Related papers: A Poisson likelihood approach to fake lepton estim…
Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…
Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a…
These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a…
Generating multivariate Poisson data is essential in many applications. Current simulation methods suffer from limitations ranging from computational complexity to restrictions on the structure of the correlation matrix. We propose a…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
This paper describes performance bounds for compressed sensing in the presence of Poisson noise when the underlying signal, a vector of Poisson intensities, is sparse or compressible (admits a sparse approximation). The signal-independent…
We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a…
Standard present day large-scale structure (LSS) analyses make a major assumption in their Bayesian parameter inference --- that the likelihood has a Gaussian form. For summary statistics currently used in LSS, this assumption, even if the…
This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point patterns. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the…
Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…
We investigate the use of the Multiple Optimised Parameter Estimation and Data compression algorithm (MOPED) for data compression and faster evaluation of likelihood functions. Since MOPED only guarantees maintaining the Fisher matrix of…
Multivariate count data are commonly encountered through high-throughput sequencing technologies in bioinformatics, text mining, or in sports analytics. Although the Poisson distribution seems a natural fit to these count data, its…
In this note we present studies of coverage and power for confidence intervals for a Poisson process with known background calculated using the Likelihood ratio (aka Feldman & Cousins) ordering with Bayesian treatment of uncertainties in…
This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…
Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that…
Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling…
In applications such as gene regulatory network analysis based on single-cell RNA sequencing data, samples often come from a mixture of different populations and each population has its own unique network. Available graphical models often…
The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. However, real data may present substantial departure from the underlying Poisson process. One of the possible departures has to…