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Dirichlet process mixture models (DPMM) play a central role in Bayesian nonparametrics, with applications throughout statistics and machine learning. DPMMs are generally used in clustering problems where the number of clusters is not known…
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to a discrete TASEP model with step initial condition. In this paper, we obtain a finite time…
A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
This article provides a mathematically rigorous introduction to denoising diffusion probabilistic models (DDPMs), sometimes also referred to as diffusion probabilistic models or diffusion models, for generative artificial intelligence. We…
We study the angular distributions of the splitting functions for processes for which a parton splits into three partons. Unlike the case of coherent branching, we find that both in vacuum and in the presence of the dense QCD matter, such…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
Determinantal point processes (DPPs) are popular probabilistic models of diversity. In this paper, we investigate DPPs from a new perspective: property testing of distributions. Given sample access to an unknown distribution $q$ over the…
A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
We propose the CliPS procedure when fitting Bayesian mixture models in the context of model-based clustering to identify the cluster distributions while simultaneously assessing the suitability of a cluster solution and validating the…
We consider the Voronoi tessellation based on a homogeneous Poisson point process in $\mathbf{R}^{d}$. For a geometric characteristic of the cells (e.g. the inradius, the circumradius, the volume), we investigate the point process of the…
In this note, we construct a $3$-dimensional generalisation of the Pascal's triangle that we named Pascal's cube, as it has the construction of a cube with entries given by extended binomial coefficients ${}^cC^{a}_{b}$. The Pascal's cube…
Propagation of ultrashort optical pulses in a dense resonant medium is considered in the semiclassical limit. In our analysis, we place emphasis on several main points. First, we study transformations of spectra in the process of pulse…
Evidence of excess filamentarity is considered for two spatial point process applications: local minima in whole earth precipitation modelling and locations of cold clumps in the Milky Way. A diagnostic test using the number of aligned…
In modern telecommunications, spatial burstiness of data traffic poses challenges to traditional Poisson-based models. This paper describes application of thinning-stable point processes, which provide a more appropriate framework for…
A number of numeric approaches to simulate Poisson point processes with arbitrary event rates are presented and implemented for R. They include the simulation of the number of points and their location as well as the determination of…
We analyze the statistical properties of bubble models for the large-scale distribution of galaxies. To this aim, we realize static simulations, in which galaxies are mostly randomly arranged in the regions surrounding bubbles. As a first…