Related papers: Doomsday: A Response to Simpson's Second Question
Many macroscopic physical processes are known to occur in a time-directed way despite the apparent time-symmetry of the known fundamental laws. A popular explanation is to postulate an unimaginably atypical state for the early universe -- a…
It is widely accepted that temporal asymmetry is largely a cosmological problem; the task of explaining temporal asymmetry reduces in the main to that of explaining an aspect of the condition of the early universe. However, cosmologists who…
The collapse of a spatial probability distribution is triggered by a measurement at a given spacetime point. It is customarily assumed that this collapse occurs along an equal-time hypersurface, say, t = 0. However, such a na\"ive…
The aim of this chapter is twofold. First, we introduce the information loss problem; second, we provide a critical assessment by thoroughly inspecting the assumptions underlying its formulations. In particular, we argue that if we work in…
Standard probabilistic models face fundamental challenges such as data scarcity, a large hypothesis space, and poor data transparency. To address these challenges, we propose a novel probabilistic model of data-driven temporal propositional…
Consider semiparametric models that display local asymptotic exponentiality (Ibragimov and Has'minskii (1981)), an asymptotic property of the likelihood associated with discontinuities of densities. Our interest goes to estimation of the…
Bayesian inference is used to estimate continuous parameter values given measured data in many fields of science. The method relies on conditional probability densities to describe information about both data and parameters, yet the notion…
For the Vlasov-Poisson equation with random uncertain initial data, we prove that the Landau damping solution given by the deterministic counterpart (Caglioti and Maffei, {\it J. Stat. Phys.}, 92:301-323, 1998) depends smoothly on the…
The standard operational probabilistic framework (within which we can formulate Operational Quantum Theory) is time asymmetric. This is clear because the conditions on allowed operations are time asymmetric. It is odd, though, because…
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 deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative importance in a given time series. To this end we extend i) the use of ordinal patterns-based probability distribution…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of…
We study Doob's Consistency Theorem and Freedman's Inconsistency Theorem from the vantage point of computable probability and algorithmic randomness. We show that the Schnorr random elements of the parameter space are computably consistent,…
A picture of dynamical collapse of the wave function which is relativistic and time symmetric is presented. The part of the model which exhibits these features is the set of collapse outcomes. These play the role of matter distributed in…
When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…
I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional…
Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…