Computation of Gaussian orthant probabilities in high dimension

We study the computation of Gaussian orthant probabilities, i.e. the probability that a Gaussian falls inside a quadrant. The Geweke-Hajivassiliou-Keane (GHK) algorithm [Genz, 1992; Geweke, 1991; Hajivassiliou et al., 1996; Keane, 1993], is currently used for integrals of dimension greater than 10. In this paper we show that for Markovian covariances GHK can be interpreted as the estimator of the normalizing constant of a state space model using sequential importance sampling (SIS). We show for an AR(1) the variance of the GHK, properly normalized, diverges exponentially fast with the dimension. As an improvement we propose using a particle filter (PF). We then generalize this idea to arbitrary covariance matrices using Sequential Monte Carlo (SMC) with properly tailored MCMC moves. We show empirically that this can lead to drastic improvements on currently used algorithms. We also extend the framework to orthants of mixture of Gaussians (Student, Cauchy etc.), and to the simulation of truncated Gaussians

An investigation of some theological interpretations of Pentecost, with special reference to Spirit-Baptism

https://place.asburyseminary.edu/ecommonsatsdissertations/2049/thumbnail.jp

Toward a Less Adversarial Relationship Between \u3cem\u3eChevron\u3c/em\u3e and \u3cem\u3eGardner\u3c/em\u3e

Veterans benefits are a creature of statute. As such, nearly every veterans benefits issue presented to the courts for resolution involves the interpretation of a statute, regulation, or sub-regulatory authority. Although veterans law has been subject to judicial review for over twenty-five years, the courts still have yet to develop a coherent doctrine regarding when to resolve ambiguity in favor of the veteran versus when to defer to the interpretations of the Department of Veterans Affairs. This Article explores three possible approaches to developing a coherent vision of how veteran friendliness and agency deference can coexist and provide more predictability in how to interpret veterans benefits laws

Hidden Markov models for time series of counts with excess zeros

International audienceInteger-valued time series are often modeled with Markov models or hidden Markov models (HMM). However, when the series represents count data it is often subject to excess zeros. In this case, usual distributions such as binomial or Poisson are unable to estimate the zero mass correctly. In order to overcome this issue, we introduce zero-inflated distributions in the hidden Markov model. The empirical results on simulated and real data show good convergence properties, while excess zeros are better estimated than with classical HMM