Search results for "probability"

Quasi conjunction and p-entailment in nonmonotonic reasoning

2010

We study, in the setting of coherence, the extension of a probability assessment defined on n conditional events to their quasi conjunction. We consider, in particular, two special cases of logical dependencies; moreover, we examine the relationship between the notion of p-entailment of Adams and the inclusion relation of Goodman and Nguyen. We also study the probabilistic semantics of the QAND rule of Dubois and Prade; then, we give a theoretical result on p-entailment.

Probabilistic squares and hexagons of opposition under coherence

2017

Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square and of the hexagon in terms of acceptability. Then, we show how to construct probabilistic versions of the square and of the hexagon of opposition by forming suitable tripartitions of the set of all coherent assessments on a finite sequence of conditional events. Finally, as an application, we present new versions of the square and of the…

Coherent Conditional Previsions and Proper Scoring Rules

2012

In this paper we study the relationship between the notion of coherence for conditional prevision assessments on a family of finite conditional random quantities and the notion of admissibility with respect to bounded strictly proper scoring rules. Our work extends recent results given by the last two authors of this paper on the equivalence between coherence and admissibility for conditional probability assessments. In order to prove that admissibility implies coherence a key role is played by the notion of Bregman divergence.

Logical Conditions for Coherent Qualitative and Numerical Probability Assessments

2003

Application of Inverse-Probability-of-Treatment Weighting to Estimate the Effect of Daytime Sleepiness in Obstructive sleep apnea patients

2022

Continuous positive airway pressure (CPAP), the first line therapy for obstructive sleep apnea (OSA), is considered effective in reducing daytime sleepiness. Its efficacy relies on adequate adherence, often defined as >4 hours per night. However, this binary threshold may limit our understanding of the causal effect of CPAP adherence and daytime sleepiness and multilevel approach for CPAP adherence can be more appropriate.

Disentangling conditional effects of multiple regime shifts on Atlantic cod productivity

2020

AbstractRegime shifts are increasingly prevalent in the ecological literature. However, definitions vary, and many detection methods are subjective. Here, we employ an operationally objective means of identifying regime shifts, using a Bayesian online change-point detection algorithm able to simultaneously identify shifts in the mean and(or) variance of time series data. We detected multiple regime shifts in long-term (59-154 years) patterns of coastal Norwegian Atlantic cod (>70% decline) and putative drivers of cod productivity: North Atlantic Oscillation (NAO); sea-surface temperature; zooplankton abundance; fishing mortality (F). The consequences of an environmental or climate-relate…

Entropy, Benford’s first digit law, and the distribution of everything

2010

Incoherent dispersive shocks in the spectral evolution of random waves

2013

We predict theoretically and numerically the existence of incoherent dispersive shock waves. They manifest themselves as an unstable singular behavior of the spectrum of incoherent waves that evolve in a noninstantaneous nonlinear environment. This phenomenon of "spectral wave breaking" develops in the weakly nonlinear regime of the random wave. We elaborate a general theoretical formulation of these incoherent objects on the basis of a weakly nonlinear statistical approach: a family of singular integro-differential kinetic equations is derived, which provides a detailed deterministic description of the incoherent dispersive shock wave phenomenon.

Spectral long-range interaction of temporal incoherent solitons.

2014

We study the interaction of temporal incoherent solitons sustained by a highly noninstantaneous (Raman-like) nonlinear response. The incoherent solitons exhibit a nonmutual interaction, which can be either attractive or repulsive depending on their relative initial distance. The analysis reveals that incoherent solitons exhibit a long-range interaction in frequency space, which is in contrast with the expected spectral short-range interaction described by the usual approach based on the Raman-like spectral gain curve. Both phenomena of anomalous interaction and spectral long-range behavior of incoherent solitons are described in detail by a long-range Vlasov equation.

Impact of self-steepening on incoherent dispersive spectral shocks and collapse-like spectral singularities

2014

International audience; Incoherent dispersive shock waves and collapselike singularities have been recently predicted to occur in the spectral evolution of an incoherent optical wave that propagates in a noninstantaneous nonlinear medium. Here we extend this work by considering the generalized nonlinear Schrödinger equation. We show that self-steepening significantly affects these incoherent spectral singularities: (i) It leads to a delay in the development of incoherent dispersive shocks, and (ii) it arrests the incoherent collapse singularity. Furthermore, we show that the spectral collapselike behavior can be exploited to achieve a significant enhancement (by two orders of magnitudes) of…