Related papers: Joint Bayesian estimation of close subspaces from …
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…
Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
The k-nearest-neighbour procedure is a well-known deterministic method used in supervised classification. This paper proposes a reassessment of this approach as a statistical technique derived from a proper probabilistic model; in…
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
Suppose that two large, multi-dimensional data sets are each noisy measurements of the same underlying random process, and principle components analysis is performed separately on the data sets to reduce their dimensionality. In some…
Determining if two histograms are consistent, whether they have been drawn from the same underlying distribution or not, is a common problem in physics. Existing approaches are not only limited in power but also inapplicable to histograms…
In this paper we consider the problem of linear unmixing hidden random variables defined over the simplex with additive Gaussian noise, also known as probabilistic simplex component analysis (PRISM). Previous solutions to tackle this…
As commonly understood, the noise spectroscopy problem---characterizing the statistical properties of a noise process affecting a quantum system by measuring its response---is ill-posed. Ad-hoc solutions assume implicit structure which is…
Extending Bayesian optimization to batch evaluation can enable the designer to make the most use of parallel computing technology. However, most of current batch approaches do not scale well with the batch size. That is, their performances…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
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…
Building on ideas from Castillo and Nickl [Ann. Statist. 41 (2013) 1999-2028], a method is provided to study nonparametric Bayesian posterior convergence rates when "strong" measures of distances, such as the sup-norm, are considered. In…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…