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We present a new inference method based on approximate Bayesian computation for estimating parameters governing an entire network based on link-traced samples of that network. To do this, we first take summary statistics from an observed…

Computation · Statistics 2017-01-17 Jack Davis , Steven K. Thompson

Wildlife monitoring for open populations can be performed using a number of different survey methods. Each survey method gives rise to a type of data and, in the last five decades, a large number of associated statistical models have been…

We propose a novel Dirichlet-based P\'olya tree (D-P tree) prior on the copula and based on the D-P tree prior, a nonparametric Bayesian inference procedure. Through theoretical analysis and simulations, we are able to show that the…

Methodology · Statistics 2017-02-24 Shaoyang Ning , Neil Shephard

This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…

Statistics Theory · Mathematics 2024-02-22 Ricardo Blum , Munir Hiabu , Enno Mammen , Joseph T. Meyer

Motivated by investigating spatio-temporal patterns of the distribution of continuous variables, we consider describing the conditional distribution function of the response variable incorporating spatio-temporal components given…

We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…

Statistics Theory · Mathematics 2020-07-22 Shota Gugushvili , Frank van der Meulen , Moritz Schauer , Peter Spreij

Benford's law describes a common phenomenon among many naturally occurring data sets and distributions in which the leading digits of the data are distributed with the probability of a first digit of $d$ base $B$ being…

Probability · Mathematics 2019-10-30 Rebecca F. Durst , Steven J. Miller

In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be…

Machine Learning · Computer Science 2023-06-13 Yuta Nakahara , Shota Saito , Naoki Ichijo , Koki Kazama , Toshiyasu Matsushima

A general setting for nested subdivisions of a bounded real set into intervals defining the digits $X_1,X_2,...$ of a random variable $X$ with a probability density function $f$ is considered. Under the weak condition that $f$ is almost…

Probability · Mathematics 2026-01-14 Jesper Møller

Due to their accuracies, methods based on ensembles of regression trees are a popular approach for making predictions. Some common examples include Bayesian additive regression trees, boosting and random forests. This paper focuses on…

Methodology · Statistics 2019-11-15 Suofei Wu , Jan Hannig , Thomas C. M. Lee

The Dirichlet-multinomial (DM) distribution plays a fundamental role in modern statistical methodology development and application. Recently, the DM distribution and its variants have been used extensively to model multivariate count data…

Methodology · Statistics 2023-02-27 Matthew D. Koslovsky

Random Forest (Breiman, 2001) is a successful and widely used regression and classification algorithm. Part of its appeal and reason for its versatility is its (implicit) construction of a kernel-type weighting function on training data,…

Machine Learning · Statistics 2022-10-13 Domagoj Ćevid , Loris Michel , Jeffrey Näf , Nicolai Meinshausen , Peter Bühlmann

We introduce a comprehensive Bayesian multivariate predictive inference framework. The basis for our framework is a hierarchical Bayesian model, that is a mixture of finite Polya trees corresponding to multiple dyadic partitions of the unit…

Methodology · Statistics 2024-11-27 Daniel Yekutieli

Dynamic linear models with Gaussian observations and Gaussian states lead to closed-form formulas for posterior simulation. However, these closed-form formulas break down when the response or state evolution ceases to be Gaussian. Dynamic,…

Computation · Statistics 2013-09-20 Jesse Windle , Carlos M. Carvalho , James G. Scott , Liang Sun

We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to…

Machine Learning · Statistics 2010-10-21 Han Liu , Min Xu , Haijie Gu , Anupam Gupta , John Lafferty , Larry Wasserman

This article is motivated by the following satisfiability question: pick uniformly at random an and/or Boolean expression of length n, built on a set of k_n Boolean variables. What is the probability that this expression is satisfiable?…

Combinatorics · Mathematics 2015-07-31 Antoine Genitrini , Cécile Mailler

Probabilistic models of data sets often exhibit salient geometric structure. Such a phenomenon is summed up in the manifold distribution hypothesis, and can be exploited in probabilistic learning. Here we present normal-bundle bootstrap…

Machine Learning · Statistics 2020-07-29 Ruda Zhang , Roger Ghanem

Let $\left(\Omega,\Sigma,p\right)$ be a probability measure space and let $X:\Omega\to{\mathbb{R}}^k$ be a (vector valued) random variable. We suppose that the probability $p_X$ induced by $X$ is absolutely continuous with respect to the…

Probability · Mathematics 2021-12-06 Luigi Negro

Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density $f_0$ of its jump sizes, as well as of its intensity $\lambda_0.$ We take a Bayesian approach to the problem and…

Statistics Theory · Mathematics 2023-02-27 Shota Gugushvili , Frank van der Meulen , Peter Spreij

We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian…

Computation · Statistics 2023-06-26 Jarkko Suuronen , Tomás Soto , Neil K. Chada , Lassi Roininen