Related papers: Bayesian Generalized Probability Calculus for Dens…
In 1989, Deutsch gave a basic physical explanation of why quantum-mechanical probabilities are squares of amplitudes. Essentially, a general state vector is transformed into a highly symmetric equal-amplitude superposition. The argument was…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy…
This paper proposes Bayesian mosaic, a parallelizable composite posterior, for scalable Bayesian inference on a broad class of multivariate discrete data models. Sampling is embarrassingly parallel since Bayesian mosaic is a multiplication…
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…
We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes' theorem and its applications. In particular we discuss about how to…
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,…
The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive definite coefficient matrices. Our CG-based implementation of…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
In statistical practice, a realistic Bayesian model for a given data set can be defined by a likelihood function that is analytically or computationally intractable, due to large data sample size, high parameter dimensionality, or complex…
Entropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of R\'enyi entropies describing probability distributions associated…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
In this paper we derive an explicit formula for calculating the marginal likelihood of a given factorization of a categorical dataset. Since the marginal likelihood is proportional to the posterior probability of the factorization, these…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
We estimate the norms of standard Gaussian random Toeplitz and circulant matrices and their inverses, mostly by means of combining some basic techniques of linear algebra. In the case of circulant matrices we obtain sharp probabilistic…
General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper we build a framework for probabilistic theories with non-fixed causal…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…
We introduce a Bayesian perspective for the structured matrix factorization problem. The proposed framework provides a probabilistic interpretation for existing geometric methods based on determinant minimization. We model input data…