Search results for "Probability measure"

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.

Infinitely Divisible Distributions

2020

For every n, the normal distribution with expectation μ and variance σ 2 is the nth convolution power of a probability measure (namely of the normal distribution with expectation μ/n and variance σ 2/n). This property is called infinite divisibility and is shared by other probability distributions such as the Poisson distribution and the Gamma distribution. In the first section, we study which probability measures on the real line are infinitely divisible and give an exhaustive description of this class of distributions by means of the Levy–Khinchin formula.

Hamilton–Jacobi semi-groups in infinite dimensional spaces

2006

AbstractLet (X,ρ) be a Polish space endowed with a probability measure μ. Assume that we can do Malliavin Calculus on (X,μ). Let d:X×X→[0,+∞] be a pseudo-distance. Consider QtF(x)=infy∈X{F(y)+d2(x,y)/2t}. We shall prove that QtF satisfies the Hamilton–Jacobi inequality under suitable conditions. This result will be applied to establish transportation cost inequalities on path groups and loop groups in the spirit of Bobkov, Gentil and Ledoux.

Discretization of harmonic measures for foliated bundles

2012

We prove in this note that there is, for some foliated bundles, a bijective correspondance between Garnett's harmonic measures and measures on the fiber that are stationary for some probability measure on the holonomy group. As a consequence, we show the uniqueness of the harmonic measure in the case of some foliations transverse to projective fiber bundles.

Survival probability approach to the relaxation of a macroscopic system in the defect-diffusion framework

2004

Effects of Grade Retention Policies: A Literature Review of Empirical Studies Applying Causal Inference

2021

The identification of the causal effects of grade retention policies is of enormous relevance for researchers and policymakers alike. Taking advantage of the availability of more detailed longitudinal datasets, researchers have been able to apply different identification strategies that address the classical problems of selection bias and unobserved heterogeneity that have plagued previous studies on the effect of retention. We present a systematic literature review of empirical studies aiming to unveil the causal effects of retention. This study underlines the need to consider and evaluate different kinds of grade retention polices as their effects vary depending on several dimensions (suc…

L∞ estimates in optimal mass transportation

2016

We show that in any complete metric space the probability measures μ with compact and connected support are the ones having the property that the optimal transportation distance to any other probability measure ν living on the support of μ is bounded below by a positive function of the L∞ transportation distance between μ and ν. The function giving the lower bound depends only on the lower bound of the μ-measures of balls centered at the support of μ and on the cost function used in the optimal transport. We obtain an essentially sharp form of this function. In the case of strictly convex cost functions we show that a similar estimate holds on the level of optimal transport plans if and onl…

Conditional convex orders and measurable martingale couplings

2014

Strassen's classical martingale coupling theorem states that two real-valued random variables are ordered in the convex (resp.\ increasing convex) stochastic order if and only if they admit a martingale (resp.\ submartingale) coupling. By analyzing topological properties of spaces of probability measures equipped with a Wasserstein metric and applying a measurable selection theorem, we prove a conditional version of this result for real-valued random variables conditioned on a random element taking values in a general measurable space. We also provide an analogue of the conditional martingale coupling theorem in the language of probability kernels and illustrate how this result can be appli…

Applications de type Lasota–Yorke à trou : mesure de probabilité conditionellement invariante et mesure de probabilité invariante sur l'ensemble des …

2003

Abstract Let T :I→I be a Lasota–Yorke map on the interval I, let Y be a nontrivial sub-interval of I and g 0 :I→ R + , be a strictly positive potential which belongs to BV and admits a conformal measure m. We give constructive conditions on Y ensuring the existence of absolutely continuous (w.r.t. m) conditionally invariant probability measures to nonabsorption in Y. These conditions imply also existence of an invariant probability measure on the set X∞ of points which never fall into Y. Our conditions allow rather “large” holes.

Variable Length Memory Chains: Characterization of stationary probability measures

2021

Variable Length Memory Chains (VLMC), which are generalizations of finite order Markov chains, turn out to be an essential tool to modelize random sequences in many domains, as well as an interesting object in contemporary probability theory. The question of the existence of stationary probability measures leads us to introduce a key combinatorial structure for words produced by a VLMC: the Longest Internal Suffix. This notion allows us to state a necessary and sufficient condition for a general VLMC to admit a unique invariant probability measure. This condition turns out to get a much simpler form for a subclass of VLMC: the stable VLMC. This natural subclass, unlike the general case, enj…