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Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

This paper proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis of high-dimensional Gaussian datasets with fewer observations than number of variables. An implicitly restarted…

Precision matrix estimation in a multivariate Gaussian model is fundamental to network estimation. Although there exist both Bayesian and frequentist approaches to this, it is difficult to obtain good Bayesian and frequentist properties…

We consider estimation in a particular semiparametric regression model for the mean of a counting process with ``panel count'' data. The basic model assumption is that the conditional mean function of the counting process is of the form…

We develop a pseudo-likelihood theory for rank one matrix estimation problems in the high dimensional limit. We prove a variational principle for the limiting pseudo-maximum likelihood which also characterizes the performance of the…

Synthetic likelihood is an attractive approach to likelihood-free inference when an approximately Gaussian summary statistic for the data, informative for inference about the parameters, is available. The synthetic likelihood method derives…

The Poisson compound decision problem is a long-standing problem in statistics, where empirical Bayes methodologies are commonly used to estimate Poisson's means in static or batch domains. In this paper, we study the Poisson compound…

Variable selection methods are required in practical statistical modeling, to identify and include only the most relevant predictors, and then improving model interpretability. Such variable selection methods are typically employed in…

Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…

This paper studies plug-and-play (PnP) Langevin sampling strategies for Bayesian inference in low-photon Poisson imaging problems, a challenging class of problems with significant applications in astronomy, medicine, and biology. PnP…

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…

A Neyman-Scott process is a special case of a Cox process. The latent and observable stochastic processes are both Poisson processes. We consider a deep Neyman-Scott process in this paper, for which the building components of a network are…

Modeling count data is important in physics and other scientific disciplines, where measurements often involve discrete, non-negative quantities such as photon or neutrino detection events. Traditional parametric approaches can be trained…

We construct uncertainty intervals for weak Poisson signals in the presence of background. We consider the case where a primary experiment yields a realization of the signal plus background, and a second experiment yields a realization of…

Species distribution modeling (SDM) plays a crucial role in investigating habitat suitability and addressing various ecological issues. While likelihood analysis is commonly used to draw ecological conclusions, it has been observed that its…

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…

High dimensional Poisson regression has become a standard framework for the analysis of massive counts datasets. In this work we estimate the intensity function of the Poisson regression model by using a dictionary approach, which…

We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains…

Presence-only data, point locations where a species has been recorded as being present, are often used in modeling the distribution of a species as a function of a set of explanatory variables---whether to map species occurrence, to…

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…