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

The prognostic value of eighth grade records with respect to pupils' achievement in the high school sciences.

Thesis (Ed.M.)--Boston Universit

Supercritical multicomponent solvent coal extraction

The yield of organic extract from the supercritical extraction of coal with larger diameter organic solvents such as toluene is increased by use of a minor amount of from 0.1 to 10% by weight of a second solvent such as methanol having a molecular diameter significantly smaller than the average pore diameter of the coal

On the changes in the physical properties of the ionized region around the Weigelt structures in Eta Carinae over the 5.54-yr spectroscopic cycle

We present HST/STIS observations and analysis of two prominent nebular structures around the central source of Eta Carinae, the knots C and D. The former is brighter than the latter for emission lines from intermediate or high ionization potential ions. The brightness of lines from intermediate and high ionization potential ions significantly decreases at phases around periastron. We do not see conspicuous changes in the brightness of lines from low ionization potential (<13.6 eV) that the total extinction towards the Weigelt structures is that the total extinction towards the Weigelt structures is AsubV =2/0. that the total extinction towards the Weigelt structures is AV = 2.0. Weigelt C and D are characterized by an electron density of that the total extinction towards the Weigelt structures is AV = 2.0. Weigelt C and D are characterized by an electron density of 10exp6.9 cm-3 that does not significantly change throughout the orbital cycle. The electron temperature varies from 5500 K (around periastron) to 7200 K (around apastron). The relative changes in the brightness of He I lines are well reproduced by the variations in the electron temperature alone. We found that, at phases around periastron, the electron temperature seems to be higher for Weigelt C than that of D. The Weigelt structures are located close to the Homunculus equatorial plane, at a distance of about 1240 AU from the central source. From the analysis of proper motion and age, the Weigelt complex can be associated with the equatorial structure called the Butterfly Nebula surrounding the central binary system.Comment: 19 pages, 18 figure

Cardiac Specific Gene Expression Changes in Long Term Culture of Murine Mesenchymal Stem Cells

Murine MSCs are a readily available source of adult stem cells enabling extensive in vitro study of this cell population. MSCs have been described as multipotent, and have been proven capable of differentiation into several connective tissue types. Furthermore some studies have suggested an ability to differentiate into non-connective tissue cell types such as the cardiomyocyte. The aim of this study was to differentiate murine MSCs toward cardiac lineage with the commonly used method of culture with 5’ Azacytidine. Critically, baseline analysis of gene expression of passage four MSCs demonstrated expression of key cardiac markers including cardiac troponin T and I, and the ryanodine receptor. Furthermore, expression analysis of these genes changed with time in culture and passage number. However, there was no significant alteration when cells were subjected to a differentiation protocol. This study therefore highlights the importance of analyzing baseline cells extensively, and indicates the limitations in extrapolating data for comparison between species. Furthermore this data brings into question the efficacy of cardiac differentiation using MSCs

Exact Level And Power Of Permutation, Bootstrap, And Asymptotic Tests Of Trend

We develop computational tools that can evaluate the exact size and power of three tests of trend (e.g., permutation, bootstrap and asymptotic) without resorting to large-sample theory or simulations. We then use these tools to compare the operating characteristics of the three tests. It is seen that the bootstrap test is ultra-conservative relative to the other two tests and as a result suffers from a severe deterioration in power. The power of the asymptotic test is uniformly larger than that of the other two tests, but it fails to preserve the Type I error for most of the range of the baseline response probability. The permutation test, being exact, is guaranteed to preserve the Type I error throughout the range of the baseline response probability. The price paid for this guarantee is a loss of power relative to the asymptotic test. The power loss is, however, small in most situations

Laser Guide Star Adaptive Optics Integral Field Spectroscopy of a Tightly Collimated Bipolar Jet from the Herbig Ae star LkHa 233

We have used the integral field spectrograph OSIRIS and laser guide star adaptive optics at Keck Observatory to obtain high angular resolution (0.06"), moderate spectral resolution (R ~ 3800) images of the bipolar jet from the Herbig Ae star LkHa 233, seen in near-IR [Fe II] emission at 1.600 & 1.644 microns. This jet is narrow and tightly collimated, with an opening angle of only 9 degrees, and has an average radial velocity of ~ 100 km/s. The jet and counterjet are asymmetric, with the red-shifted jet much clumpier than its counterpart at the angular resolution of our observations. The observed properties are in general similar to jets seen around T Tauri stars, though it has a relatively large mass flux of (1.2e-7 +- 0.3e-7) M_sun/year, near the high end of the observed mass flux range around T Tauri stars. We also spatially resolve an inclined circumstellar disk around LkHa 233, which obscures the star from direct view. By comparison with numerical radiative transfer disk models, we estimate the disk midplane to be inclined i = 65 +- 5 degrees relative to the plane of the sky. Since the star is seen only in scattered light at near-infrared wavelengths, we detect only a small fraction of its intrinsic flux. Because previous estimates of its stellar properties did not account for this, either LkHa 233 must be located closer than the previously believed, or its true luminosity must be greater than previously supposed, consistent with its being a ~4 M_sun star near the stellar birthline.Comment: Accepted for publication in the Ap