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Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…

The state estimation problem for nonlinear systems with stochastic uncertainties can be formulated in the Bayesian framework, where the objective is to replace the state completely by its probability density function. Without the…

In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate…

Recently, machine learning-based channel estimation has attracted much attention. The performance of machine learning-based estimation has been validated by simulation experiments. However, little attention has been paid to the theoretical…

The expected information gain is an important quality criterion of Bayesian experimental designs, which measures how much the information entropy about uncertain quantity of interest $\theta$ is reduced on average by collecting relevant…

For many cancer sites low-dose risks are not known and must be extrapolated from those observed in groups exposed at much higher levels of dose. Measurement error can substantially alter the dose-response shape and hence the extrapolated…

Dramatic increases in the size and dimensionality of many recent data sets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation-maximization…

We consider the problem of estimating the missing mass, partition function or evidence and its probability distribution in the case that for each sample point in the discrete sample space its (unnormalized) probability mass is revealed.…

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…

Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…

We study asymptotic behaviors of Bayes type estimators and give sufficient conditions to obtain asymptotic limit distribution of estimation error. We assume polynomial type large deviation inequalities and prove asymptotic equivalence of…

A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…

To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge about unobserved covariates can be incorporated in the prior distributions. However, given the analytic…

The interpretation of cosmological observables requires the use of increasingly sophisticated theoretical models. Since these models are becoming computationally very expensive and display non-trivial uncertainties, the use of standard…

We consider a linear minimum mean squared error (LMMSE) estimation framework with model mismatch where the assumed model order is smaller than that of the underlying linear system which generates the data used in the estimation process. By…

The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…

Most conventional risk analysis methods rely on a single best estimate of exposure per person which does not allow for adjustment for exposure-related uncertainty. Here, we propose a Bayesian model averaging method to properly quantify the…