Advanced Network Sampling with Heterogeneous Multiple Chains

Honest Importance Sampling with Multiple Markov Chains.

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asym...

Heterogeneous Force Chains in Cellularized Biopolymer Network

Biopolymer Networks play an important role in coordinating and regulating collective cellular dynamics via a number of signaling pathways. Here, we investigate the mechanical response of a model biopolymer network due to the active contraction of embedded cells. Specifically, a graph (bond-node) model derived from confocal microscopy data is used to represent the network microstructure, and cel...

On sampling with Markov chains

Exact Sampling with Markov Chains

Random sampling has found numerous applications in computer science, statistics, and physics. The most widely applicable method of random sampling is to use a Markov chain whose steady state distribution is the probability distribution r from which we wish to sample. After the Markov chain has been run for long enough, its state is approximately distributed according to 7r. The principal proble...

Sampling Good Motifs with Markov Chains

Markov chain Monte Carlo (MCMC) techniques have been used with some success in bioin­ formatics [LAB93]. However, these results rely on heuristic estimates of a Markov chain’s mixing time. Without provable results, we cannot accurately judge the quality of an algorithm or the output it produces. Our goal is to remedy this situation in the context of the motif­finding problem. Using combinatoria...