相关论文: Asymptotic Analysis of MAP Estimation via the Repl…

We propose a general framework for nonasymptotic covariance matrix estimation making use of concentration inequality-based confidence sets. We specify this framework for the estimation of large sparse covariance matrices through…

A demanding challenge in Bayesian inversion is to efficiently characterize the posterior distribution. This task is problematic especially in high-dimensional non-Gaussian problems, where the structure of the posterior can be very chaotic…

We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…

Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…

Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal…

Nearest neighbor imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the nearest neighbor imputation estimator for general population parameters, including…

In this paper, we present an information theoretic analysis of the blind signal classification algorithm. We show that the algorithm is equivalent to a Maximum A Posteriori (MAP) estimator based on estimated parametric probability models.…

Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…

Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…

In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes,…

We characterize the measurement complexity of compressed sensing of signals drawn from a known prior distribution, even when the support of the prior is the entire space (rather than, say, sparse vectors). We show for Gaussian measurements…

We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…

Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…

The performance of Maximum a posteriori (MAP) estimation is studied analytically for binary symmetric multi-channel Hidden Markov processes. We reduce the estimation problem to a 1D Ising spin model and define order parameters that…

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…

Several hypothesis testing methods have been proposed to validate the assumption of isotropy in spatial point patterns. A majority of these methods are characterised by an unknown distribution of the test statistic under the null hypothesis…