Related papers: Fast Bayesian Updates via Harmonic Representations
This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of…
Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…
Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
Bayesian analyses are often performed using so-called noninformative priors, with a view to achieving objective inference about unknown parameters on which available data depends. Noninformative priors depend on the relationship of the data…
Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While…
The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…
Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural…
Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
Motivation: The mapping of RNA-seq reads to their transcripts of origin is a fundamental task in transcript expression estimation and differential expression scoring. Where ambiguities in mapping exist due to transcripts sharing sequence,…
Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…
How can one perform Bayesian inference on stochastic simulators with intractable likelihoods? A recent approach is to learn the posterior from adaptively proposed simulations using neural network-based conditional density estimators.…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
In this paper we show that the classical problem of frequency estimation can be formulated and solved efficiently in an empirical Bayesian framework by assigning a uniform a priori probability distribution to the unknown frequency. We…
We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the…
This paper is concerned with making Bayesian inference from data that are assumed to be drawn from a Bingham distribution. A barrier to the Bayesian approach is the parameter-dependent normalising constant of the Bingham distribution,…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability…
Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is…
Bayesian methods are commonly applied to solve image analysis problems such as noise-reduction, feature enhancement and object detection. A primary limitation of these approaches is the computational complexity due to the interdependence of…