Search results for " approximation"

showing 10 items of 575 documents

Modeling accident risk at the road level through zero-inflated negative binomial models: A case study of multiple road networks

2021

Abstract This paper presents a case study carried out in multiple cities of the Valencian Community (Spain) to determine the effect of sociodemographic and road characteristics on traffic accident risk. The analyzes are performed at the road segment level, considering the linear network representing the road structure of each city as a spatial lattice. The number of accidents observed in each road segment from 2010 to 2019 is taken as the response variable, and a zero-inflated modeling approach is considered. Count overdispersion and spatial dependence are also accounted for. Despite the complexity and sparsity of the data, the fitted models performed considerably well, with few exceptions.…

Statistics and ProbabilityComputer sciencespatial dependence0208 environmental biotechnologyAccident riskMagnitude (mathematics)Distribution (economics)02 engineering and technologyManagement Monitoring Policy and Law01 natural sciencestraffic accidents010104 statistics & probabilityOverdispersionCovariateStatisticsZero-inflated model0101 mathematicsComputers in Earth SciencesSpatial dependencelattice structurebusiness.industryIntegrated Nested Laplace Approximationzero-inflated model020801 environmental engineeringVariable (computer science)linear networksbusiness
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MLML2R: an R package for maximum likelihood estimation of DNA methylation and hydroxymethylation proportions.

2019

Abstract Accurately measuring epigenetic marks such as 5-methylcytosine (5-mC) and 5-hydroxymethylcytosine (5-hmC) at the single-nucleotide level, requires combining data from DNA processing methods including traditional (BS), oxidative (oxBS) or Tet-Assisted (TAB) bisulfite conversion. We introduce the R package MLML2R, which provides maximum likelihood estimates (MLE) of 5-mC and 5-hmC proportions. While all other available R packages provide 5-mC and 5-hmC MLEs only for the oxBS+BS combination, MLML2R also provides MLE for TAB combinations. For combinations of any two of the methods, we derived the pool-adjacent-violators algorithm (PAVA) exact constrained MLE in analytical form. For the…

Statistics and ProbabilityDNA HydroxymethylationEpigenomicsIterative methodMaximum likelihood03 medical and health sciencessymbols.namesake0302 clinical medicineGeneticsHumansMolecular Biology030304 developmental biologyMathematics0303 health sciencesLikelihood FunctionsComputational BiologyHigh-Throughput Nucleotide SequencingProbability and statisticsDNA MethylationComputational MathematicsR packageLagrange multiplierDNA methylationsymbolsIterative approximationAlgorithm030217 neurology & neurosurgeryStatistical applications in genetics and molecular biology
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Mean square rate of convergence for random walk approximation of forward-backward SDEs

2020

AbstractLet (Y,Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk$B^n$from the underlying Brownian motionBby Skorokhod embedding, one can show$L_2$-convergence of the corresponding solutions$(Y^n,Z^n)$to$(Y, Z).$We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in$C^{2,\alpha}$. The proof relies on an approximative representation of$Z^n$and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to t…

Statistics and ProbabilityDiscretizationapproximation schemeMalliavin calculus01 natural sciences010104 statistics & probabilityconvergence rateMathematics::ProbabilityConvergence (routing)random walk approximation 2010 Mathematics Subject Classification: Primary 60H10FOS: MathematicsApplied mathematics0101 mathematicsBrownian motionrandom walk approximationMathematicsstokastiset prosessitSmoothness (probability theory)konvergenssiApplied Mathematics010102 general mathematicsProbability (math.PR)Backward stochastic differential equationsFunction (mathematics)Random walkfinite difference equation[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]Rate of convergencebackward stochastic differential equations60G50 Secondary 60H3060H35approksimointidifferentiaaliyhtälötMathematics - Probability
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Analyzing environmental‐trait interactions in ecological communities with fourth‐corner latent variable models

2021

In ecological community studies it is often of interest to study the effect of species related trait variables on abundances or presence-absences. Specifically, the interest may lay in the interactions between environmental and trait variables. An increasingly popular approach for studying such interactions is to use the so-called fourth-corner model, which explicitly posits a regression model where the mean response of each species is a function of interactions between covariate and trait predictors (among other terms). On the other hand, many of the fourth-corner models currently applied in the literature are too simplistic to properly account for variation in environmental and trait resp…

Statistics and ProbabilityEcological ModelingLatent variableeliöyhteisötcommunity analysisGeneralized linear mixed modelekologiajoint species distribution modelgeneralized linear mixed modelmultivariate abundance datamonimuuttujamenetelmätCommunity analysisEconometricsTraitvariational approximationtilastolliset mallitfourth-corner problemympäristönmuutoksetMathematics
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Can the Adaptive Metropolis Algorithm Collapse Without the Covariance Lower Bound?

2011

The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step $n+1$ \[ S_n = Cov(X_1,...,X_n) + \epsilon I, \] that is, the sample covariance matrix of the history of the chain plus a (small) constant $\epsilon>0$ multiple of the identity matrix $I$. The lower bound on the eigenvalues of $S_n$ induced by the factor $\epsilon I$ is theoretically convenient, but practically cumbersome, as a good value for the parameter $\epsilon$ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitly bound the eigenvalues of $S_n$ away …

Statistics and ProbabilityFOS: Computer and information sciencesIdentity matrixMathematics - Statistics TheoryStatistics Theory (math.ST)Upper and lower boundsStatistics - Computation93E3593E15Combinatorics60J27Mathematics::ProbabilityLaw of large numbers65C40 60J27 93E15 93E35stochastic approximationFOS: MathematicsEigenvalues and eigenvectorsComputation (stat.CO)Metropolis algorithmMathematicsProbability (math.PR)Zero (complex analysis)CovariancestabilityUniform continuityBounded function65C40Statistics Probability and Uncertaintyadaptive Markov chain Monte CarloMathematics - Probability
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Fractional Brownian motion and Martingale-differences

2004

Abstract We generalize a result of Sottinen (Finance Stochastics 5 (2001) 343) by proving an approximation theorem for the fractional Brownian motion, with H> 1 2 , using martingale-differences.

Statistics and ProbabilityGeometric Brownian motionFractional Brownian motionMathematics::ProbabilityDiffusion processReflected Brownian motionMathematical analysisBrownian excursionStatistics Probability and UncertaintyHeavy traffic approximationMartingale (probability theory)Martingale representation theoremMathematicsStatistics & Probability Letters
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Posterior moments and quantiles for the normal location model with Laplace prior

2021

We derive explicit expressions for arbitrary moments and quantiles of the posterior distribution of the location parameter η in the normal location model with Laplace prior, and use the results to approximate the posterior distribution of sums of independent copies of η.

Statistics and ProbabilityLaplace priorsLaplace priorLocation parameterreflected generalized gamma priorSettore SECS-P/05Posterior probability0211 other engineering and technologiesSettore SECS-P/05 - Econometria02 engineering and technology01 natural sciencesCornish-Fisher approximation010104 statistics & probabilityStatistics::Methodologyposterior quantile0101 mathematicsposterior moments and cumulantsMathematicsreflected generalized gamma priors021103 operations researchLaplace transformLocation modelMathematical analysisStatistics::Computationposterior moments and cumulantCornish–Fisher approximationSettore SECS-S/01 - StatisticaNormal location modelposterior quantilesQuantileCommunications in Statistics - Theory and Methods
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Quantile regression via iterative least squares computations

2012

We present an estimating framework for quantile regression where the usual L 1-norm objective function is replaced by its smooth parametric approximation. An exact path-following algorithm is derived, leading to the well-known ‘basic’ solutions interpolating exactly a number of observations equal to the number of parameters being estimated. We discuss briefly possible practical implications of the proposed approach, such as early stopping for large data sets, confidence intervals, and additional topics for future research.

Statistics and ProbabilityMathematical optimizationEarly stoppingquantile regressionsmooth approximationApplied MathematicsRegression analysisLeast squaresQuantile regressionleast squareModeling and SimulationNon-linear least squaresApplied mathematicsStatistics Probability and UncertaintyTotal least squaresSettore SECS-S/01 - StatisticaQuantileParametric statisticsMathematicsJournal of Statistical Computation and Simulation
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A generalization of the Binomial distribution based on the dependence ratio

2014

We propose a generalization of the Binomial distribution, called DR-Binomial, which accommodates dependence among units through a model based on the dependence ratio (Ekholm et al., Biometrika, 82, 1995, 847). Properties of the DR-Binomial are discussed, and the constraints on its parameter space are studied in detail. Likelihood-based inference is presented, using both the joint and profile likelihoods; the usefulness of the DR-Binomial in applications is illustrated on a real dataset displaying negative unit-dependence, and hence under-dispersion compared with the Binomial. Although the DR-Binomial turns out to be a reparameterization of Altham's Additive-Binomial and Kupper–Haseman's Cor…

Statistics and ProbabilityMathematics::Commutative AlgebraBinomial approximationNegative binomial distributionBinomial testNegative multinomial distributionBinomial distributionBeta-binomial distributionStatisticsApplied mathematicsMultinomial theoremMultinomial distributionStatistics Probability and UncertaintyMathematicsStatistica Neerlandica
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Cavity losses for the dissipative Jaynes–Cummings Hamiltonian beyond rotating wave approximation

2007

A microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis [Scala M. {\em et al.} 2007 Phys. Rev. A {\bf 75}, 013811], where a microscopic derivation was given in the framework of the Rotating Wave Approximation.

Statistics and ProbabilityPhysicsQuantum PhysicsGeneral Physics and AstronomyDissipatorFOS: Physical sciencesStatistical and Nonlinear Physics01 natural sciences010305 fluids & plasmassymbols.namesakeJaynes–Cummings modelModeling and SimulationQuantum mechanics0103 physical sciencesMaster equationsymbolsDissipative systemRotating wave approximation010306 general physicsHamiltonian (quantum mechanics)Quantum Physics (quant-ph)Mathematical PhysicsRabi frequency
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