Related papers: Nonparametric Bayesian intensity estimation for co…
Cascades of Poisson processes are probabilistic models for spatio-temporal phenomena in which (i) previous events may trigger subsequent events, and (ii) both the background and triggering processes are conditionally Poisson. Such phenomena…
The Power Law Process, also known as Non-Homogeneous Poisson Process, has been used in various aspects, one of which is the software reliability assessment. Specifically, by using its intensity function to compute the rate of change of a…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
We study adaptive sensing of Cox point processes, a widely used model from spatial statistics. We introduce three tasks: maximization of captured events, search for the maximum of the intensity function and learning level sets of the…
We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…
We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…
In this paper, we consider statistical inference for Poisson-Laguerre tessellations in $\mathbb{R}^d$. The object of interest is a distribution function $F$ which uniquely determines the intensity measure of the underlying Poisson process.…
Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong.…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
In this paper, we harness a result in point process theory, specifically the expectation of the weighted $K$-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an…
This paper deals with feature selection procedures for spatial point processes intensity estimation. We consider regularized versions of estimating equations based on Campbell theorem derived from two classical functions: Poisson likelihood…
We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying…
Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis,…
Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…
We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…
The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…
The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…
We present a novel approach for the analysis of multivariate case-control georeferenced data using Bayesian inference in the context of disease mapping, where the spatial distribution of different types of cancers is analyzed. Extending…