Search results for "PROBABILITY"
showing 10 items of 3417 documents
Probabilistic and team PFIN-type learning: General properties
2008
We consider the probability hierarchy for Popperian FINite learning and study the general properties of this hierarchy. We prove that the probability hierarchy is decidable, i.e. there exists an algorithm that receives p_1 and p_2 and answers whether PFIN-type learning with the probability of success p_1 is equivalent to PFIN-type learning with the probability of success p_2. To prove our result, we analyze the topological structure of the probability hierarchy. We prove that it is well-ordered in descending ordering and order-equivalent to ordinal epsilon_0. This shows that the structure of the hierarchy is very complicated. Using similar methods, we also prove that, for PFIN-type learning…
Compressed Particle Methods for Expensive Models With Application in Astronomy and Remote Sensing
2021
In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model selection or uncertainty quantification. Bayesian inference requires the approximation of complicated integrals involving (often costly) posterior distributions. Generally, this approximation is obtained by means of Monte Carlo (MC) methods. In order to reduce the computational cost of the corresponding technique, surrogate models (also called emulators) are often employed. Another alternative approach is the so-called Approximate Bayesian Computation (ABC) sc…
A Review of Multiple Try MCMC algorithms for Signal Processing
2018
Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of {\it a-posteriori} estimators which are often expressed as complicated multi-dimensional integrals. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and Monte Carlo methods are the only feasible approach. A very powerful class of Monte Carlo techniques is formed by the Markov Chain Monte Carlo (MCMC) algorithms. They generate a Markov chain such that its stationary distribution coincides with the target posterior density. In this work, we perform a t…
Impact of LTE’s Periodic Interference on Heterogeneous Wi-Fi Transmissions
2018
The problem of Wi-Fi and LTE coexistence has been significantly debated in the last years, with the emergence of LTE extensions enabling the utilization of unlicensed spectrum for carrier aggregation. Rather than focusing on the problem of resource sharing between the two technologies, in this paper, we study the effects of LTE's structured transmissions on the Wi-Fi random access protocol. We show how the scheduling of periodic LTE transmissions modifies the behavior of 802.11's distributed coordination function (DCF), leading to a degradation of Wi-Fi performance, both in terms of channel utilization efficiency and in terms of channel access fairness. We also discuss the applicability and…
Right-jumps and pattern avoiding permutations
2015
We study the iteration of the process "a particle jumps to the right" in permutations. We prove that the set of permutations obtained in this model after a given number of iterations from the identity is a class of pattern avoiding permutations. We characterize the elements of the basis of this class and we enumerate these "forbidden minimal patterns" by giving their bivariate exponential generating function: we achieve this via a catalytic variable, the number of left-to-right maxima. We show that this generating function is a D-finite function satisfying a nice differential equation of order~2. We give some congruence properties for the coefficients of this generating function, and we sho…
Optimal one-shot quantum algorithm for EQUALITY and AND
2017
We study the computation complexity of Boolean functions in the quantum black box model. In this model our task is to compute a function $f:\{0,1\}\to\{0,1\}$ on an input $x\in\{0,1\}^n$ that can be accessed by querying the black box. Quantum algorithms are inherently probabilistic; we are interested in the lowest possible probability that the algorithm outputs incorrect answer (the error probability) for a fixed number of queries. We show that the lowest possible error probability for $AND_n$ and $EQUALITY_{n+1}$ is $1/2-n/(n^2+1)$.
Modeling temporal treatment effects with zero inflated semi-parametric regression models: The case of local development policies in France
2017
International audience; A semi-parametric approach is proposed to estimate the variation along time of the effects of two distinct public policies that were devoted to boost rural development in France over a similar period of time. At a micro data level, it is often observed that the dependent variable, such as local employment, does not vary along time, so that we face a kind of zero inflated phenomenon that cannot be dealt with a continuous response model. We introduce a conditional mixture model which combines a mass at zero and a continuous response. The suggested zero inflated semi-parametric statistical approach relies on the flexibility and modularity of additive models with the abi…
Do-search -- a tool for causal inference and study design with multiple data sources
2020
Epidemiologic evidence is based on multiple data sources including clinical trials, cohort studies, surveys, registries, and expert opinions. Merging information from different sources opens up new possibilities for the estimation of causal effects. We show how causal effects can be identified and estimated by combining experiments and observations in real and realistic scenarios. As a new tool, we present do-search, a recently developed algorithmic approach that can determine the identifiability of a causal effect. The approach is based on do-calculus, and it can utilize data with nontrivial missing data and selection bias mechanisms. When the effect is identifiable, do-search outputs an i…
Fractional generalized cumulative entropy and its dynamic version
2021
Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with distributions satisfying the proportional reversed hazard model. We study the connection with fractional integrals, and some bounds and comparisons based on stochastic orderings, that allow to show that the proposed measure is actually a variability measure. The investigation also involves various notions of reliability theory, since the considered dynamic measure is a suitable extension of the mean inactivity time. We also introduce the empirical generalized fract…
On resampling schemes for particle filters with weakly informative observations
2022
We consider particle filters with weakly informative observations (or `potentials') relative to the latent state dynamics. The particular focus of this work is on particle filters to approximate time-discretisations of continuous-time Feynman--Kac path integral models -- a scenario that naturally arises when addressing filtering and smoothing problems in continuous time -- but our findings are indicative about weakly informative settings beyond this context too. We study the performance of different resampling schemes, such as systematic resampling, SSP (Srinivasan sampling process) and stratified resampling, as the time-discretisation becomes finer and also identify their continuous-time l…