An Introduction to Twisted Particle Filters and Parameter Estimation in Non-linear State-space Models

Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to extend the twisted particle filtering methodology, establish accessible theoretical results which convey its rationale, and provide a demonstration of its practical performance within particle Markov chain Monte Carlo for estimating static model parameters. We derive twisted particle filters that incorporate systematic or multinomial resampling and information from historical particle states, and a transparent proof which identifies the optimal algorithm for marginal likelihood estimation. We demonstrate how to approximate the optimal algorithm for nonlinear state-space models with Gaussian noise and we apply such approximations to two examples: a range and bearing tracking problem and an indoor positioning problem with Bluetooth signal strength measurements. We demonstrate improvements over standard algorithms in terms of variance of marginal likelihood estimates and Markov chain autocorrelation for given CPU time, and improved tracking performance using estimated parameters.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Fluctuations, stability and instability of a distributed particle filter with local exchange

We study a distributed particle filter proposed by Boli\'c et al.~(2005). This algorithm involves $m$ groups of $M$ particles, with interaction between groups occurring through a "local exchange" mechanism. We establish a central limit theorem in the regime where $M$ is fixed and $m\to\infty$. A formula we obtain for the asymptotic variance can be interpreted in terms of colliding Markov chains, enabling analytic and numerical evaluations of how the asymptotic variance behaves over time, with comparison to a benchmark algorithm consisting of $m$ independent particle filters. We prove that subject to regularity conditions, when $m$ is fixed both algorithms converge time-uniformly at rate $M^{-1/2}$. Through use of our asymptotic variance formula we give counter-examples satisfying the same regularity conditions to show that when $M$ is fixed neither algorithm, in general, converges time-uniformly at rate $m^{-1/2}$.Comment: 49 pages, 7 figure

Bayesian Inference for Duplication-Mutation with Complementarity Network Models

We observe an undirected graph $G$ without multiple edges and self-loops, which is to represent a protein-protein interaction (PPI) network. We assume that $G$ evolved under the duplication-mutation with complementarity (DMC) model from a seed graph, $G_0$, and we also observe the binary forest $\Gamma$ that represents the duplication history of $G$. A posterior density for the DMC model parameters is established, and we outline a sampling strategy by which one can perform Bayesian inference; that sampling strategy employs a particle marginal Metropolis-Hastings (PMMH) algorithm. We test our methodology on numerical examples to demonstrate a high accuracy and precision in the inference of the DMC model's mutation and homodimerization parameters

Bridging trees for posterior inference on Ancestral Recombination Graphs

We present a new Markov chain Monte Carlo algorithm, implemented in software Arbores, for inferring the history of a sample of DNA sequences. Our principal innovation is a bridging procedure, previously applied only for simple stochastic processes, in which the local computations within a bridge can proceed independently of the rest of the DNA sequence, facilitating large-scale parallelisation.Comment: 23 pages, 9 figures, accepted for publication in Proceedings of the Royal Society

Regression models for linking patterns of growth to a later outcome:Infant growth and childhood overweight

Abstract Background Regression models are widely used to link serial measures of anthropometric size or changes in size to a later outcome. Different parameterisations of these models enable one to target different questions about the effect of growth, however, their interpretation can be challenging. Our objective was to formulate and classify several sets of parameterisations by their underlying growth pattern contrast, and to discuss their utility using an expository example. Methods We describe and classify five sets of model parameterisations in accordance with their underlying growth pattern contrast (conditional growth; being bigger v being smaller; becoming bigger and staying bigger; growing faster v being bigger; becoming and staying bigger versus being bigger). The contrasts are estimated by including different sets of repeated measures of size and changes in size in a regression model. We illustrate these models in the setting of linking infant growth (measured on 6 occasions: birth, 6 weeks, 3, 6, 12 and 24 months) in weight-for-height-for-age z-scores to later childhood overweight at 8y using complete cases from the Norwegian Childhood Growth study (n = 900). Results In our expository example, conditional growth during all periods, becoming bigger in any interval and staying bigger through infancy, and being bigger from birth were all associated with higher odds of later overweight. The highest odds of later overweight occurred for individuals who experienced high conditional growth or became bigger in the 3 to 6 month period and stayed bigger, and those who were bigger from birth to 24 months. Comparisons between periods and between growth patterns require large sample sizes and need to consider how to scale associations to make comparisons fair; with respect to the latter, we show one approach. Conclusion Studies interested in detrimental growth patterns may gain extra insight from reporting several sets of growth pattern contrasts, and hence an approach that incorporates several sets of model parameterisations. Co-efficients from these models require careful interpretation, taking account of the other variables that are conditioned on

Language endangerment and language documentation in Africa

Non peer reviewe

Density functional theory based screening of ternary alkali-transition metal borohydrides: A computational material design project

The dissociation of molecules, even the most simple hydrogen molecule, cannot be described accurately within density functional theory because none of the currently available functionals accounts for strong on-site correlation. This problem led to a discussion of properties that the local Kohn-Sham potential has to satisfy in order to correctly describe strongly correlated systems. We derive an analytic expression for the nontrivial form of the Kohn-Sham potential in between the two fragments for the dissociation of a single bond. We show that the numerical calculations for a one-dimensional two-electron model system indeed approach and reach this limit. It is shown that the functional form of the potential is universal, i.e., independent of the details of the two fragments.We acknowledge funding by the Spanish MEC (Grant No. FIS2007-65702-C02-01), “Grupos Consolidados UPV/EHU del Gobierno Vasco” (Grant No. IT-319-07), and the European Community through e-I3 ETSF project (Grant Agreement No. 211956).Peer reviewe