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

Coal desulfurization by aqueous chlorination

A method of desulfurizing coal is described in which chlorine gas is bubbled through an aqueous slurry of coal at low temperature below 130 degrees C., and at ambient pressure. Chlorinolysis converts both inorganic and organic sulfur components of coal into water soluble compounds which enter the aqueous suspending media. The media is separated after chlorinolysis and the coal dechlorinated at a temperature of from 300 C to 500 C to form a non-caking, low-sulfur coal product

Changing Labor Market Opportunities for Women and the Quality of Teachers 1957-1992

School officials and policy makers have grown increasingly concerned about their ability to attract and retain talented teachers. A number of authors have shown that in recent years the brightest students at least those with the highest verbal and math scores on standardized tests are less likely to enter teaching. In addition, it is frequently claimed that the ability of schools to attract these top students has been steadily declining for years. There is, however, surprisingly little evidence measuring the extent to which this popular proposition is true. We have good reason to suspect that the quality of those entering teaching has fallen over time. Teaching has remained a predominately female profession for years; at the same time, the employment opportunities for talented women outside of teaching have soared. In this paper, we combine data from four longitudinal surveys of high school graduates spanning the years 1957-1992 to examine how the propensity for talented women to enter teaching has changed over time. We find that while the quality of the average new female teacher has fallen only slightly over this period, the likelihood that a female from the top of her high school class will eventually enter teaching has fallen dramatically from 1964 to 1992 by our estimation, from almost 20% to under 4%.

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

Dementia management: an occupational therapy home-based intervention for caregivers.

This paper describes an occupational therapy intervention designed for family caregivers of persons with dementia. The intervention, based on the framework of a competence-environmental press model and the principle of collaboration, was implemented during 5 home visits. Each visit was designed to build caregiving skills through collaboration in identifying problem areas, developing and implementing environmental strategies, and modifying management approaches. A case vignette illustrates the therapeutic process and outcomes. The theoretical rationale and structure of the intervention and innovative documentation for evaluation of the theoretic process are also presented

Income Inequality, the Median Voter, and the Support for Public Education

Using a panel of U.S. school districts spanning 1970 – 2000, we examine the relationship between income inequality and fiscal support for public education. In contrast with recent theoretical and empirical work suggesting a negative relationship between inequality and public spending, we find results consistent with a median voter model, in which inequality that reduces the median voter’s tax share induces higher local spending on public education. We estimate that 12 to 22 percent of the increase in local school spending over this period is attributable to rising inequality.

Waiting in the Wings: Reflected X-ray Emission from the Homunculus Nebula

We report the first detection of X-ray emission associated with the Homunculus Nebula which surrounds the supermassive star Eta Carinae. The emission is characterized by a temperature in excess of 100 MK, and is consistent with scattering of the time-delayed X-ray flux associated with the star. The nebular emission is bright in the northwestern lobe and near the central regions of the Homunculus, and fainter in the southeastern lobe. We also report the detection of an unusually broad Fe K fluorescent line, which may indicate fluorescent scattering off the wind of a companion star or some other high velocity outflow. The X-ray Homunculus is the nearest member of the small class of Galactic X-ray reflection nebulae, and the only one in which both the emitting and reflecting sources are distinguishable.Comment: 17 pages, 5 figures, accepted by Ap

A Model for the Strings of Eta Carinae

We propose a model based on ionization shadows to explain the formation of the long and narrow strings of Eta Carinae. Five strings are known, all located along the symmetry axis outside the Homunculus. The model assumes that each string is formed in a shadow behind a dense clump near the symmetry axis. The surrounding gas is ionized first, becomes much hotter, and compresses the gas in the shadow. This leads to the formation of a radial, dense, long, and narrow region, i.e., a string. Later the neutral material in the strings is ionized, and becomes brighter. Still later it re-expands, and we predict that in about 200 years the strings will fade. The condition for the model to work is that the ionization front, due to the diffuse ionizing recombination radiation of the surrounding gas, proceeds into the shadow at a velocity slower than the compression speed. From that we get a condition on the mass loss rate of the mass loss episode that formed the strings, which should be less than 10^{-4} Mo/year. The model can also explain the strings in the planetary nebula NGC 6543.Comment: 8 pages; Submitted to A&

A numerical renormalisation group method for the analysis of critical spreading activity in spiking neural networks

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