Particle Filtering and Smoothing Using Windowed Rejection Sampling

"Particle methods" are sequential Monte Carlo algorithms, typically involving importance sampling, that are used to estimate and sample from joint and marginal densities from a collection of a, presumably increasing, number of random variables. In particular, a particle filter aims to estimate the current state $X_{n}$ of a stochastic system that is not directly observable by estimating a posterior distribution $\pi(x_{n}|y_{1},y_{2}, \ldots, y_{n})$ where the $\{Y_{n}\}$ are observations related to the $\{X_{n}\}$ through some measurement model $\pi(y_{n}|x_{n})$. A particle smoother aims to estimate a marginal distribution $\pi(x_{i}|y_{1},y_{2}, \ldots, y_{n})$ for $1 \leq i < n$. Particle methods are used extensively for hidden Markov models where $\{X_{n}\}$ is a Markov chain as well as for more general state space models. Existing particle filtering algorithms are extremely fast and easy to implement. Although they suffer from issues of degeneracy and "sample impoverishment", steps can be taken to minimize these problems and overall they are excellent tools for inference. However, if one wishes to sample from a posterior distribution of interest, a particle filter is only able to produce dependent draws. Particle smoothing algorithms are complicated and far less robust, often requiring cumbersome post-processing, "forward-backward" recursions, and multiple passes through subroutines. In this paper we introduce an alternative algorithm for both filtering and smoothing that is based on rejection sampling "in windows" . We compare both speed and accuracy of the traditional particle filter and this "windowed rejection sampler" (WRS) for several examples and show that good estimates for smoothing distributions are obtained at no extra cost

CP violation and rare Bs decays at the Tevatron

This note gives updates on three results from the Fermilab Tevatron p¯p collider operating at √s = 1.96TeV. The results presented include: the D0 dimuon charge asymmetry; the measurement of the CP-violating phase φs in the decay Bs → J/ψφ from both CDF and D0; and the most recent results from both CDF and D0 on the search for the ultra-rare decay Bs → μ+μ−

Approaching zero : temporal effects of a restrictive antibiotic policy on hospital-acquired Clostridium difficile, extended-spectrum β-lactamase-producing coliforms and meticillin-resistant Staphylococcus aureus

A restrictive antibiotic policy banning routine use of ceftriaxone and ciprofloxacin was implemented in a 450-bed district general hospital following an educational campaign. Monthly consumption of nine antibiotics was monitored in defined daily doses (DDDs) per 1000 patient-occupied bed-days (1000 pt-bds) 9 months before until 16 months after policy introduction. Hospital-acquired Clostridium difficile, meticillin-resistant Staphylococcus aureus (MRSA) and extended-spectrum -lactamase (ESBL)- producing coliform cases per month/1000 pt-bds were identified and reviewed throughout the hospital. Between the first and final 6 months of the study, average monthly consumption of ceftriaxone reduced by 95% (from 46.213 to 2.129 DDDs/1000 pt-bds) and that for ciprofloxacin by 72.5% (109.804 to 30.205 DDDs/1000 pt-bds). Over the same periods, hospital-acquisition rates for C. difficile reduced by 77% (2.398 to 0.549 cases/1000 pt-bds), for MRSA by 25% (1.187 to 0.894 cases/1000 pt-bds) and for ESBL-producing coliforms by 17% (1.480 to 1.224 cases/1000 pt-bds). Time-lag modelling confirmed significant associations between ceftriaxone and C. difficile cases at 1 month (correlation 0.83; P < 0.005), and between ciprofloxacin and ESBL-producing coliform cases at 2 months (correlation 0.649; P = 0.002). An audit performed 3 years after the policy showed sustained reduction in C. difficile rates (0.259 cases/1000 pt-bds), with additional decreases for MRSA (0.409 cases/1000 pt-bds) and ESBL-producing coliforms (0.809 cases/1000 pt-bds). In conclusion, banning two antibiotics resulted in an immediate and profound reduction in hospital-acquired C. difficile, with possible longer-term effects on MRSA and ESBL-producing coliform rates. Antibiotic stewardship is fundamental in the control of major hospital pathogens

An evolution strategy to estimate emission source distributions on a regional scale from atmospheric observations

International audienceIn this paper we present an Evolution Strategy (ES) approach towards the estimation of the location and strength of surface emissions of trace gases based on atmospheric concentration measurements and back-trajectory analyses. The details of the ES developed are outlined. The ES is tested using artificial emission maps at different grid resolutions and the results compared to those obtained on the same problems using Singular Value Decomposition (SVD). In almost all cases, the ES improves on SVD at equivalent resolutions. In addition, a number of insights, which the ES approach brings to the problem of source location and emission strength, are discussed, particularly the limitations on the use of measurement and meteorological data in the determination of emission source distribution