Search results for "Random variable"
showing 10 items of 151 documents
Equivalence of the Pecka–Ponec Correlation Probability and the Statistical F Significance for MLR Models
2004
In an article of this journal Pecka and Ponec [J. Math. Chem. 27 (2000) 13] have proposed, by means of a probability calculation, a method to evaluate the statistical importance of correlations obtained from multilinear regression equations involving an arbitrary number of experimental points and parameters. Here, it is demonstrated how this probability exactly coincides with a more general concept: the confidence probability of an F distribution having the appropriate degrees of freedom.
Embedding Quantum into Classical: Contextualization vs Conditionalization
2014
We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is "automatically" labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Bell-type ine…
On the use of adaptive spatial weight matrices from disease mapping multivariate analyses
2020
Conditional autoregressive distributions are commonly used to model spatial dependence between nearby geographic units in disease mapping studies. These distributions induce spatial dependence by means of a spatial weights matrix that quantifies the strength of dependence between any two neighboring spatial units. The most common procedure for defining that spatial weights matrix is using an adjacency criterion. In that case, all pairs of spatial units with adjacent borders are given the same weight (typically 1) and the remaining non-adjacent units are assigned a weight of 0. However, assuming all spatial neighbors in a model to be equally influential could be possibly a too rigid or inapp…
Second-order interaction in a Trivariate Generalized Gamma Distribution
2004
The concept of second- (and higher-) order interaction is widely used in categorical data analysis, where it proves useful for explaining the interdependence among three (or more) variables. Its use seems to be less common for continuous multivariate distributions, most likely owing to the predominant role of the Multivariate Normal distribution, for which any interaction involving more than two variables is necessarily zero. In this paper we explore the usefulness of a second-order interaction measure for studying the interdependence among three continuous random variables, by applying it to a trivariate Generalized Gamma distribution proposed by Bologna(2000).
Algorithms for the inference of causality in dynamic processes: Application to cardiovascular and cerebrovascular variability
2015
This study faces the problem of causal inference in multivariate dynamic processes, with specific regard to the detection of instantaneous and time-lagged directed interactions. We point out the limitations of the traditional Granger causality analysis, showing that it leads to false detection of causality when instantaneous and time-lagged effects coexist in the process structure. Then, we propose an improved algorithm for causal inference that combines the Granger framework with the approach proposed by Pearl for the study of causality among multiple random variables. This new approach is compared with the traditional one in theoretical and simulated examples of interacting processes, sho…
Low-energy excitations from interacting tunneling units in the mean-field approximation
1991
Abstract The low-energy excitation spectrum of dilute concentrations of interacting tunneling quadrupoles randomly distributed in a non-polar medium was studied in the mean-field approximation. In particular the case of six-orientational tunneling quadrupoles (TQs) with a r−3 (elastic) interaction was considered. Because of the random position of the TQs, the internal field in a random variable and for relatively low concentrations has a Lorenzian probability distribution. The low-energy density of states is a constant and the low-energy excitations arise from the large internal fields, i.e. strongly interacting tunneling quadrupoles. The low-energy excitations were compared with those obta…
No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics
2013
Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov's probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice-Bob EPR paradigm, non-contextuality means that the identity of Alice's spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis \alphai chosen by Alice, irrespective of Bob's axis \betaj (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice's and Bob's spins are identified as Aij and Bij, even though their distributions are determined by, respectively, \alphai alone and \betaj alone, in accordance with the no-signaling requir…
Proof of a Conjecture on Contextuality in Cyclic Systems with Binary Variables
2015
We present a proof for a conjecture previously formulated by Dzhafarov, Kujala, and Larsson (Foundations of Physics, in press, arXiv:1411.2244). The conjecture specifies a measure for the degree of contextuality and a criterion (necessary and sufficient condition) for contextuality in a broad class of quantum systems. This class includes Leggett-Garg, EPR/Bell, and Klyachko-Can-Binicioglu-Shumovsky type systems as special cases. In a system of this class certain physical properties $q_{1},...,q_{n}$ are measured in pairs $(q_{i},q_{j})$; every property enters in precisely two such pairs; and each measurement outcome is a binary random variable. Denoting the measurement outcomes for a proper…
The Wigner Distribution of Sum-of-Cissoids and Sum-of-Chirps Processes for the Modelling of Stationary and Non-Stationary Mobile Channels
2016
This paper concerns the time-frequency analysis of stationary and non-stationary multipath flat fading channels. For the modelling of stationary multipath fading channels, we use a sum-of-cisoids (SOCi) process, while the non-stationary channel is modelled by a sum-of-chirps (SOCh) process that captures the time-variant Doppler effect caused by speed variations of the mobile station. For the time-frequency analysis, we apply the concept of the Wigner distribution. Closed-form solutions are provided for the Wigner distribution of SOCi and SOCh processes. It is shown that the obtained Wigner distributions can be expressed by the sum of an auto-term representing the true Doppler power spectral…
A New Non-stationary Channel Model Based on Drifted Brownian Random Paths
2014
This paper utilizes Brownian motion (BM) processes with drift to model mobile radio channels under non-stationary conditions. It is assumed that the mobile station (MS) starts moving in a semi-random way, but subject to follow a given direction. This moving scenario is modelled by a BM process with drift (BMD). The starting point of the movement is a fixed point in the two-dimensional (2D) propagation area, while its destination is a random point along a predetermined drift. To model the propagation area, we propose a non-centred one-ring scattering model in which the local scatterers are uniformly distributed on a ring that is not necessarily centred on the MS. The semi-random movement of …