Related papers: The multivariate Dirichlet-multinomial distributio…
Many Mendelian randomization (MR) papers have been conducted only in people of European ancestry, limiting transportability of results to the global population. Expanding MR to diverse ancestry groups is essential to ensure equitable…
Mixed-effects models are among the most commonly used statistical methods for the exploration of multispecies data. In recent years, also Joint Species Distribution Models and Generalized Linear Latent Variale Models have gained in…
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…
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…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
Identifying disease-associated changes in DNA methylation can help to gain a better understanding of disease etiology. Bisulfite sequencing technology allows the generation of methylation profiles at single base of DNA. We previously…
Latent Dirichlet allocation (LDA) obtains essential information from data by using Bayesian inference. It is applied to knowledge discovery via dimension reducing and clustering in many fields. However, its generalization error had not been…
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…
Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over…
RNA-Seq data characteristically exhibits large variances, which need to be appropriately accounted for in the model. We first explore the effects of this variability on the maximum likelihood estimator (MLE) of the overdispersion parameter…
Given a collection of categorical data, we want to find the parameters of a Dirichlet distribution which maximizes the likelihood of that data. Newton's method is typically used for this purpose but current implementations require reading…
Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…
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…
Covariate-adaptive randomization is widely employed to balance baseline covariates in interventional studies such as clinical trials and experiments in development economics. Recent years have witnessed substantial progress in inference…
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
The univariate distorted distribution were introduced in risk theory to represent changes (distortions) in the expected distributions of some risks. Later they were also applied to represent distributions of order statistics, coherent…
Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these…
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient…