相关论文: On the Birnbaum Argument for the Strong Likelihood…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
We prove the large deviation principle (LDP) for posterior distributions arising from subfamilies of full exponential families, allowing misspecification of the model. Moreover, motivated by the so-called inverse Sanov Theorem (see e.g.…
In this paper we introduce the three main notions of probability used by physicists and discuss how these are to be used when invoking spacelike separated observers in a relativistic format. We discuss a standard EPRB experiment and…
Statistical and machine learning theory has developed several conditions ensuring that popular estimators such as the Lasso or the Dantzig selector perform well in high-dimensional sparse regression, including the restricted eigenvalue,…
Entanglement and nonlocality are studied in the framework of pre-/post-selected ensembles with the aid of weak measurements and the Two-State-Vector Formalism. In addition to the EPR-Bohm experiment, we revisit the Hardy and Cheshire Cat…
A long range Weak Equivalence Principle (WEP) violating force between Dark Matter (DM) particles, mediated by an ultralight scalar, is tightly constrained by galactic dynamics and large scale structure formation. We examine the implications…
Although living organisms are affected by many interrelated and unidentified variables, this complexity does not automatically impose a fundamental limitation on statistical inference. Nor need one invoke such complexity as an explanation…
The concept of Logical Entropy, $S_L = 1- \sum_{i=1}^n p_i^2$, where the $p_i$ are normalized probabilities, was introduced by David Ellerman in a series of recent papers. Although the mathematical formula itself is not new, Ellerman…
Consider a supercritical superdiffusion (X_t) on a domain D subset R^d with branching mechanism -\beta(x) z+\alpha(x) z^2 + int_{(0,infty)} (e^{-yz}-1+yz) Pi(x,dy). The skeleton decomposition provides a pathwise description of the process…
When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
This paper has a flaw in an argument that uses the weak-* convergence of measures. The paper was replaced by "Entropy and Its Variational Principle for Locally Compact Metrizable Systems", by the same authors.
Causal effect estimation from observational data is an important and much studied research topic. The instrumental variable (IV) and local causal discovery (LCD) patterns are canonical examples of settings where a closed-form expression…
Berliner (Likelihood and Bayesian prediction for chaotic systems, J. Am. Stat. Assoc. 1991) identified a number of difficulties in using the likelihood function within the Bayesian paradigm which arise both for state estimation and for…
The recent paper [F. Arute et al. Nature {\bf 574}, 505 (2019)] considered exact classical sampling of the output probability distribution of the globally depolarized random quantum circuit. In this paper, we show three results. First, we…
The "significance filter" refers to focusing exclusively on statistically significant results. Since frequentist properties such as unbiasedness and coverage are valid only before the data have been observed, there are no guarantees if we…
We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the…
Hypothesis testing in singular statistical models is often regarded as inherently problematic due to non-identifiability and degeneracy of the Fisher information. We show that the fundamental obstruction to testing in such models is not…
Quantum theory has evolved from a set of provisional rules to an indispensable framework that underlies much of modern technology and infrastructure. Yet, after a century, Born's probability postulate remains at odds with the theory's…
Strong laws of large numbers are established for random fields with weak or strong dependence. These limit theorems are applicable to random fields with heavy-tailed distributions including fractional stable random fields. The conditions…