Hierarchical Models for Relational Event Sequences

Interaction within small groups can often be represented as a sequence of events, where each event involves a sender and a recipient. Recent methods for modeling network data in continuous time model the rate at which individuals interact conditioned on the previous history of events as well as actor covariates. We present a hierarchical extension for modeling multiple such sequences, facilitating inferences about event-level dynamics and their variation across sequences. The hierarchical approach allows one to share information across sequences in a principled manner---we illustrate the efficacy of such sharing through a set of prediction experiments. After discussing methods for adequacy checking and model selection for this class of models, the method is illustrated with an analysis of high school classroom dynamics

Testing for Equilibrium Multiplicity in Dynamic Markov Games

This paper proposes several statistical tests for finite state Markov games to examine the null hypothesis that the data are generated from a single equilibrium. We formulate tests of (i) the conditional choice probabilities, (ii) the steady-state distribution of states and (iii) the conditional distribution of states conditional on an initial state. In a Monte Carlo study we find that the chi-squared test of the steady-state distribution performs well and has high power even with a small number of markets and time periods. We apply the chi-squared test to the empirical application of Ryan (2012) that analyzes dynamics of the U.S. Portland Cement industry and test if his assumption of single equilibrium is supported by the data

MCMC with Strings and Branes: The Suburban Algorithm (Extended Version)

Motivated by the physics of strings and branes, we develop a class of Markov chain Monte Carlo (MCMC) algorithms involving extended objects. Starting from a collection of parallel Metropolis-Hastings (MH) samplers, we place them on an auxiliary grid, and couple them together via nearest neighbor interactions. This leads to a class of "suburban samplers" (i.e., spread out Metropolis). Coupling the samplers in this way modifies the mixing rate and speed of convergence for the Markov chain, and can in many cases allow a sampler to more easily overcome free energy barriers in a target distribution. We test these general theoretical considerations by performing several numerical experiments. For suburban samplers with a fluctuating grid topology, performance is strongly correlated with the average number of neighbors. Increasing the average number of neighbors above zero initially leads to an increase in performance, though there is a critical connectivity with effective dimension d_eff ~ 1, above which "groupthink" takes over, and the performance of the sampler declines.Comment: v2: 55 pages, 13 figures, references and clarifications added. Published version. This article is an extended version of "MCMC with Strings and Branes: The Suburban Algorithm

Particle algorithms for optimization on binary spaces

We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier problems

Meta-Analysis of Quantitative Trait Association and Mapping Studies using Parametric and Non-Parametric Models

Meta-analysis is an important method for integration of information from multiple studies. In quantitative trait association and mapping experiments, combining results from several studies allows greater statistical power for detection of causal loci and more precise estimation of their effects, and thus can yield stronger conclusions than individual studies. Various meta-analysis methods have been proposed for synthesizing information from multiple candidate gene studies and QTL mapping experiments, but there are several questions and challenges associated with these methods. For example, meta-analytic fixed-effect models assume homogeneity of outcomes from individual studies, which may not always be true. Whereas random-effect models takes into account the heterogeneity among studies they typically assume a normal distribution of study-specific outcomes. However in reality, the observed distribution pattern tends to be multi-modal, suggesting a mixture whose underlying components are not directly observable. In this paper, we examine several existing parametric meta-analysis methods, and propose the use of a non-parametric model with a Dirichlet process prior (DPP), which relaxes the normality assumptions about study- specific outcomes. With a DPP model, the posterior distribution of outcomes is discrete, reflecting a clustering property that may have biological implications. Features of these methods were illustrated and compared using both simulation data and real QTL data extracted from the Animal QTLdb (http://www.animalgenome.org/cgi-bin/QTLdb/index). The meta analysis of reported average daily body weight gain (ADG) QTL suggested that there could be from six to eight distinct ADG QTL on swine chromosome 1