Electronic Journal of Probability, ISSN 1083-6489, 2015, Volume 20, pp. 1 - 28

We combine Malliavin calculus with Stein's method to derive bounds for the Variance-Gamma approximation of functionals of isonormal Gaussian processes, in...

Wiener chaos | Laplace distribution | Stein’s method | Contractions | Rates of convergence | Variance-Gamma distribution | Gaussian processes | Non-central limit theorem | Malliavin calculus | Universality | Cumulants | universality | STATISTICS & PROBABILITY | rates of convergence | cumulants | non-central limit theorem | RATES | Stein's method

Wiener chaos | Laplace distribution | Stein’s method | Contractions | Rates of convergence | Variance-Gamma distribution | Gaussian processes | Non-central limit theorem | Malliavin calculus | Universality | Cumulants | universality | STATISTICS & PROBABILITY | rates of convergence | cumulants | non-central limit theorem | RATES | Stein's method

Journal Article

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, ISSN 0378-3758, 03/2018, Volume 194, pp. 25 - 31

When applying Laplace's method to approximate an integral, we require an exact mode of its integrand. In this paper, we derive a Laplace approximation using an...

Asymptotic expansion | DENSITIES | Laplace's approximation | STATISTICS & PROBABILITY | GARCH model | MODEL | Bayesian analysis

Asymptotic expansion | DENSITIES | Laplace's approximation | STATISTICS & PROBABILITY | GARCH model | MODEL | Bayesian analysis

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 03/2009, Volume 130, Issue 12, pp. 127101 - 127101-2

The recently proposed minimax quadrature for Laplace-transformed energy denominators in second order Møller-Plesset perturbation theory is compared to the...

least squares approximations | electron correlations | Laplace transforms | organic compounds | perturbation theory | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL

least squares approximations | electron correlations | Laplace transforms | organic compounds | perturbation theory | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL

Journal Article

Journal of the Royal Statistical Society: Series C (Applied Statistics), ISSN 0035-9254, 01/2019, Volume 68, Issue 1, pp. 199 - 215

Summary The integrated nested Laplace approximation (INLA) is a convenient way to obtain approximations to the posterior marginals for parameters in Bayesian...

Disease mapping | Spatial econometrics | Bayesian inference | Markov chain Monte Carlo methods | Integrated nested Laplace approximation | INLA | STATISTICS & PROBABILITY | BAYESIAN-INFERENCE | Monte Carlo method | Parameter estimation | Correlation | Approximation | Disease | Computer simulation | Dependence | Markov chains | Inference | Mapping | Econometrics | Bayesian analysis

Disease mapping | Spatial econometrics | Bayesian inference | Markov chain Monte Carlo methods | Integrated nested Laplace approximation | INLA | STATISTICS & PROBABILITY | BAYESIAN-INFERENCE | Monte Carlo method | Parameter estimation | Correlation | Approximation | Disease | Computer simulation | Dependence | Markov chains | Inference | Mapping | Econometrics | Bayesian analysis

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 04/2013, Volume 256, pp. 17 - 28

► A rotation-free mixed natural element approximation of RM plate is introduced. ► The Voronoi polygon-discretized RM plate is formulated according to the...

Voronoi polygons | Reissner–Mindlin plate | Laplace interpolation function | Shear locking | Rotation-free mixed natural element approximation | Constant curvature | Reissner-Mindlin plate | BOUNDARY-LAYER | HIERARCHICAL-MODELS | BENDING ELEMENTS | FORMULATION | INTERPOLATION | MECHANICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | SHELL-LIKE STRUCTURES | PARTIAL-DIFFERENTIAL-EQUATIONS

Voronoi polygons | Reissner–Mindlin plate | Laplace interpolation function | Shear locking | Rotation-free mixed natural element approximation | Constant curvature | Reissner-Mindlin plate | BOUNDARY-LAYER | HIERARCHICAL-MODELS | BENDING ELEMENTS | FORMULATION | INTERPOLATION | MECHANICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | SHELL-LIKE STRUCTURES | PARTIAL-DIFFERENTIAL-EQUATIONS

Journal Article

Statistics and Computing, ISSN 0960-3174, 7/2019, Volume 29, Issue 4, pp. 753 - 773

We propose the Laplace method to derive approximate inference for Gaussian process (GP) regression in the location and scale parameters of the student- $$...

Statistics and Computing/Statistics Programs | Location-scale regression | Riemannian metric | Artificial Intelligence | Heteroscedastic noise | Approximate inference | Statistical Theory and Methods | Statistics | Fisher information matrix | Gaussian processes | Student- t model | Natural gradient | Probability and Statistics in Computer Science | Laplace approximation | Student-t model | STATISTICS & PROBABILITY | INFERENCE | BAYES FACTORS | COMPUTER SCIENCE, THEORY & METHODS | Markov processes | Monte Carlo method | Information management | Analysis

Statistics and Computing/Statistics Programs | Location-scale regression | Riemannian metric | Artificial Intelligence | Heteroscedastic noise | Approximate inference | Statistical Theory and Methods | Statistics | Fisher information matrix | Gaussian processes | Student- t model | Natural gradient | Probability and Statistics in Computer Science | Laplace approximation | Student-t model | STATISTICS & PROBABILITY | INFERENCE | BAYES FACTORS | COMPUTER SCIENCE, THEORY & METHODS | Markov processes | Monte Carlo method | Information management | Analysis

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 14

In this paper, we study the irregular growth of an entire function defined by the Laplace-Stieltjes transform of finite order convergent in the whole complex...

44A10 | Laplace-Stieltjes transform | Analysis | irregular growth | approximate | Mathematics, general | Mathematics | Applications of Mathematics | error | 30D15 | MATHEMATICS | MATHEMATICS, APPLIED | RIGHT HALF-PLANE | GROWTH | CONVERGENT | VALUES | DIRICHLET SERIES | Queuing theory | Error analysis | Approximation | Transformations (mathematics) | Entire functions | Research

44A10 | Laplace-Stieltjes transform | Analysis | irregular growth | approximate | Mathematics, general | Mathematics | Applications of Mathematics | error | 30D15 | MATHEMATICS | MATHEMATICS, APPLIED | RIGHT HALF-PLANE | GROWTH | CONVERGENT | VALUES | DIRICHLET SERIES | Queuing theory | Error analysis | Approximation | Transformations (mathematics) | Entire functions | Research

Journal Article

JOURNAL OF APPROXIMATION THEORY, ISSN 0021-9045, 12/2019, Volume 248

In this paper we obtain an approximation for the multivariate Laplace's integral with a large parameter and estimate error term for two cases, when the maximum...

MATHEMATICS | Error estimates | Central limit theorem | Law of large numbers | Asymptotic approximation of integrals | Multivariate Laplace's method | Limit theorems

MATHEMATICS | Error estimates | Central limit theorem | Law of large numbers | Asymptotic approximation of integrals | Multivariate Laplace's method | Limit theorems

Journal Article

Theoretical and Applied Genetics, ISSN 0040-5752, 2/2016, Volume 129, Issue 2, pp. 215 - 225

A novel reparametrization-based INLA approach as a fast alternative to MCMC for the Bayesian estimation of genetic parameters in multivariate animal model is...

Life Sciences | Biochemistry, general | Biotechnology | Plant Biochemistry | Plant Breeding/Biotechnology | Agriculture | Plant Genetics & Genomics | HORTICULTURE | AGRONOMY | MIXED MODELS | GENETICS & HEREDITY | BREEDING VALUES | BLUP | LINEAR UNBIASED PREDICTION | SELECTION | PLANT SCIENCES | Likelihood Functions | Markov Chains | Algorithms | Animals | Quantitative Trait, Heritable | Breeding | Pedigree | Computer Simulation | Bayes Theorem | Models, Genetic | Monte Carlo Method | Quantitative trait loci | Usage | Models | Laplace transformation | Mathematical models | Approximation theory | Original

Life Sciences | Biochemistry, general | Biotechnology | Plant Biochemistry | Plant Breeding/Biotechnology | Agriculture | Plant Genetics & Genomics | HORTICULTURE | AGRONOMY | MIXED MODELS | GENETICS & HEREDITY | BREEDING VALUES | BLUP | LINEAR UNBIASED PREDICTION | SELECTION | PLANT SCIENCES | Likelihood Functions | Markov Chains | Algorithms | Animals | Quantitative Trait, Heritable | Breeding | Pedigree | Computer Simulation | Bayes Theorem | Models, Genetic | Monte Carlo Method | Quantitative trait loci | Usage | Models | Laplace transformation | Mathematical models | Approximation theory | Original

Journal Article

IET Generation, Transmission & Distribution, ISSN 1751-8687, 6/2017, Volume 11, Issue 8, pp. 2050 - 2055

The authors present a methodology to improve the rational modelling of non-uniform lines (NuLs). First, they formulate a segmented chain matrix representation...

Research Article | rational modelling improvement | DEPENDENT TRANSMISSION-LINES | poorly observable mode identification | transmission towers | segmented chain matrix representation | rational functions | ELECTRICAL CHARACTERISTICS | rational approximation | poles and towers | approximation theory | admittance matrix | NuL modelling | pole identification improvement | numerical Laplace transform | IMPLEMENTATION | transmission line matrix methods | Laplace transforms | nonuniform line modelling | SIMULATION | TRANSIENT ANALYSIS | ENGINEERING, ELECTRICAL & ELECTRONIC | mode revealing transformation matrix | electric admittance | power overhead lines | nodal admittance formulation | MULTIPORT SYSTEMS | WAVE-PROPAGATION

Research Article | rational modelling improvement | DEPENDENT TRANSMISSION-LINES | poorly observable mode identification | transmission towers | segmented chain matrix representation | rational functions | ELECTRICAL CHARACTERISTICS | rational approximation | poles and towers | approximation theory | admittance matrix | NuL modelling | pole identification improvement | numerical Laplace transform | IMPLEMENTATION | transmission line matrix methods | Laplace transforms | nonuniform line modelling | SIMULATION | TRANSIENT ANALYSIS | ENGINEERING, ELECTRICAL & ELECTRONIC | mode revealing transformation matrix | electric admittance | power overhead lines | nodal admittance formulation | MULTIPORT SYSTEMS | WAVE-PROPAGATION

Journal Article

Communications in Statistics - Simulation and Computation, ISSN 0361-0918, 01/2015, Volume 44, Issue 1, pp. 154 - 167

Recently, Kambo and his co-researchers (2012) proposed a method of approximation for evaluating the one-dimensional renewal function based on the first three...

Free replacement warranty | Two-dimensional renewal function | Primary 60K05 | Bivariate Laplace transform | Bivariate renewal process | Secondary 60K20 | LAPLACE TRANSFORMS | SERIES | EQUATIONS | STATISTICS & PROBABILITY | NUMERICAL INVERSION | RELIABILITY | PRODUCT WARRANTY MANAGEMENT | WEIBULL | POLICIES | BOUNDS | 2-DIMENSIONAL WARRANTY | Laplace transforms | Warranties | Approximation | Computer simulation | Mathematical analysis | Pareto optimality | Mathematical models | Two dimensional | Weibull distribution

Free replacement warranty | Two-dimensional renewal function | Primary 60K05 | Bivariate Laplace transform | Bivariate renewal process | Secondary 60K20 | LAPLACE TRANSFORMS | SERIES | EQUATIONS | STATISTICS & PROBABILITY | NUMERICAL INVERSION | RELIABILITY | PRODUCT WARRANTY MANAGEMENT | WEIBULL | POLICIES | BOUNDS | 2-DIMENSIONAL WARRANTY | Laplace transforms | Warranties | Approximation | Computer simulation | Mathematical analysis | Pareto optimality | Mathematical models | Two dimensional | Weibull distribution

Journal Article

Engineering Analysis with Boundary Elements, ISSN 0955-7997, 10/2018, Volume 95, pp. 124 - 141

The cuckoo search (CS) algorithm combined with Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm (CS-BFGS) is proposed to identify time-dependent boundary...

DRBEM | Boundary conditions | Inverse problems | Cuckoo search algorithm | Polynomial approximation | Broyden-Fletcher-Goldfarb-Shanno algorithm | LAPLACE EQUATION | ELEMENT METHOD | CAUCHY-PROBLEM | CONJUGATE-GRADIENT METHOD | HEAT-CONDUCTION PROBLEMS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | NONLINEAR INVERSE PROBLEM | FUNCTIONALLY GRADED MATERIALS | LEVENBERG-MARQUARDT ALGORITHM | FUNDAMENTAL SOLUTION | Algorithms

DRBEM | Boundary conditions | Inverse problems | Cuckoo search algorithm | Polynomial approximation | Broyden-Fletcher-Goldfarb-Shanno algorithm | LAPLACE EQUATION | ELEMENT METHOD | CAUCHY-PROBLEM | CONJUGATE-GRADIENT METHOD | HEAT-CONDUCTION PROBLEMS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | NONLINEAR INVERSE PROBLEM | FUNCTIONALLY GRADED MATERIALS | LEVENBERG-MARQUARDT ALGORITHM | FUNDAMENTAL SOLUTION | Algorithms

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 7/2019, Volume 113, Issue 3, pp. 2665 - 2677

In the paper, by means of the monotonicity rule for the ratio of two Laplace transform we determine the best $$a,b>0$$ a , b > 0 such that the double...

Primary 33B15 | 26A51 | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Applications of Mathematics | 26A48 | Gamma function | Laplace transform | Complete monotonicity | Secondary 26D15 | Inequality | MATHEMATICS | Asymptotic series | Laplace transforms

Primary 33B15 | 26A51 | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Applications of Mathematics | 26A48 | Gamma function | Laplace transform | Complete monotonicity | Secondary 26D15 | Inequality | MATHEMATICS | Asymptotic series | Laplace transforms

Journal Article

Transport in Porous Media, ISSN 0169-3913, 9/2012, Volume 94, Issue 3, pp. 775 - 793

We introduce a finite-difference method to simulate pore scale steady-state creeping fluid flow in porous media. First, a geometrical approximation is invoked...

Earth Sciences | Hydrogeology | Pore scale | Finite differences | Civil Engineering | Geotechnical Engineering & Applied Earth Sciences | Permeability | Geometrical pore approximation | Industrial Chemistry/Chemical Engineering | Classical Continuum Physics | Generalized Laplace equation | ENGINEERING, CHEMICAL | GAS-FLOW | NANOPORES | NETWORK MODEL | Approximation | Computational fluid dynamics | Computer simulation | Fluid flow | Laplace equation | Porous media flow | Ground truth | Model accuracy | Fluid pressure | Convergence | Porous media | Flow simulation | Mathematical analysis | Equilibrium flow | Modelling | Grid refinement (mathematics) | Porosity | Finite difference method

Earth Sciences | Hydrogeology | Pore scale | Finite differences | Civil Engineering | Geotechnical Engineering & Applied Earth Sciences | Permeability | Geometrical pore approximation | Industrial Chemistry/Chemical Engineering | Classical Continuum Physics | Generalized Laplace equation | ENGINEERING, CHEMICAL | GAS-FLOW | NANOPORES | NETWORK MODEL | Approximation | Computational fluid dynamics | Computer simulation | Fluid flow | Laplace equation | Porous media flow | Ground truth | Model accuracy | Fluid pressure | Convergence | Porous media | Flow simulation | Mathematical analysis | Equilibrium flow | Modelling | Grid refinement (mathematics) | Porosity | Finite difference method

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 717 - 727

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to...

Ruin probability | Classical risk model | Uniform rate of approximation | Laplace transform inversion | Moment-recovered approximation | HAUSDORFF MOMENT PROBLEM | MATHEMATICS, APPLIED | Occupational health and safety | Analysis | Algorithms | Usage | Epidemiology

Ruin probability | Classical risk model | Uniform rate of approximation | Laplace transform inversion | Moment-recovered approximation | HAUSDORFF MOMENT PROBLEM | MATHEMATICS, APPLIED | Occupational health and safety | Analysis | Algorithms | Usage | Epidemiology

Journal Article

Computational Mechanics, ISSN 0178-7675, 11/2010, Volume 46, Issue 6, pp. 805 - 812

Meshless local Petrov-Galerkin (MLPG) method is discussed for solving 2D, nonlinear, elliptic p-Laplace or p-harmonic equation in this article. The problem is...

Injection gate | Engineering | MLPG method | p -Laplace equation | Meshless method | Divergence theorem | Computational Science and Engineering | Theoretical and Applied Mechanics | MLS approximation | Classical Continuum Physics | p-Laplace equation | MESHLESS | LBIE METHOD | SCHRODINGER-EQUATION | KERNEL PARTICLE METHODS | DISCRETIZATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | FINITE-ELEMENT | POINT COLLOCATION METHOD | COMPUTATIONAL MECHANICS | HEAT-CONDUCTION | PETROV-GALERKIN METHOD | Finite element method | Domains | Interpolation | Divergence | Approximation | Mathematical analysis | Integral equations | Meshless methods | Boundary integral method | Galerkin method | Computation | Spreads | Boundaries

Injection gate | Engineering | MLPG method | p -Laplace equation | Meshless method | Divergence theorem | Computational Science and Engineering | Theoretical and Applied Mechanics | MLS approximation | Classical Continuum Physics | p-Laplace equation | MESHLESS | LBIE METHOD | SCHRODINGER-EQUATION | KERNEL PARTICLE METHODS | DISCRETIZATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | FINITE-ELEMENT | POINT COLLOCATION METHOD | COMPUTATIONAL MECHANICS | HEAT-CONDUCTION | PETROV-GALERKIN METHOD | Finite element method | Domains | Interpolation | Divergence | Approximation | Mathematical analysis | Integral equations | Meshless methods | Boundary integral method | Galerkin method | Computation | Spreads | Boundaries

Journal Article

Technometrics, ISSN 0040-1706, 08/2012, Volume 54, Issue 3, p. 225

Journal Article

IEEE Transactions on Cybernetics, ISSN 2168-2267, 12/2014, Volume 44, Issue 12, pp. 2613 - 2625

In order to deal with the sequential decision problems with large or continuous state spaces, feature representation and function approximation have been a...

Laplace equations | Economic indicators | value function approximation | Markov decision processes | Clustering algorithms | Aerospace electronics | learning control | Approximation algorithms | Approximate dynamic programming | clustering | Function approximation | reinforcement learning | POLICY ITERATION | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, CYBERNETICS | Models, Theoretical | Algorithms | Numerical Analysis, Computer-Assisted | Artificial Intelligence | Computer Simulation | Reinforcement (Psychology) | Pattern Recognition, Automated - methods | Optimization | Markov analysis | Learning | Policies | Approximation | Mathematical analysis | Clusters | Graphs | Mathematical models | Representations

Laplace equations | Economic indicators | value function approximation | Markov decision processes | Clustering algorithms | Aerospace electronics | learning control | Approximation algorithms | Approximate dynamic programming | clustering | Function approximation | reinforcement learning | POLICY ITERATION | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, CYBERNETICS | Models, Theoretical | Algorithms | Numerical Analysis, Computer-Assisted | Artificial Intelligence | Computer Simulation | Reinforcement (Psychology) | Pattern Recognition, Automated - methods | Optimization | Markov analysis | Learning | Policies | Approximation | Mathematical analysis | Clusters | Graphs | Mathematical models | Representations

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 16

By utilizing the concept of generalized order, we investigate the growth of Laplace–Stieltjes transform converging in the half plane and obtain one equivalence...

Laplace–Stieltjes transform | Approximation | 44A10 | Analysis | Half plane | Mathematics, general | Error | Mathematics | Applications of Mathematics | 30D15 | MATHEMATICS | MATHEMATICS, APPLIED | Laplace-Stieltjes transform | Research

Laplace–Stieltjes transform | Approximation | 44A10 | Analysis | Half plane | Mathematics, general | Error | Mathematics | Applications of Mathematics | 30D15 | MATHEMATICS | MATHEMATICS, APPLIED | Laplace-Stieltjes transform | Research

Journal Article