arXiv subjects

Brunero Liseo

Publications and source records attributed to Brunero Liseo.

21 records · Page 2Linked to original sources

arXiv2012

Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(λ)$ can be written as $f(λ)=|λ|^{-2d}g(|λ|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is continuous and positive. We propose a novel Bayesian nonparametric approach for the estimation of the spectral density of such processes. We prove posterior consistency for both $d$ and $g$, under appropriate conditions on the prior distribution. We establish the rate of convergence for a general class of priors and apply our results to the family of fractionally exponential priors. Our approach is based on the true likelihood and does not resort to Whittle's approximation.

stat.ME↗

arXiv2011

A hierarchical Bayesian approach to record linkage and population size problems

We propose and illustrate a hierarchical Bayesian approach for matching statistical records observed on different occasions. We show how this model can be profitably adopted both in record linkage problems and in capture--recapture setups, where the size of a finite population is the real object of interest. There are at least two important differences between the proposed model-based approach and the current practice in record linkage. First, the statistical model is built up on the actually observed categorical variables and no reduction (to 0--1 comparisons) of the available information takes place. Second, the hierarchical structure of the model allows a two-way propagation of the uncertainty between the parameter estimation step and the matching procedure so that no plug-in estimates are used and the correct uncertainty is accounted for both in estimating the population size and in performing the record linkage. We illustrate and motivate our proposal through a real data example and simulations.

stat.AP↗

arXiv2007

Bayesian nonparametric estimation of the spectral density of a long memory Gaussian time series

Let $\mathbf {X}=\{X_t, t=1,2,... \}$ be a stationary Gaussian random process, with mean $EX_t=μ$ and covariance function $γ(τ)=E(X_t-μ)(X_{t+τ}-μ)$. Let $f(λ)$ be the corresponding spectral density; a stationary Gaussian process is said to be long-range dependent, if the spectral density $f(λ)$ can be written as the product of a slowly varying function $\tilde{f}(λ)$ and the quantity $λ^{-2d}$. In this paper we propose a novel Bayesian nonparametric approach to the estimation of the spectral density of $\mathbf {X}$. We prove that, under some specific assumptions on the prior distribution, our approach assures posterior consistency both when $f(\cdot)$ and $d$ are the objects of interest. The rate of convergence of the posterior sequence depends in a significant way on the structure of the prior; we provide some general results and also consider the fractionally exponential (FEXP) family of priors (see below). Since it has not a well founded justification in the long memory set-up, we avoid using the Whittle approximation to the likelihood function and prefer to use the true Gaussian likelihood.

math.ST↗