23 research outputs found
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
Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions
We give conditions under which a Markov chain constructed via parallel or
simulated tempering is guaranteed to be rapidly mixing, which are applicable to
a wide range of multimodal distributions arising in Bayesian statistical
inference and statistical mechanics. We provide lower bounds on the spectral
gaps of parallel and simulated tempering. These bounds imply a single set of
sufficient conditions for rapid mixing of both techniques. A direct consequence
of our results is rapid mixing of parallel and simulated tempering for several
normal mixture models, and for the mean-field Ising model.Comment: Published in at http://dx.doi.org/10.1214/08-AAP555 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org