The Time Machine: A Simulation Approach for Stochastic Trees

In the following paper we consider a simulation technique for stochastic trees. One of the most important areas in computational genetics is the calculation and subsequent maximization of the likelihood function associated to such models. This typically consists of using importance sampling (IS) and sequential Monte Carlo (SMC) techniques. The approach proceeds by simulating the tree, backward in time from observed data, to a most recent common ancestor (MRCA). However, in many cases, the computational time and variance of estimators are often too high to make standard approaches useful. In this paper we propose to stop the simulation, subsequently yielding biased estimates of the likelihood surface. The bias is investigated from a theoretical point of view. Results from simulation studies are also given to investigate the balance between loss of accuracy, saving in computing time and variance reduction.Comment: 22 Pages, 5 Figure

Bayesian Inference for PCFGs via Markov Chain Monte Carlo

8 page(s

Probabilistic Graphical Model Representation in Phylogenetics

Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation of the chosen model is crucial for: (1) reproducibility of an analysis, (2) model development and (3) software design. Moreover, a unified, clear and understandable framework for model representation lowers the barrier for beginners and non-specialists to grasp complex phylogenetic models, including their assumptions and parameter/variable dependencies. Graphical modeling is a unifying framework that has gained in popularity in the statistical literature in recent years. The core idea is to break complex models into conditionally independent distributions. The strength lies in the comprehensibility, flexibility, and adaptability of this formalism, and the large body of computational work based on it. Graphical models are well-suited to teach statistical models, to facilitate communication among phylogeneticists and in the development of generic software for simulation and statistical inference. Here, we provide an introduction to graphical models for phylogeneticists and extend the standard graphical model representation to the realm of phylogenetics. We introduce a new graphical model component, tree plates, to capture the changing structure of the subgraph corresponding to a phylogenetic tree. We describe a range of phylogenetic models using the graphical model framework and introduce modules to simplify the representation of standard components in large and complex models. Phylogenetic model graphs can be readily used in simulation, maximum likelihood inference, and Bayesian inference using, for example, Metropolis-Hastings or Gibbs sampling of the posterior distribution

Hybrid automated reliability predictor integrated work station (HiREL)

The Hybrid Automated Reliability Predictor (HARP) integrated reliability (HiREL) workstation tool system marks another step toward the goal of producing a totally integrated computer aided design (CAD) workstation design capability. Since a reliability engineer must generally graphically represent a reliability model before he can solve it, the use of a graphical input description language increases productivity and decreases the incidence of error. The captured image displayed on a cathode ray tube (CRT) screen serves as a documented copy of the model and provides the data for automatic input to the HARP reliability model solver. The introduction of dependency gates to a fault tree notation allows the modeling of very large fault tolerant system models using a concise and visually recognizable and familiar graphical language. In addition to aiding in the validation of the reliability model, the concise graphical representation presents company management, regulatory agencies, and company customers a means of expressing a complex model that is readily understandable. The graphical postprocessor computer program HARPO (HARP Output) makes it possible for reliability engineers to quickly analyze huge amounts of reliability/availability data to observe trends due to exploratory design changes

Projecting Ising Model Parameters for Fast Mixing

Inference in general Ising models is difficult, due to high treewidth making tree-based algorithms intractable. Moreover, when interactions are strong, Gibbs sampling may take exponential time to converge to the stationary distribution. We present an algorithm to project Ising model parameters onto a parameter set that is guaranteed to be fast mixing, under several divergences. We find that Gibbs sampling using the projected parameters is more accurate than with the original parameters when interaction strengths are strong and when limited time is available for sampling.Comment: Advances in Neural Information Processing Systems 201