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Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the L\'evy density of a L\'evy process belonging to a flexible class of infinite activity subordinators. Posterior…
In this paper, we propose a novel Bayesian approach for nonparametric estimation in Wicksell's problem. This has important applications in astronomy for estimating the distribution of the positions of the stars in a galaxy given projected…
The purpose of this study is to provide a new methodology of how one can consistently estimate a change-point in time series data. In contrast with previous studies, the suggested methodology employs only the empirical spectral density and…
The main goal of this paper is to study the parameter estimation problem, using the Bayesian methodology, for the drift coefficient of some linear (parabolic) SPDEs driven by a multiplicative noise of special structure. We take the spectral…
We study the problem of estimating the intensity function of a covariate-driven point process based on observations of the points and covariates over a large window. We consider the nonparametric Bayesian approach, and show that a wide…
In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In…
Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…
Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…
Existing frequency domain methods for bootstrapping time series have a limited range. Consider for instance the class of spectral mean statistics (also called integrated periodograms) which includes many important statistics in time series…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional…
Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…
Spatial Gaussian process regression models typically contain finite dimensional covariance parameters that need to be estimated from the data. We study the Bayesian estimation of covariance parameters including the nugget parameter in a…
We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…
State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in…
Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a…
Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely…
Local volatility is an important quantity in option pricing, portfolio hedging, and risk management. It is not directly observable from the market; hence calibrations of local volatility models are necessary using observable market data.…