Statistics for Spatial Data.

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

http://www.thelancet.com/article/S0140673621027240/pdf

Global burden of bacterial antimicrobial resistance in 2019: a systematic analysis

Dirichlet process (DP) mixture models are the cornerstone of non- parametric Bayesian statistics, and the development of Monte-Carlo Markov chain (MCMC) sampling methods for DP mixtures has enabled the application of non- parametric Bayesian methods to a variety of practical data analysis problems. However, MCMC sampling can be prohibitively slow, and it is important to ex- plore alternatives. One class of alternatives is provided by variational methods, a class of deterministic algorithms that convert inference problems into optimization problems (Opper and Saad 2001; Wainwright and Jordan 2003). Thus far, varia- tional methods have mainly been explored in the parametric setting, in particular within the formalism of the exponential family (Attias 2000; Ghahramani and Beal 2001; Blei et al. 2003). In this paper, we present a variational inference algorithm for DP mixtures. We present experiments that compare the algorithm to Gibbs sampling algorithms for DP mixtures of Gaussians and present an application to a large-scale image analysis problem.

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Variational Inference for Dirichlet Process Mixtures

Survival Analysis: Techniques for Censored and Truncated Data (2nd ed.) (Book)

Customary modeling for continuous point-referenced data assumes a Gaussian process that is often taken to be stationary. When such models are fitted within a Bayesian framework, the unknown parameters of the process are assumed to be random, so a random Gaussian process results. Here we propose a novel spatial Dirichlet process mixture model to produce a random spatial process that is neither Gaussian nor stationary. We first develop a spatial Dirichlet process model for spatial data and discuss its properties. Because of familiar limitations associated with direct use of Dirichlet process models, we introduce mixing by convolving this process with a pure error process. We then examine properties of models created through such Dirichlet process mixing. In the Bayesian framework, we implement posterior inference using Gibbs sampling. Spatial prediction raises interesting questions, but these can be handled. Finally, we illustrate the approach using simulated data, as well as a dataset involving precipitati...

Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing

In recent years, the number of pulsars with secure mass measurements has increased to a level that allows us to probe the underlying neutron star mass distribution in detail. We critically review radio pulsar mass measurements and present a detailed examination through which we are able to put stringent constraints on the underlying neutron star mass distribution. For the first time, we are able to analyze a sizable population of neutron star-white dwarf systems in addition to double neutron star systems with a technique that accounts for systematically different measurement errors. We find that neutron stars that have evolved through different evolutionary paths reflect distinctive signatures through dissimilar distribution peak and mass cutoff values. Neutron stars in double neutron star and neutron star-white dwarf systems show consistent respective peaks at 1.35 Msun and 1.50 Msun which suggest significant mass accretion (Delta m~0.15 Msun) has occurred during the spin up phase. The width of the mass distribution implied by double neutron star systems is indicative of a tight initial mass function while the inferred mass range is significantly wider for neutron stars that have gone through recycling. We find a mass cutoff at 2 Msun for neutron stars with white dwarf companions which establishes a firm lower bound for the maximum neutron star mass. This rules out the majority of strange quark and soft equation of state models as viable configurations for neutron star matter. The lack of truncation close to the maximum mass cutoff suggests that the 2 Msun limit is set by evolutionary constraints rather than nuclear physics or general relativity, and the existence of rare super-massive neutron stars is possible.

The Neutron Star Mass Distribution

In recent years, the number of pulsars with secure mass measurements has increased to a level that allows us to probe the underlying neutron star (NS) mass distribution in detail. We critically review the radio pulsar mass measurements. For the first time, we are able to analyze a sizable population of NSs with a flexible modeling approach that can effectively accommodate a skewed underlying distribution and asymmetric measurement errors. We find that NSs that have evolved through different evolutionary paths reflect distinctive signatures through dissimilar distribution peak and mass cutoff values. NSs in double NS and NS-white dwarf (WD) systems show consistent respective peaks at 1.33 M and 1.55 M, suggesting significant mass accretion (Δm 0.22 M) has occurred during the spin-up phase. The width of the mass distribution implied by double NS systems is indicative of a tight initial mass function while the inferred mass range is significantly wider for NSs that have gone through recycling. We find a mass cutoff at 2.1 M for NSs with WD companions, which establishes a firm lower bound for the maximum NS mass. This rules out the majority of strange quark and soft equation of state models as viable configurations for NS matter. The lack of truncation close to the maximum mass cutoff along with the skewed nature of the inferred mass distribution both enforce the suggestion that the 2.1 M limit is set by evolutionary constraints rather than nuclear physics or general relativity, and the existence of rare supermassive NSs is possible. © 2013. The American Astronomical Society. All rights reserved..

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The neutron star mass distribution

Median regression models become an attractive alternative to mean regression models when employing flexible families of distributions for the errors. Classical approaches are typically algorithmic with desirable properties emerging asymptotically. However, nonparametric error models may be most attractive in the case of smaller sample sizes where parametric specifications are difficult to justify. Hence, a Bayesian approach, enabling exact inference given the observed data, may be appealing. In this context there is little Bayesian work. We develop two fully Bayesian modeling approaches, employing mixture models, for the errors in a median regression model. The associated families of error distributions allow for increased variability, skewness, and flexible tail behavior. The first family is semiparametric with extra variability captured nonparametrically through mixing and skewness handled parametrically. The second family, a fully nonparametric one, includes all unimodal densities on the real line with...

Bayesian Semiparametric Median Regression Modeling

Widely used parametric generalized linear models are, unfortunately, a somewhat limited class of specifications. Nonparametric aspects are often introduced to enrich this class, resulting in semiparametric models. Focusing on single or k-sample problems, many classical nonparametric approaches are limited to hypothesis testing. Those that allow estimation are limited to certain functionals of the underlying distributions. Moreover, the associated inference often relies upon asymptotics when nonparametric specifications are often most appealing for smaller sample sizes. Bayesian nonparametric approaches avoid asymptotics but have, to date, been limited in the range of inference. Working with Dirichlet process priors, we overcome the limitations of existing simulation-based model fitting approaches which yield inference that is confined to posterior moments of linear functionals of the population distribution. This article provides a computational approach to obtain the entire posterior distribution for mor...

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Athanasios Kottas

Papers

Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing

The Neutron Star Mass Distribution

The neutron star mass distribution

Bayesian Semiparametric Median Regression Modeling

A Computational Approach for Full Nonparametric Bayesian Inference Under Dirichlet Process Mixture Models