Related papers: Multinomial, Poisson and Gaussian statistics in co…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
I describe a Bayesian method to account for measurement errors in linear regression of astronomical data. The method allows for heteroscedastic and possibly correlated measurement errors, and intrinsic scatter in the regression…
This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study the multivariate Poisson approximation of the distribution…
By exploiting the well-known observation that size-biasing or zero-biasing an infinitely divisible random variable may be achieved by adding an independent increment, combined with tools from Stein's method for compound Poisson and Gaussian…
One of the fundamental problems in Bayesian statistics is the approximation of the posterior distribution. Gibbs sampler and coordinate ascent variational inference are renownedly utilized approximation techniques that rely on stochastic…
Converting neutron scattering data to real-space time-dependent structures can only be achieved through suitable models, which is particularly challenging for geometrically disordered structures. We address this problem by introducing…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
Applying the standard weighted mean formula, [sum_i {n_i sigma^{-2}_i}] / [sum_i {sigma^{-2}_i}], to determine the weighted mean of data, n_i, drawn from a Poisson distribution, will, on average, underestimate the true mean by ~1 for all…
The objective Bayesian treatment of a model representing two independent Poisson processes, labelled as "signal" and "background" and both contributing additively to the total number of counted events, is considered. It is shown that the…
Large-scale datasets with count outcome variables are widely present in various applications, and the Poisson regression model is among the most popular models for handling count outcomes. This paper considers the high-dimensional sparse…
Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural…
In a variety of application areas, there is a growing interest in analyzing high dimensional sparse count data, with sparsity exhibited by an over-abundance of zeros and small non-zero counts. Existing approaches for analyzing multivariate…
Bayesian hierarchical models are commonly employed for inference in count datasets, as they account for multiple levels of variation by incorporating prior distributions for parameters at different levels. Examples include Beta-Binomial,…
The C statistics, also known as the Cash statistic, is often used in astronomy for the analysis of low-count Poisson data. One of the challenges of the C statistic is that its probability distribution, under the null hypothesis that the…
We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…