two discrete time models: a discretization of the continuous model via an Euler scheme and a discrete model in which the returns are a zero mean iid sequence where the volatility is a fractional ARIMA process. Using a particle filtering algorithm we estimate the empirical distribution of the unobserved volatility process for all three models. Based on the volatility filter, we construct a multinomial recombining tree for option pricing. We also discuss appropriate parameter estimation techniques for each model. For the long memory parameter, we compute an implied value by calibrating the model with real data. Finally, we compare the different models using simulated data and we price options on the S&P 500 index. Wednesday, February 1, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Todd Gross (Allergan Medical & PSTAT UCSB) Title: Statistical Application, and the Role of Biostatistician, in Pharmaceutical and Medical Device Development Abstract: Statistical theory and application offer fundamental tools for the development and evaluation of new drugs and medical devices. During each phase of development, accept/reject decisions must be made based on sampled experimental data, culminating in decisions by regulatory and reimbursement agencies to approve or reject the product. The spectrum of statistical models and methods used, and their impact on corresponding study design and objectives, sample size, measures of clinical outcome, hypothesis tests and multiplicity, will be presented. In addition, the role of biostatistician as practitioner, project manager, communicator, and advocate for the application of statistically-based decision making within the biotech industry will be discussed. Wednesday, February 8, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. M. Elizabeth Halloran (University of Washington) Title: The Minicommunity Design to Assess Indirect Effects of Vaccination ABSTRACT: We propose the minicommunity design to estimate indirect effects of vaccination. Establishing indirect effects of vaccination in unvaccinated subpopulations could have important implications for global vaccine policies. In the minicommunity design, the household or other small transmission unit serves as the cluster in which to estimate indirect effects of vaccination, similar to studies in larger communities to estimate indirect, total, and overall effects. Examples from the literature include studies in small transmission units to estimate indirect effects of pertussis, pneumococcal, influenza, and cholera vaccines. The minicommunity study for indirect effects is contrasted with studies to estimate vaccine effects on infectiousness and protective effects under conditions of household exposure within small transmission units. The minicommunity design can be easily implemented in individually randomized studies by enrolling and following members of households of the randomized individuals. We show how these studies are developed in the framework of causal inference with interference. We will also show one or two microsimulations of vaccination programs for infectious diseases. Wednesday, February 15, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Garrett Glasgow (UCSB Political Science) Title: New Empirical Strategies for the Study of Parliamentary Government Formation ABSTRACT: In recent years a consensus has developed in political science that the conditional logit (CL) model is the most appropriate strategy for modeling parliamentary government choice (the choice of governing coalition after a parliamentary election). In this paper, we reconsider this approach and make three methodological contributions. First, we employ a mixed model with random coefficients (a mixed conditional logit) that allows us to take account of unobserved heterogeneity in the government formation process and relax the restrictive independence of irrelevant alternatives (IIA) assumption. Second, we demonstrate that the procedure used in the political science literature to test the IIA assumption is biased against finding IIA violations. An improved testing procedure reveals clear evidence of IIA violations, indicating that the CL model is inappropriate for the study of government formation. Third, we note that studies of government formation often contain tens of thousands of unique potential coalitions, most of which have near-zero predicted probability. Thus, substantive interpretation of these models poses a challenge. We develop several strategies for interpreting the substantive influence of variables in models of government choice, including javascript-based interactive graphs. Tue, February 21, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Jichun Xie (Temple U) Title: Covariate Adjusted Precision Matrix Estimation Wed, February 22, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Aleksey Polunchenko (USC) Title: State-of-the-Art in Sequential Change-Point Detection Abstract: We consider the problem of sequential change-point detection. This problem is concerned with the design and analysis of fastest ways to detect a change in the statistical pro le of a random time process, given a tolerable risk of making false detection. The subject nds applications, e.g., in quality control, anomaly detection, failure detection, surveillance, process control, intrusion detection, boundary tracking, etc. We provide an overview of the state-of-the-art in the eld. The overview spans over all major formulations of the underlying optimization problem, namely, Bayesian, generalized Bayesian, and minimax. We pay particular attention to the latest advances made in each. Also, we link together the generalized Bayesian problem with multi-cyclic disorder detection in a stationary regime when the change occurs at a distant time horizon. We conclude with a case study to show the eld's best detection procedures at work. This is joint work with Alexander G. Tartakovsky. Wed, February 29, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Joscha Diehl (TU Berlin) Title: Rough path theory: a quick overview and some applications Abstract: Differential equations of the form dY = f(Y) dX are covered by classical theory in the case where X is a smooth path. Rough path theory treats such equations when the driving signal X is very irregular in time, e.g. only Hölder continuous for some exponent larger then zero. It turns out that in general the information given by the path itself is not sufficient to build a satisfying theory. The missing piece is some kind of 'higher order' process, which can be thought of as encoding iterated integrals of the path against itself. I will sketch the main ideas of the theory, using an approach that only requires knowledge of undergraduate mathematics. Thu, March 1, South Hall 5607F, 11:00-12:30PM, Refreshments served at 10:45 AM Dr. Kobi Ako Abayomi (Georgia Institute of Technology) Title: Statistics for re-identification in networked data models Abstract: Re-identification in networked data models involves testing procedures for the identification of similar observations. We consider this testing problem from first principles: we derive probability distributions for a version of a similarity score for three well known network data models. Our method is unique in that it suggests a sufficiency property for (at least) these distributions, an unexplored area of network/graphical modeling. Wed, March 7, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Abel Rodriguez (UCSC) Title: Bayesian Inference for General Gaussian Graphical Models with Application to Multivariate Lattice Data Abstract: We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using a simulated example and a real-world application which concerns cancer mortality surveillance. Supplementary materials with computer code and the datasets needed to replicate our numerical results together with additional tables of results are available online. This is joint work with Adrian Dobra (University of Washington) and Alex Lenkoski (Universitat Heidelberg) Wednesday, April 11, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Travis Loux (PSTAT-UCSB) Title: Causal Inference, Propensity Scores, and Odds Ratios Abstract: We will begin with an introduction to the field of causal inference, including basic goals, the main issues with inference, and the potential outcomes model. We then explain how randomization accomplishes these goals and the assumptions necessary for observational studies to mimic randomized studies. A number of uses of the propensity score, a common tool for causal inference, are introduced. We then investigate various odds ratio parameters in the context of potential outcomes. Finally, we perform a simulation study using numerous propensity score methods to estimate the marginal odds ratio and conclude with a few insights into the use of propensity scores. Wednesday, May 2, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Shejie Ma (UC Riverside) Title: Simultaneous Variable Selection and Estimation in Semiparametric Modeling of Longititudinal/Clustered Data Abstract: We consider the problem of simultaneous variable selection and estimation in additive partially linear model for logitudinal/clustered data. We propose an estimation procedure via polynomial splines to estimate the nonparametric components and apply proper penalty functions to achieve sparsity in the linear part. Under reasonable conditions, we obtain the asymptotic normality of the estimators for the linear components and the consistency of the estimators for the nonparametric components. We further demonstrate that, with proper choice of the regularization parameter, the penalized estimators of the nonzero coefficients achieve the asymptotic oracle property. The finite sample behavior of the penalized estimators is evaluated with simulation studies and illustrated by a longitudinal CD4 cell count dataset. Wednesday, May 9, BUCHN 1940, 3:30-5PM, Refreshments served at 3:15 PM Dr. David Aldous (UC Berkeley) Title: Reflections on devising a "Probability in the Real World" course Abstract: Undergraduate textbooks on probability often deal with "things that are like dice" and hypothetical stories that have little connection with our experience of chance outside the classroom. As part of a broader project to articulate critically what mathematical probability says about the real world, Professor Aldous teaches an occasional course at UC, Berkeley giving 20 lectures on different, maximally diverse, topics relating to probability, and students choose some project involving new and real data. This talk, which is completely non-technical, will describe some of the content of that course, not found in other probability courses.
Wednesday, May 16, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Kaushik Ghosh (Univ of Nevada, Las Vegas) Title: Modeling relational data using nested partition models Abstract: We introduce a flexible class of models for relational data based on a hierarchical extension of the two-parameter Poisson-Dirichlet process. The models are motivated by two different applications: 1) A study of cancer mortality rates in the U.S., where rates for different types of cancer are available for each state, and 2) the analysis of microarray data, where expression levels are available for a large number of genes in a sample of subjects. In both these settings, we are interested in improving the estimation by flexibly borrowing information across rows and columns while partitioning the data into homogeneous subpopulations. Our model allows for a novel nested partitioning structure in the data not provided by existing nonparametric methods, in which rows are clustered while simultaneously grouping together columns within each cluster of rows. The number of partitions are assumed to be unknown and are estimated from the data. We illustrate our models using some real data examples. Friday, May 25, South Hall 5607F, special time: 2-3PM, Refreshments served at 1:45 PM Dr. Niklas Karlsson (Vice President of Research & Development, Advertising.com Group, AoL) Title: Applications of Statistics, Optimization, and Feedback Control in Online Advertising Abstract: Internet advertising revenues in the US hit $7.88 billion for the fourth quarter of 2012. This already large number together with the forecast of 23.3% year-over-year growth underscores the significance of online advertising as an industry and reflects the fact that the world is entering the media economy. Despite the current state of the economy, internet ad spending is expected to continue increasing faster than most other industry sectors. One way of turning this growing industry into a viable business is by providing algorithmic match making between advertisers and publishers in an ad network; i.e., by figuring out where, when, and how to show ads to the satisfaction of publishers and advertisers while maximizing the profit of the network. An ad network is a good example of a complex and very high-dimensional optimization problem and the presentation will describe interesting properties of this system. The presentation will also show how the problem leads to interesting and challenging problems in statistical inference, game theory, and feedback control and will suggest how some of these problems can be solved.
Wednesday, May 30, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Jeff Moehlis (Department of Mechanical Engineering, UC Santa Barbara) Title: Group Decision-Making Models for Sequential Tasks Abstract: The sequential probability ratio test (SPRT) and related drift-diffusion model (DDM) are optimal for choosing between two Wednesday, September 26, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Petr Plechac (University of Delaware) Title: Multilevel approximations and coarse-graining of lattice jump processes Abstract: We discuss a hierarchy of approximation methods developed for accelerated sampling of microscopic dynamics in stochastic lattice systems. The approach is based on efficient coupling of different resolution levels, taking advantage of the low sampling cost in a coarse space and the local reconstructions. We discuss error estimates for (a) long-time stationary dynamics in terms of relative entropy, and (b) finite-time weak error estimates that control mesoscale observables. From the computational point of view the multilevel nature of the method allows for speeding up sampling algorithms such as kinetic Monte Carlo applied to systems with complex lattice geometries and particle interactions. We also briefly discuss related mathematical, numerical and algorithmic issues arising in the parallelization of spatially distributed kinetic Monte Carlo simulations, by developing a hierarchical operator splitting of the underlying high-dimensional generator. Wednesday, October 3, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Jinchi Lv (University of Southern California) Title: High-Dimensional Sparse Additive Hazards Regression Abstract: High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of regularization methods for simultaneous variable selection and estimation in the additive hazards model, by combining the nonconcave penalized likelihood approach and the pseudoscore method. In a high-dimensional setting where the dimensionality can grow fast, polynomially or nonpolynomially, with the sample size, we establish the weak oracle property and oracle property under mild, interpretable conditions, thus providing strong performance guarantees for the proposed methodology. Moreover, we show that the regularity conditions required by the $L_1$ method are substantially relaxed by a certain class of sparsity-inducing concave penalties. As a result, concave penalties such as the smoothly clipped absolute deviation (SCAD), minimax concave penalty (MCP), and smooth integration of counting and absolute deviation (SICA) can significantly improve on the $L_1$ method and yield sparser models with better prediction performance. We present a coordinate descent algorithm for efficient implementation and rigorously investigate its convergence properties. The practical utility and effectiveness of the proposed methods are demonstrated by simulation studies and a real data example. Wednesday, October 10, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Zhaoxia Yu (University of California Irvine) Title: Some new methods for improving gene discovery using family-based designs Abstract: In this talk I will discuss how to address two challenges in family-based association studies of complex diseases.
In genetic studies it is critical to develop methods that can efficiently analyzing multiple genetic markers, as complex diseases are caused by multiple risk factors. For family-based association studies, we address this challenge by evaluating two pseudosibship methods: the 1:1 matching, which matches each affected offspring to the pseudo sibling formed by the alleles not transmitted to the affected offspring; the exhaustive matching, which matches each affected offspring to the pseudo siblings formed by all the other possible combinations of parental alleles. We prove that the two matching strategies use exactly and approximately the same amount of information from data under additive and multiplicative genetic models, respectively. This result paves the way for many existing multi-locus analysis methods developed for the case-control (or matched case-control) design to be applied to case-parents data with minor modifications. As an example, we apply an L1 regularized regression to a Crohn’s disease dataset using the 1:1 matching. Dr. Sreenivas R. Jammalamadaka (UCSB) Title: A matter of Direction Abstract: This talk describes various scenarios where measurements on directions come into play, and was presented recently at the Swedish University of Agricultural Sciences, on the occasion of the speaker receiving an Honorary Doctorate from that University. Wednesday, October 31, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Emanuele Taufer (University of Trento and UCSB) Title: Semi-parametric estimation of the tail index of a distribution Abstract: The concept of regularly varying function is an essential analytical tool for analyzing data in economics and finance, since a remarkable number of regularities, or “laws”, are considered to follow an approximate power law, at least in the upper tail, in these fields. Available estimators of the tail index of a distribution are usually based on extreme order statistics which are often too few to provide exhaustive information on the problem.
In the talk, a different approach, based on a regression-type estimator, which utilizes all sample data will be considered. The method discussed exploits the fact that, under some conditions, the behavior of the distribution function near infinity is reflected in the behavior of the characteristic function near the origin. The approach is semi-parametric as only an assumption about the tail of the distribution is used.
Theoretical properties of the estimator, including its bias, variance and asymptotic distribution are derived as well as rules for its practical application. Monday, November 26, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Madhu Mazumdar (Cornell University) Title: Role of Biostatistician in a Medical College:Examples of Impactful Clinical Applications and Valuable Statistical Methods Development Abstract: Nationally representative studies of perioperative outcomes including, morbidity, mortality, and safety for major surgery is important to clinicians, researchers, patients, and administrators alike. However, despite the staggering numbers of orthopedic procedures being performed in the United States each year, there is a paucity of literature in these areas. Available studies on perioperative morbidity and mortality primarily report data from single, specialized and often academic institutions with relatively small cohorts. These studies are limited by their low external validity and their inability to effectively study subpopulations and low incidence outcomes. To address this void, our interdisciplinary team has used nationally representative databases (NHDS, HCUP-NIS, NSAS, and Premier Inc.’s Perspective) to study various aspects of the perioperative epidemiology including the incidence, risk factors and trends of morbidity and mortality, changes in the population receiving care and –following the concept of comparative effectiveness research- outcomes associated with different surgical approaches and anesthetic techniques for the same medical problem. Some of the results have led to supplemental clinical studies and in some cases policy for patient selection has changed at the institutional level. Efforts towards consensus building to transport the policy change at national level are underway. Wednesday, January 30, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Subir Ghosh (UCR) Title: Some Heuristic Methods of Parameter Estimation in Linear and Nonlinear Models Abstract: This presentation will consider the situation where the exact expressions of the estimators of the model parameters are not available based on all the data and the numerical methods are performed to obtain the estimates. Models for both discrete and continuous response variables will be discussed in presence of explanatory variables. The proposed heuristic methods and their statistical properties will be presented for these models. Performance of the proposed methods will also be demonstrated using simulations. Wednesday, Feburary 6, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Mark F. Schilling (California State University Northridge) Title: A Coverage Probability Approach to Finding an Optimal Binomial Confidence Procedure Abstract: The problem of obtaining a confidence interval for a binomial success parameter is one of the most common and basic of statistical situations. Despite the simplicity of the model and data structure, there is remarkable complexity to this problem. Existing procedures have been developed based on normal approximations, inversion of hypothesis tests, etc; the coverage probability function (cpf) of a given procedure is a key instrument for judging the adequacy of its performance. I will present a new procedure that is optimal in a fundamental sense, by employing an alternative approach: Choose the cpf optimally from the set of all possible cpfs, since stipulating the cpf is equivalent to specifying the confidence procedure. Performance of the procedure obtained from this approach is assessed both for the case when the confidence level represents a lower bound on coverage as well as for the situation when it is achieved only approximately. A new measure is introduced to help evaluate procedures in the latter case. Our procedure is compared to that of popular existing procedures on several measures and shown to be superior in essential ways. Wednesday, Febuary 13, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Stephen DeSalvo (UCLA) Title: Probabilistic Divide-and-Conquer - a new method for exact simulation Abstract: We describe a general method for the generation of a random sample from a se<t of objects under a given distribution, typically of the combinatorial type. For example, the uniform distribution over the set of all integer partitions.
The general setup is roughly as follows. Suppose the random objects $S$ can be described as $S = (A,B)$, where $A\in \mathcal{A}$ and $B\in \mathcal{B}$ can be simulated separately. Suppose there is a matching function $h: \mathcal{A} \times \mathcal{B} \to \{0,1\}$ that determines which As and Bs can be paired together to form a matching pair in $S$, so that the desired distribution on the set of objects $S$ is equal in distribution to $( (A,B) | h(A,B) = 1)$.
We will focus in this talk on the application to the random generation of integer partitions to demonstrate how one would carry out this technique. Our main result says that our algorithm is O( \sqrt{n} ), which is also the lower entropy limit of a random ensemble.
Only basic probability will be assumed. Wednesday, Febuary 27, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Theofanis Sapatinas (University of Cyprus and UCSB) Title: Functional Deconvolution in a Periodic Setting: Continuous and Discrete Models Abstract: We present an extension of deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover initial or boundary conditions on the basis of observations from a noisy solution of a partial differential equation. In the case when it is observed at a finite number of distinct points, the proposed functional deconvolution model can also be viewed as a multichannel deconvolution model. We present adaptive minimax wavelet block-thresholding estimators over a wide range of Besov spaces and investigate when the availability of continuous data gives advantages over observations at the asymptotically large number of points. As an illustration, we discuss particular examples for both continuous and discrete settings. Some recent developments are also briefly discussed. Wednesday, March 13, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Dmitry Kramkov (Carnegie Mellon) Title: Integral representation of martingales motivated by the problem of endogenous completeness in financial economics Abstract: Let Q and P be equivalent probability measures and
let psi be a J-dimensional vector of random variables such that
d Q/ d P and psi are defined in terms of a
weak solution X to a d-dimensional stochastic differential equation.
Motivated by the problem of endogenous completeness in financial
economics we present conditions which guarantee that every local
martingale under Q is a stochastic integral with respect to
the J-dimensional martingale S_t \set
E^{Q}[psi|F_t]. While the drift b=b(t,x)
and the volatility sigma = sigma(t,x) coefficients for X need to
have only minimal regularity properties with respect to x, they are
assumed to be analytic functions with respect to t. We provide a
counter-example showing that this $t$-analyticity assumption for
sigma cannot be removed. Wednesday, April 10, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Samuel J. Frame (Cal Poly) Title: Assessing Driver Risk using Mobile Phone Sensor Data Abstract: Mobile phones and other technologies allow individuals, companies, and insurance providers to monitor driver risk. Monitoring (and predicting) driver risk has substantial implications for individual safety, driver training, company incident exposure, and pricing insurance premiums. Cal Poly Technology Park firm Mentor eData has developed a mobile phone application that acquires GPS data and provides users with a continuous driver risk score and trip summaries. In this talk, we first discuss using the Virginia Tech Transportation Institute's 100-Car Naturalistic Driving Data to estimate Mentor eData's scoring method. We also discuss providing feedback for driving phases and for risky driving events. Wednesday, April 17, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Theofanis Sapatinas (University of Cyprus and UCSB) Title: Short-Term Load Forecasting: The Similar Shape Functional Time Series Predictor Abstract: A novel functional time series methodology for short-term load forecasting is introduced. The prediction is performed by means of a weighted average of past daily load segments, the shape of which is similar to the expected shape of the load segment to be predicted. The past load segments are identified from the available history of the observed load segments by means of their closeness to a so-called reference load segment. The later is selected in a manner that captures the expected qualitative and quantitative characteristics of the load segment to be predicted. Weak consistency of the suggested similar shape functional time series predictor is established. As an illustration, the suggested functional time series forecasting methodology is applied to historical daily load data in Cyprus. Its performance is compared to some recently proposed alternative methodologies for short-term load forecasting.
Wednesday, April 24, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Hernando Ombao (UC Irvine) Title: Modeling Complex Oscillatory Cross-Dependence in Multivariate Time Series Abstract:In this talk, we shall discuss approaches for characterizing dependence between components of a multivariate time series (e.g., between brain regions). My own interest in this area stems from a growing body of evidence suggesting that various neurological disorders, including Alzheimer’s disease, depression, and Parkinson’s disease may be associated with altered brain connectivity. Tuesday, May 7, Engg. Sciences Bldg. Room1001, 3:30-5PM, Refreshments served at 3:15 PM Dr. Peter Hall (UC Davis) Title: Nonparametric Methods for Estimating Periodic Functions, With Applications in Astronomy Abstract:If the intensity of light radiating from a star varies in a periodic fashion over time, then there are significant opportunities for accessing information about the star's origins, age and structure. For example, if two stars have similar periodicity and light curves, and if we can gain information about the structure of one of them (perhaps because it is relatively close to Earth, and therefore amenable to direct observation), then we can make deductions about the structure of the other. Therefore period lengths, and light-curve shapes, are of significant interest. In this talk we shall briefly outline the history and current status of the study of periodic variable stars, and review some of the statistical methods used for their analysis. Wednesday, May 8, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Shige Peng (Shandong University, Global Scholar of Princeton) Title: BSDE, PDE, Nonlinear Expectation and Model Uncertainty Abstract:Nonlinear Feynman-Kac formula tells us that, when the coefficients depend only on the state of the path of a Brownian, then a Backward Stochastic Differential Equation (BSDE) becomes a quasilinear PDE of parabolic type. This reveals that, in general, a BSDE is in fact a new type of PDE called path dependent PDE, in which the continuous path plays the role of state variable x. The nonlinear semigroup associated to this PDE is a nonlinear expectation.
Wednesday, May 15, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Esteban Chavez (UCSB) Title: Limit Theorems in Stochastic Homogenization Abstract: Problems in stochastic homogenization typically deal with approximating solutions to PDEs with rapidly oscillatory random coefficients by solutions of homogenized deterministic PDEs. Even though many convergence results have been obtained in the form of a law of large numbers, very little is known about the rate of convergence or the large deviations of this approximation, especially in spatial dimensions greater than one. In this talk I will establish some analytic results concerning the rate of convergence and large deviations for some stochastic homogenization problems in higher spatial dimensions.
Wednesday, May 22, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Kaushik Ghosh (University of Nevada Las Vegas) Title: A Unified Approach to Variations of Ranked Set Sampling Abstract:In this talk, we develop a general theory of inference using data collected from different variations of ranked set sampling. Such variations include balanced and unbalanced ranked set sampling, balanced and unbalanced k-tuple ranked set sampling, nomination sampling, simple random sampling, as well as a combination of them. We provide methods of estimating the underlying distribution function as well as its functionals and establish the asymptotic properties of the resulting estimators. The results so obtained can be used to develop nonparametric procedures for one- and two-sample problems. We also investigate small-sample properties of these estimators and conclude with an application. Wednesday, May 29, South Hall 5607F, 3:30-5PM, Refreshments served at 3:15 PM Dr. Magnus Ekstrom (Umea University & UCSB) Title: Powerful Parametric Tests Based on Sum-Functions of Spacings Abstract:Assume that we have a sequence of n independent and identically distributed random variables with a continuous distribution function F, which is specified up to a few unknown parameters. In this seminar, tests based on sum-functions of sample spacings are proposed, and large sample theory of the tests are presented under simple null hypotheses as well as under close alternatives. Tests which are optimal within this class are constructed, and it is noted that these tests have properties that closely parallel those of the likelihood ratio test in regular parametric models. Some examples are given, which show that the proposed tests work also in situations where the likelihood ratio test breaks down. Extensions to more general hypotheses are discussed.
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