Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain

Extended Stromgren Photoelectric Photometry in NGC 752

Photoelectric photometry on the extended Stromgren system (uvbyCa) is presented for 7 giants and 21 main sequence stars in the old open cluster, NGC 752. Analysis of the hk data for the turnoff stars yields a new determination of the cluster mean metallicity. From 10 single-star members, [Fe/H] = -0.06 +/- 0.03, where the error quoted is the standard error of the mean and the Hyades abundance is set at [Fe/H] = +0.12. This result is unchanged if all 20 stars within the limits of the hk metallicity calibration are included. The derived [Fe/H] is in excellent agreement with past estimates using properly-zeroed m1 data, transformed moderate-dispersion spectroscopy, and recent high dispersion spectroscopy.Comment: 14 tex'd pages including 2 tables; 2 separate files with eps figures Accepted for PASP March 200

Mine Fire Detection in the Presence Of Diesel Emissions

A series of four coal combustion experiments was conducted at the National Institute for Occupational Safety and Health\u27s (NIOSH) Pittsburgh Research Laboratory (PRL) in the Safety Research Coal Mine (SRCM) to evaluate the response of fire sensors to a small 0.61 m square smoldering coal fire which transitions to flaming combustion in the presence of diesel emissions. An optical path smoke sensor alarmed earlier than a point type diffusion mode ionization smoke sensor, which alarmed prior to a co alert value of 5 PPM above ambient. The presence of steady state diesel emissions resulted in a decrease in the optical smoke sensor analog output voltage signal by less than 1.4 pet for the three coal fire experiments in which a diesel engine was operating, whereas the ionization smoke sensor output decreased between 10.8 and 26.7 pet after the initial surge of the diesel engine. A commercial diesel discriminating fire sensor did not alarm for a fire in the one experiment for which it was used. The results of the experiments demonstrated that an optical path smoke sensor might be used to detect a coal fire under the experimental conditions considered of starting a diesel engine followed by a slowly developing coal fire

Stellar Evolution in NGC 6791: Mass Loss on the Red Giant Branch and the Formation of Low Mass White Dwarfs

We present the first detailed study of the properties (temperatures, gravities, and masses) of the NGC 6791 white dwarf population. This unique stellar system is both one of the oldest (8 Gyr) and most metal-rich ([Fe/H] ~ 0.4) open clusters in our Galaxy, and has a color-magnitude diagram (CMD) that exhibits both a red giant clump and a much hotter extreme horizontal branch. Fitting the Balmer lines of the white dwarfs in the cluster, using Keck/LRIS spectra, suggests that most of these stars are undermassive, = 0.43 +/- 0.06 Msun, and therefore could not have formed from canonical stellar evolution involving the helium flash at the tip of the red giant branch. We show that at least 40% of NGC 6791's evolved stars must have lost enough mass on the red giant branch to avoid the flash, and therefore did not convert helium into carbon-oxygen in their core. Such increased mass loss in the evolution of the progenitors of these stars is consistent with the presence of the extreme horizontal branch in the CMD. This unique stellar evolutionary channel also naturally explains the recent finding of a very young age (2.4 Gyr) for NGC 6791 from white dwarf cooling theory; helium core white dwarfs in this cluster will cool ~3 times slower than carbon-oxygen core stars and therefore the corrected white dwarf cooling age is in fact ~7 Gyr, consistent with the well measured main-sequence turnoff age. These results provide direct empirical evidence that mass loss is much more efficient in high metallicity environments and therefore may be critical in interpreting the ultraviolet upturn in elliptical galaxies.Comment: 15 pages, 9 figures, 2 tables. Accepted for publication in Astrophys. J. Very minor changes from first versio

Abundance Gradients and the Formation of the Milky Way

In this paper we adopt a chemical evolution model, which is an improved version of the Chiappini, Matteucci and Gratton (1997) model, assuming two main accretion episodes for the formation of the Galaxy. The present model takes into account in more detail than previously the halo density distribution and explores the effects of a threshold density in the star formation process, during both the halo and disk phases. In the comparison between model predictions and available data, we have focused our attention on abundance gradients as well as gas, stellar and star formation rate distributions along the disk. We suggest that the mechanism for the formation of the halo leaves detectable imprints on the chemical properties of the outer regions of the disk, whereas the evolution of the halo and the inner disk are almost completely disentangled. This is due to the fact that the halo and disk densities are comparable at large Galactocentric distances and therefore the gas lost from the halo can substantially contribute to building up the outer disk. We also show that the existence of a threshold density for the star formation rate, both in the halo and disk phase, is necessary to reproduce the majority of observational data in the solar vicinity and in the whole disk. Moreover, we predict that the abundance gradients along the Galactic disk must have increased with time and that the average [alpha/Fe] ratio in stars (halo plus disk) slightly decrease going from 4 to 10 Kpcs from the Galactic center. We also show that the same ratios increase substantially towards the outermost disk regions and the expected scatter in the stellar ages decreases, because the outermost regions are dominated by halo stars.Comment: 41 pages (including the figures), To be published in Ap

Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.Comment: 26 pages, 2 figures, accepted in Journal of Computational and Graphical Statistics (http://www.amstat.org/publications/jcgs.cfm

Hubble Space Telescope Observations of Element Abundances in Low-redshift Damped Lyman-alpha Galaxies and Implications for the Global Metallicity-Redshift Relation

Most models of cosmic chemical evolution predict that the mass-weighted mean interstellar metallicity of galaxies should rise with time from a low value $\sim 1/30$ solar at $z \sim 3$ to a nearly solar value at $z = 0$. In the absence of any selection effects, the damped Lyman-alpha absorbers (DLAs) in quasar spectra are expected to show such a rise in global metallicity. However, it has been difficult to determine whether or not DLAs show this effect, primarily because of the very small number of DLA metallicity measurements at low redshifts. In an attempt to put tighter constraints on the low-redshift end of the DLA metallicity-redshift relation, we have observed Zn II and Cr II lines in four DLAs at $0.09 < z < 0.52$, using the Space Telescope Imaging Spectrograph (STIS) onboard the Hubble Space Telescope (HST). These observations have provided the first constraints on Zn abundances in DLAs with $z < 0.4$. In all the three DLAs for which our observations offer meaningful constraints on the metallicity, the data suggest that the metallicities are much lower than the solar value. These results are consistent with recent imaging studies indicating that these DLAs may be associated with dwarf or low surface brightness galaxies. We combine our results with higher redshift data from the literature to estimate the global mean metallicity-redshift relation for DLAs. We find that the global mean metallicity shows at most a slow increase with decreasing redshift. ...(Please see the paper for the complete abstract).Comment: 56 pages, including 13 figures. Accepted for publication in the Astrophysical Journa

Transport behavior of holes in boron delta-doped diamond structures

Boron delta-doped diamond structures have been synthesized using microwave plasma chemical vapor deposition and fabricated into FET and gated Hall bar devices for assessment of the electrical characteristics. A detailed study of variable temperature Hall, conductivity, and field-effect mobility measurements was completed. This was supported by Schr€dinger-Poisson and relaxation time o calculations based upon application of Fermi’s golden rule. A two carrier-type model was developed with an activation energy of $0.2 eV between the delta layer lowest subband with mobility$1 cm2/Vs and the bulk valence band with high mobility. This new understanding of the transport of holes in such boron delta-doped structures has shown that although Hall mobility as high as 900 cm2/Vs was measured at room temperature, this dramatically overstates the actual useful performance of the device