相关论文: Mathematical Basis for Physical Inference
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
Born's rule is the recipe for calculating probabilities from quantum mechanical amplitudes. There is no generally accepted derivation of Born's rule from first principles. In this paper, it is motivated from assumptions that link the…
Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
We consider an agent seeking to obtain an item, potentially available at different locations in a physical environment. The traveling costs between locations are known in advance, but there is only probabilistic knowledge regarding the…
This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for $I(1)$ linear processes with moderately large cross-sectional dimension. The approach is based on empirical canonical correlations…
The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in the initial axioms and has in particular Bayes theorem as a…
Firth-type logistic regression has become a standard approach for the analysis of binary outcomes with small samples. Whereas it reduces the bias in maximum likelihood estimates of coefficients, bias towards 1/2 is introduced in the…
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the…
The paper evaluates the power of best-first search over AND/OR search spaces for solving the Most Probable Explanation (MPE) task in Bayesian networks. The main virtue of the AND/OR representation of the search space is its sensitivity to…
The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from…
Statistical mechanics is generalized on the basis of an additive information theory for incomplete probability distributions. The incomplete normalization $\sum_{i=1}^wp_i^q=1$ is used to obtain generalized entropy $S=-k\sum_{i=1}^wp_i^q\ln…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
The objective is a foundation of physics from the operationalization of its basic observables. We begin with classical and relativistic kinematics. Seizing on a programmatic proposal by Heinrich Hertz we arrive via quantification of…
In a recent paper, the author introduced an operational description of physical theories where probabilities are replaced by counterfactual statements belonging to a three-valued (i.e. possibilistic) semantic domain. The complete axiomatic…
The growing availability of large health databases has expanded the use of observational studies for comparative effectiveness research. Unlike randomized trials, observational studies must adjust for systematic differences in patient…