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Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…

Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…

We consider nonparametric Bayesian estimation and prediction for nonhomogeneous Poisson process models with unknown intensity functions. We propose a class of improper priors for intensity functions. Nonparametric Bayesian inference with…

We explore the construction of nonsubjective prior distributions in Bayesian statistics via a posterior predictive relative entropy regret criterion. We carry out a minimax analysis based on a derived asymptotic predictive loss function and…

In this paper several related estimation problems are addressed from a Bayesian point of view and optimal estimators are obtained for each of them when some natural loss functions are considered. Namely, we are interested in estimating a…

We consider Bayesian optimization in settings where observations can be adversarially biased, for example by an uncontrolled hidden confounder. Our first contribution is a reduction of the confounded setting to the dueling bandit model.…

In highly nonlinear systems such as the ones commonly found in astrodynamics, Gaussian distributions generally evolve into non-Gaussian distributions. This paper introduces a method for effectively controlling non-Gaussian distributions in…

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

This paper resolves a pivotal open problem on nonparametric inference for nonlinear functionals of volatility matrix. Multiple prominent statistical tasks can be formulated as functionals of volatility matrix, yet a unified statistical…

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…

We propose nonparametric identification and semiparametric estimation of joint potential outcome distributions in the presence of confounding. First, in settings with observed confounding, we derive tighter, covariate-informed bounds on the…

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…

In this paper we develop a nonparametric maximum likelihood estimate of the mixing distribution of the parameters of a linear stochastic dynamical system. This includes, for example, pharmacokinetic population models with process and…

Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability…

In this paper we consider the current status continuous mark model where, if the event takes place before an inspection time $T$ a "continuous mark" variable is observed as well. A Bayesian nonparametric method is introduced for estimating…

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…

Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models.…

In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…

Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…