Related papers: Sufficient digits and density estimation: A Bayesi…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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,…
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…
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?…
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…
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…
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…
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…