Related papers: Ratio of counts vs ratio of rates in Poisson proce…

Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…

The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions…

Proportional rate models are among the most popular methods for analyzing the rate function of counting processes. Although providing a straightforward rate-ratio interpretation of covariate effects, the proportional rate assumption implies…

When a planner must decide whether it has enough evidence to make a decision based on probability, it faces the sample size problem. Current planners using probabilities need not deal with this problem because they do not generate their…

Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of…

A group of approaches for calculating forensic likelihood ratios first calculates scores which quantify the degree of difference or the degree of similarity between pairs of samples, then converts those scores to likelihood ratios. In order…

Some large scale inference problems are considered based on using the relative belief ratio as a measure of statistical evidence. This approach is applied to the multiple testing problem. A particular application of this is concerned with…

Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…

In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is…

It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…

The Risk Ratio (RR) is the ratio of the outcome among the exposed to risk of the outcome among the unexposed. This is a simple concept, which makes one wonder why it has not gained the same popularity as the odds ratio. Using logistic…

Poisson-like behavior for event count data is ubiquitous in nature. At the same time, differencing of such counts arises in the course of data processing in a variety of areas of application. As a result, the Skellam distribution -- defined…

The experimental problem of converting a measured binomial quantity, the fraction of events in a sample that pass a cut, into a physical binomial quantity, the fraction of events originating from a signal source, is described as a system of…

An important aspect of Bayesian model selection is how to deal with huge model spaces, since exhaustive enumeration of all the models entertained is unfeasible and inferences have to be based on the very small proportion of models visited.…

Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…

We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…

In multivariate statistics, the question of finding direct interactions can be formulated as a problem of network inference - or network reconstruction - for which the Gaussian graphical model (GGM) provides a canonical framework.…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…