English
Related papers

Related papers: Bayesian density regression for count data

200 papers

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…

Methodology · Statistics 2021-06-22 Jingyu He , Nicholas Polson , Jianeng Xu

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

Statistics Theory · Mathematics 2011-08-16 Suprateek Kundu , David B. Dunson

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

We propose a new family of error distributions for model-based quantile regression, which is constructed through a structured mixture of normal distributions. The construction enables fixing specific percentiles of the distribution while,…

Methodology · Statistics 2017-02-10 Yifei Yan , Athanasios Kottas

Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…

Methodology · Statistics 2024-07-02 Qingyang Liu , Xianzheng Huang , Rai Bai

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

Statistics Theory · Mathematics 2012-11-26 Stefano Favaro , Antonio Lijoi , Igor Prünster

Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis,…

Machine Learning · Computer Science 2023-09-15 Haleh Akrami , Omar Zamzam , Anand Joshi , Sergul Aydore , Richard Leahy

Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and…

Methodology · Statistics 2023-11-27 Zihang Lu , Noirrit Kiran Chandra

The Dirichlet Process Mixture Model (DPMM) is a Bayesian non-parametric approach widely used for density estimation and clustering. In this manuscript, we study the choice of prior for the variance or precision matrix when Gaussian kernels…

Methodology · Statistics 2022-02-09 Wei Jing , Michail Papathomas , Silvia Liverani

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…

Data Analysis, Statistics and Probability · Physics 2017-02-21 Diego Sevilla

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

Computation · Statistics 2010-05-04 M. G. B. Blum , O. Francois

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…

Econometrics · Economics 2021-12-08 Koen Jochmans , Martin Weidner

In vitro cell biology experiments are routinely used to characterize cell migration properties under various experimental conditions. These experiments can be interpreted using lattice-based random walk models to provide insight into…

Applied Physics · Physics 2024-06-25 Yihan Liu , David J Warne , Matthew J Simpson

This paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions, also known as the quantile crossing problem. The method consists in sorting or monotone…

Methodology · Statistics 2017-10-04 Victor Chernozhukov , Ivan Fernandez-Val , Alfred Galichon

Bayesian geoacoustic inversion problems are conventionally solved by Markov chain Monte Carlo methods or its variants, which are computationally expensive. This paper extends the classic Bayesian geoacoustic inversion framework by deriving…

Machine Learning · Statistics 2024-07-09 Guoli Wu , Jingya Zhang , Junqiang Song

A quantile is defined as a value below which random draws from a given distribution falls with a given probability. In a centralized setting where the cumulative distribution function (CDF) is unknown, the empirical CDF (ECDF) can be used…

Systems and Control · Computer Science 2018-05-02 Jongmin Lee , Cihan Tepedelenlioglu , Andreas Spanias

The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…

Methodology · Statistics 2013-10-02 Ernesto Barrios , Antonio Lijoi , Luis E. Nieto-Barajas , Igor Prünster

Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used…

Machine Learning · Statistics 2020-07-17 Avinava Dubey , Michael Minyi Zhang , Eric P. Xing , Sinead A. Williamson

The problem of overdispersion in multivariate count data is a challenging issue. Nowadays, it covers a central role mainly due to the relevance of modern technologies data, such as Next Generation Sequencing and textual data from the web or…

Methodology · Statistics 2025-02-24 Noemi Corsini , Cinzia Viroli

As a competitive alternative to least squares regression, quantile regression is popular in analyzing heterogenous data. For quantile regression model specified for one single quantile level $\tau$, major difficulties of semiparametric…

Methodology · Statistics 2017-05-29 Kani Chen , Yuanyuan Lin , Zhanfeng Wang , Zhiliang Ying