Related papers: Throwing Stones and Collecting Bones: Looking for …
The random measures on the space of continuous functions are considered. Stationary random measures are described. The weak solutions of the stochastic equations are substituted by the strong measure-valued solutions.
In counting experiments, one can set an upper limit on the rate of a Poisson process based on a count of the number of events observed due to the process. In some experiments, one makes several counts of the number of events, using…
Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal…
We consider free multiple stochastic measures in the combinatorial framework of the lattice of all diagonals of an n-dimensional space. In this free case, one can restrict the analysis to only the noncrossing diagonals. We give definitions…
The goal of subsampling is to select an informative subset of all observations, when using the full data for statistical analysis is not viable. We construct locally $ D $-optimal subsampling designs under a Poisson regression model with a…
We investigate different randomizations for mirror descent method. We try to propose such a randomization that allows us to use sparsity of the problem as much as it possible. In the paper one can also find a generalization of randomizaed…
A semi-measure is a generalization of a probability measure obtained by relaxing the additivity requirement to super-additivity. We introduce and study several randomness notions for left-c.e. semi-measures, a natural class of effectively…
In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on…
This paper deals with Poisson approximation to weighted sums of locally dependent random variables using Stein's method. The derived result represents a significant improvement of existing results. To illustrate the effectiveness of our…
Can you decide if there is a coincidence in the numbers counting two different combinatorial objects? For example, can you decide if two regions in $\mathbb{R}^3$ have the same number of domino tilings? There are two versions of the…
The analysis of single-cell RNA sequencing (scRNA-seq) data often involves fitting a latent variable model to learn a low-dimensional representation for the cells. Validating such a model poses a major challenge. If we could sequence the…
Poisson random effect models with a shared random effect have been widely used in actuarial science for analyzing the number of claims. In particular, the random effect is a key factor in a posteriori risk classification. However, the…
We present a mixture Poisson model for claims counts in which the number of components in the mixture are estimated by reversible jump MCMC methods.
A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are `Brownian local minima' and `unordered infinite sample'. They are identically distributed; the former ad hoc proof of this…
We introduce the problem of Poisson sampling over joins: compute a sample of the result of a join query by conceptually performing a Bernoulli trial for each join tuple, using a non-uniform and tuple-specific probability. We propose an…
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 demonstrate that two approximations to the chi^2 statistic as popularly employed by observational astronomers for fitting Poisson-distributed data can give rise to intrinsically biased model parameter estimates, even in the high counts…
Overdispersed count data are modelled with likelihood and non-likelihood approaches. Likelihood approaches include the Poisson mixtures with three distributions, the gamma, the lognormal, and the inverse Gaussian distributions.…
In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized P\'olya-Aeppli process. It is shown that these processes…
We propose two novel ways of introducing dependence among Poisson counts through the use of latent variables in a three levels hierarchical model. Marginal distributions of the random variables of interest are Poisson with strict…