Related papers: A bang-bang principle for the conditional expectat…
We establish three variational principles for the upper metric mean dimension with potential of level sets of continuous maps in terms of the entropy of partitions and Katok's entropy of the underlying system. Our results hold for dynamical…
We introduce a modified Consensus-Based Optimization model that admits a fully unified and rigorous analysis of its finite-particle dynamics, the associated McKean--Vlasov equation, and their optimization behavior under a single set of…
Incorporation of expert information in inference or decision settings is often important, especially in cases where data are unavailable, costly or unreliable. One approach is to elicit prior quantiles from an expert and then to fit these…
Using the quantum transition path time probability distribution we show that time averaging of weak values leads to unexpected results. We prove a weak value time energy uncertainty principle and time energy commutation relation. We also…
We forecast the full conditional distribution of macroeconomic outcomes by systematically integrating three key principles: using high-dimensional data with appropriate regularization, adopting rigorous out-of-sample validation procedures,…
The Bessel point process is a rigid point process on the positive real line and its conditional measure on a bounded interval $[0,R]$ is almost surely an orthogonal polynomial ensemble. In this article, we show that if $R$ tends to…
To begin with, it is pointed out that the form of the quantum probabil- ity formula originates in the very initial state of the object system as seen when the state is expanded with the eigen-projectors of the measured ob- servable. Making…
The separate tasks of denoising, least squares expectation, and manifold learning can often be posed in a common setting of finding the conditional expectations arising from a product of two random variables. This paper focuses on this more…
Scoring rules measure the deviation between a probabilistic forecast and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
Application of the uncertainty principle to conditional measurements is investigated, and found to be valid for measurements on separated sub-systems. In light of this, an apparent violation of the uncertainty principle obtained by Kim and…
We prove a vector-valued almost sure invariance principle for some classes of time dependent non-uniformly distance expanding dynamical systems. The models we have in mind are certain sequential versions of the smooth non-uniformly distance…
We develop a convergent variational perturbation theory for conditional probability densities of Markov processes. The power of the theory is illustrated by applying it to the diffusion of a particle in an anharmonic potential.
We study the problem of deriving policies, or rules, that when enacted on a complex system, cause a desired outcome. Absent the ability to perform controlled experiments, such rules have to be inferred from past observations of the system's…
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…
The gauge Brezis-Browder Principle in Turinici [Bull. Acad. Pol. Sci. (Math.), 30 (1982), 161-166] is obtainable from the Principle of Dependent Choices (DC) and implies Ekeland's Variational Principle (EVP); hence, it is equivalent with…
We prove that systems satisfying the specification property are saturated in the sense that the topological entropy of the set of generic points of any invariant measure is equal to the measure-theoretic entropy of the measure. We study…
Conformal predictors are set predictors that are automatically valid in the sense of having coverage probability equal to or exceeding a given confidence level. Inductive conformal predictors are a computationally efficient version of…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
In clinical trials, inferences on clinical outcomes are often made conditional on specific selective processes. For instance, only when a treatment demonstrates a significant effect on the primary outcome, further analysis is conducted to…