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Penalized and robust regression, especially when approached from a Bayesian perspective, can involve the problem of simulating a random variable $\boldsymbol z$ from a posterior distribution that includes a term proportional to a sum of…
We propose a cautious Bayesian variable selection routine by investigating the sensitivity of a hierarchical model, where the regression coefficients are specified by spike and slab priors. We exploit the use of latent variables to…
Finite mixture models provide a flexible framework for approximating and estimating multivariate probability densities. We study mixtures formed from translated and rescaled copies of a fixed density kernel and obtain explicit results for…
In the context of statistical supervised learning, the noiseless linear model assumes that there exists a deterministic linear relation $Y = \langle \theta_*, X \rangle$ between the random output $Y$ and the random feature vector $\Phi(U)$,…
We study the frequentist properties of Bayesian statistical inference for the stochastic block model, with an unknown number of classes of varying sizes. We equip the space of vertex labellings with a prior on the number of classes and,…
Nonresponse weighting adjustment using the response propensity score is a popular tool for handling unit nonresponse. Statistical inference after the nonresponse weighting adjustment is complicated because the effect of estimating the…
The Inverse-Wishart (IW) distribution is a standard and popular choice of priors for covariance matrices and has attractive properties such as conditional conjugacy. However, the IW family of priors has crucial drawbacks, including the lack…
State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…
We develop a mixture model for transition density approximation, together with soft model selection, in the presence of noisy and heterogeneous nonlinear dynamics. Our model builds on the Gaussian mixture transition distribution (MTD) model…
Unlinked regression, in which covariates and responses are observed separately without known correspondence, has recently gained increasing attention. Deconvolution, on the other hand, is a fundamental and challenging problem in…
Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this…
Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…
In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…
We investigate Bayesian nonparametric density estimation via orthogonal polynomial expansions in weighted Sobolev spaces. A core challenge is establishing minimax optimal posterior convergence rates, especially for densities on unbounded…
We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…
We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…
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.…
This paper deals with nonparametric estimation of conditional den-sities in mixture models in the case when additional covariates are available. The proposed approach consists of performing a prelim-inary clustering algorithm on the…
We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the multivariate density of the finite dimensional distributions of which we aim to estimate. We assume that we observe the…
A filament consists of local maximizers of a smooth function $f$ when moving in a certain direction. A filamentary structure is an important feature of the shape of an object and is also considered as an important lower dimensional…