Statistical Inference on Random Graphs: Comparative Power Analyses via Monte Carlo

Statistical Inference on Random Graphs: Comparative Power Analyses via Monte Carlo

We present a comparative power analysis, via Monte Carlo, of various graph invariants used as statistics for testing graph homogeneity versus a “chatter” alternative – the existence of a local region of excessive activity. Our results indicate that statistical inference on random graphs, even in a relatively simple setting, can be decidedly non-trivial. We find that none of the graph invariants...

Monte Carlo Techniques for Bayesian Statistical Inference – A comparative review

In this article, we summariseMonte Carlo simulationmethods commonly used in Bayesian statistical computing. We give descriptions for each algorithm and provide R codes for their implementation via a simple 2-dimensional example. We compare the relative merits of these methods qualitatively by considering their general user-friendliness, and numerically in terms of mean squared error and computa...

Markov Chain Monte Carlo for Statistical Inference

Monte Carlo inference via greedy importance sampling

We present a new method for conducting Monte Carlo inference in graphical models which combines explicit search with generalized importance sampling. The idea is to reduce the variance of importance sampling by searching for significant points in the target distribution. We prove that it is possible to introduce search and still maintain unbiasedness. We then demonstrate our procedure on a few ...

Phylogenetic Inference via Sequential Monte Carlo

Bayesian inference provides an appealing general framework for phylogenetic analysis, able to incorporate a wide variety of modeling assumptions and to provide a coherent treatment of uncertainty. Existing computational approaches to bayesian inference based on Markov chain Monte Carlo (MCMC) have not, however, kept pace with the scale of the data analysis problems in phylogenetics, and this ha...