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We present a new modeling technique for solving the problem of ecological inference, in which individual-level associations are inferred from labeled data available only at the aggregate level. We model aggregate count data as arising from…
This paper deals with the study of dependencies between two given events modeled by point processes. In particular, we focus on the context of DNA to detect favored or avoided distances between two given motifs along a genome suggesting…
Consider two forms of sampling from a population: (i) drawing $s$ samples of $n$ elements with replacement and (ii) drawing a single sample of $ns$ elements. In this paper, under the setting where the descending order population frequency…
1. Species distribution models (SDM) are tools used to determine environmental features that influence the geographic distribution of species' abundance and have been used to analyze presence-only records. Analysis of presence-only records…
Mixture models are a standard tool in statistical analyses, widely used for density modeling and model-based clustering. In this work, we propose a Bayesian mixture model with repulsion between mixture components. Such repulsion helps…
This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical…
In this paper, we discuss the construction of a multivariate generalisation of the Dirichlet-multinomial distribution. An example from forensic genetics in the statistical analysis of DNA mixtures motivates the study of this multivariate…
We build a general framework which establishes a one-to-one correspondence between species abundance distribution (SAD) and species accumulation curve (SAC). The appearance rates of the species and the appearance times of individuals of…
Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new…
Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
We use a functional analogue of the quantile function for probability measures on $\mathbb{R}^d$ to characterize a novel limit Poisson point process for radially recentred and rescaled random vectors under a radial-directional…
Generative modeling of non-negative, discrete data, such as symbolic music, remains challenging due to two persistent limitations in existing methods. Firstly, many approaches rely on modeling continuous embeddings, which is suboptimal for…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
In this paper, a Bayesian semiparametric copula approach is used to model the underlying multivariate distribution $F_{true}$. First, the Dirichlet process is constructed on the unknown marginal distributions of $F_{true}$. Then a Gaussian…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…
The "rare type match problem" is the situation in which the suspect's DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. The evaluation of this match in the light of the two competing hypotheses…
This paper is concerned with the study of the random variable $K_n$ denoting the number of distinct elements in a random sample $(X_1, \dots, X_n)$ of exchangeable random variables driven by the two parameter Poisson-Dirichlet distribution,…
We investigate a model of random spatial permutations on two-dimensional tori, and establish that the joint distribution of large cycles is asymptotically given by the Poisson--Dirichlet distribution with parameter one. The asymmetry of the…