Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been object several recent works. These versions have expressed language Hilbert spaces. In this paper, we derive expression Petz recovery map within any quasiprobability representation, with explicit formulas for two canonical choices normal representatio...

We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies demonstrate that the proposed have excellent comparative performance scale well to very large sample sizes due a binning strategy. Moreover, approach is fully...

We develop methods for robust Bayesian inference in structural vector autoregressions (SVARs) where the parameters of interest are set-identified using external instruments, or ‘proxy SVARs’. Set-identification these models typically occurs when there multiple instruments shocks. Existing approaches to proxy SVARs require researchers specify a single prior over model’s parameters, but, under se...

Abstract We present a Bayesian method for inferring axisymmetric plasma equilibria from the magnetic field and pressure measurements. The calculates all possible solutions current distributions consistent with measurements magnetohydrodynamic (MHD) force balance. Toroidal coils are modelled as set of current-carrying solid beams. other parameters such poloidal flux given function flux, which is...

This paper develops default priors for Bayesian analysis that reproduce familiar frequentist and Bayesian analyses for models that are exponential or location. For the vector parameter case there is an information adjustment that avoids the Bayesian marginalization paradoxes and properly targets the prior on the parameter of interest thus adjusting for any complicating nonlinearity the details ...

To formalise our discussion of model uncertainty we will rely on probabilistic modelling, and more specifically on Bayesian modelling. Bayesian probability theory offers us the machinery we need to develop our tools. Together with techniques for approximate inference in Bayesian models, in the next chapter we will present the main results of this work. But prior to that, let us review the main ...

This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inf...