The Annals of Statistics, ISSN 0090-5364, 12/2004, Volume 32, Issue 6, pp. 2385 - 2411

The term "sequential Monte Carlo methods" or, equivalently, "particle filters," refers to a general class of iterative algorithms that performs Monte Carlo...

Monte Carlo methods | Central limit theorem | Filtration | Approximation | Algorithms | Particle density | Bayesian Methodology | Mathematical functions | Data smoothing | Weighting functions | Genetic algorithms | Residual resampling | Recursive Monte Carlo filter | Resample-move algorithms | State-space model | Markov chain Monte Carlo | Particle filter | resample-move algorithms | APPROXIMATION | STABILITY | state-space model | STATISTICS & PROBABILITY | recursive Monte Carlo filter | particle filter | residual resampling | MODELS | PARTICLE FILTERS | SYSTEMS | EQUATION | Statistics | Mathematics | 65C05 | 82C80 | 62F15 | 60F05 | 62L10

Monte Carlo methods | Central limit theorem | Filtration | Approximation | Algorithms | Particle density | Bayesian Methodology | Mathematical functions | Data smoothing | Weighting functions | Genetic algorithms | Residual resampling | Recursive Monte Carlo filter | Resample-move algorithms | State-space model | Markov chain Monte Carlo | Particle filter | resample-move algorithms | APPROXIMATION | STABILITY | state-space model | STATISTICS & PROBABILITY | recursive Monte Carlo filter | particle filter | residual resampling | MODELS | PARTICLE FILTERS | SYSTEMS | EQUATION | Statistics | Mathematics | 65C05 | 82C80 | 62F15 | 60F05 | 62L10

Journal Article

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Numerical approximation of BSDEs using local polynomial drivers and branching processes

Monte Carlo Methods and Applications, ISSN 0929-9629, 12/2017, Volume 23, Issue 4, pp. 241 - 263

We propose a new numerical scheme for Backward Stochastic Differential Equations (BSDEs) based on branching processes. We approximate an arbitrary (Lipschitz)...

Monte Carlo methods | 60J85 | 60J60 | branching process | 65C05 | BSDE | 60H35 | Stochastic differential equations | Approximation theory | Polynomials | Branching processes | Analysis | Branching (mathematics) | Computer simulation | Picard iterations | Mathematical analysis | Differential equations | Markov processes | Random variables | Iterative methods | Probability | Mathematics

Monte Carlo methods | 60J85 | 60J60 | branching process | 65C05 | BSDE | 60H35 | Stochastic differential equations | Approximation theory | Polynomials | Branching processes | Analysis | Branching (mathematics) | Computer simulation | Picard iterations | Mathematical analysis | Differential equations | Markov processes | Random variables | Iterative methods | Probability | Mathematics

Journal Article

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Equi-energy sampler with applications in statistical inference and statistical mechanics

Annals of Statistics, ISSN 0090-5364, 08/2006, Volume 34, Issue 4, pp. 1581 - 1619

We introduce a new sampling algorithm, the equi-energy sampler, for efficient statistical sampling and estimation. Complementary to the widely used...

Density of states | Temperature | Energy | Protein folding | Estimation | Microcanonical distribution | Motif sampling | Sampling | MOTIFS | motif sampling | MARKOV-CHAINS | SEQUENCES | sampling | ALGORITHM | STATISTICS & PROBABILITY | DISCOVERY | CHAIN MONTE-CARLO | estimation | micro-canonical distribution | ALIGNMENT | MODELS | temperature | protein folding | SIMULATIONS | energy | density of states | POSTERIOR DISTRIBUTIONS | 65C40 | microcanonical distribution | 65C05 | 82B80 | 62F15

Density of states | Temperature | Energy | Protein folding | Estimation | Microcanonical distribution | Motif sampling | Sampling | MOTIFS | motif sampling | MARKOV-CHAINS | SEQUENCES | sampling | ALGORITHM | STATISTICS & PROBABILITY | DISCOVERY | CHAIN MONTE-CARLO | estimation | micro-canonical distribution | ALIGNMENT | MODELS | temperature | protein folding | SIMULATIONS | energy | density of states | POSTERIOR DISTRIBUTIONS | 65C40 | microcanonical distribution | 65C05 | 82B80 | 62F15

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 8/2006, Volume 16, Issue 3, pp. 1462 - 1505

In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the...

Ergodic theory | Transition probabilities | Integers | Approximation | Logical proofs | Markov chains | Metropolitan areas | Poisson equation | Martingales | Perceptron convergence procedure | Adaptive Markov chain Monte Carlo | Self-tuning algorithm | Randomly varying truncation | Martingale | Poisson method | State-dependent noise | Stochastic approximation | Metropolis-Hastings algorithm | HASTINGS | randomly varying truncation | STATISTICS & PROBABILITY | self-tuning algorithm | STOCHASTIC-APPROXIMATION | METROPOLIS ALGORITHMS | POISSON EQUATION | RATES | EM ALGORITHM | adaptive Markov chain Monte Carlo | martingale | CONVERGENCE | stochastic approximation | state-dependent noise | Mathematics - Probability | Metropolis–Hastings algorithm | 65C40 | 93E35 | 60J27 | 65C05 | 60J35

Ergodic theory | Transition probabilities | Integers | Approximation | Logical proofs | Markov chains | Metropolitan areas | Poisson equation | Martingales | Perceptron convergence procedure | Adaptive Markov chain Monte Carlo | Self-tuning algorithm | Randomly varying truncation | Martingale | Poisson method | State-dependent noise | Stochastic approximation | Metropolis-Hastings algorithm | HASTINGS | randomly varying truncation | STATISTICS & PROBABILITY | self-tuning algorithm | STOCHASTIC-APPROXIMATION | METROPOLIS ALGORITHMS | POISSON EQUATION | RATES | EM ALGORITHM | adaptive Markov chain Monte Carlo | martingale | CONVERGENCE | stochastic approximation | state-dependent noise | Mathematics - Probability | Metropolis–Hastings algorithm | 65C40 | 93E35 | 60J27 | 65C05 | 60J35

Journal Article

Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 06/2019, Volume 29, Issue 6, p. 063107

We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by diffusion. The scheme is based on...

MATHEMATICS, APPLIED | STOCHASTIC DIFFERENTIAL-EQUATIONS | RISK-SENSITIVE CONTROL | PHYSICS, MATHEMATICAL | LARGE DEVIATIONS

MATHEMATICS, APPLIED | STOCHASTIC DIFFERENTIAL-EQUATIONS | RISK-SENSITIVE CONTROL | PHYSICS, MATHEMATICAL | LARGE DEVIATIONS

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 11/2005, Volume 15, Issue 4, pp. 2422 - 2444

We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection...

Brownian motion | Gaussian distributions | Algorithms | Approximation | Differential equations | Coordinate systems | Skeleton | Random variables | Probabilities | Brownian bridge | Boundary hitting time | Rejection sampling | Exact simulation | Girsanov theorem | exact simulation | STATISTICS & PROBABILITY | boundary hitting time | rejection sampling | Mathematics - Probability | 65C05 | 60J60

Brownian motion | Gaussian distributions | Algorithms | Approximation | Differential equations | Coordinate systems | Skeleton | Random variables | Probabilities | Brownian bridge | Boundary hitting time | Rejection sampling | Exact simulation | Girsanov theorem | exact simulation | STATISTICS & PROBABILITY | boundary hitting time | rejection sampling | Mathematics - Probability | 65C05 | 60J60

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2008, Volume 46, Issue 3, pp. 1519 - 1553

We define a Walsh space which contains all functions whose partial mixed derivatives up to order 6 ≥ 1 exist and have finite variation. In particular, for a...

Integers | Series convergence | Prime numbers | Numerical integration | Real numbers | Walsh function | Mathematical functions | Matrices | Mathematics | Sobolev spaces | Digital nets and sequences | Quasi-Monte Carlo | Walsh functions | Walsh | MATHEMATICS, APPLIED | numerical integration | SERIES | functions | DIGITAL NETS | LATTICE RULES | ALGORITHMS | MULTIVARIATE INTEGRATION | SOBOLEV SPACES | quasi-Monte Carlo | digital nets and sequences | NUMERICAL-INTEGRATION | DISCREPANCY | WEIGHTS | CONSTRUCTIONS | Mathematics - Numerical Analysis

Integers | Series convergence | Prime numbers | Numerical integration | Real numbers | Walsh function | Mathematical functions | Matrices | Mathematics | Sobolev spaces | Digital nets and sequences | Quasi-Monte Carlo | Walsh functions | Walsh | MATHEMATICS, APPLIED | numerical integration | SERIES | functions | DIGITAL NETS | LATTICE RULES | ALGORITHMS | MULTIVARIATE INTEGRATION | SOBOLEV SPACES | quasi-Monte Carlo | digital nets and sequences | NUMERICAL-INTEGRATION | DISCREPANCY | WEIGHTS | CONSTRUCTIONS | Mathematics - Numerical Analysis

Journal Article

The Annals of Statistics, ISSN 0090-5364, 10/2005, Volume 33, Issue 5, pp. 1983 - 2021

Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform computations in general state space models. We discuss and compare...

Monte Carlo methods | Approximation | Central limit theorem | Filtration | Monte Carlo in State Space Models | Sampling rates | Recursion | Data smoothing | Density | Estimators | Induction assumption | Sampling importance resampling | State space models | Auxiliary variables | Hidden Markov models | Filtering and smoothing | Particle filters | state space models | hidden Markov models | sampling importance resampling | central limit theorem | MODELS | filtering and smoothing | STABILITY | particle filters | auxiliary variables | STATISTICS & PROBABILITY | LIKELIHOOD | 60G35 | 62M09 | 65C05 | 60J22

Monte Carlo methods | Approximation | Central limit theorem | Filtration | Monte Carlo in State Space Models | Sampling rates | Recursion | Data smoothing | Density | Estimators | Induction assumption | Sampling importance resampling | State space models | Auxiliary variables | Hidden Markov models | Filtering and smoothing | Particle filters | state space models | hidden Markov models | sampling importance resampling | central limit theorem | MODELS | filtering and smoothing | STABILITY | particle filters | auxiliary variables | STATISTICS & PROBABILITY | LIKELIHOOD | 60G35 | 62M09 | 65C05 | 60J22

Journal Article

Communications in Statistics - Simulation and Computation, ISSN 0361-0918, 02/2017, Volume 46, Issue 2, pp. 1611 - 1627

A characterization of Burr Type III and Type XII distributions based on the method of percentiles (MOP) is introduced and contrasted with the method of...

Method of Percentiles | Method of Moments | Primary 62E17, 62F40, 62G05, 62G09, 62H05, 62H10, 62H12, 62H20; Secondary 65C05 | Monte Carlo Simulation | 62G05 | 62H05 | Primary 62E17 | Secondary 65C05 | 62G09 | STATISTICS & PROBABILITY | RELIABILITY | 62F40 | 62H20 | 62H10 | 62H12 | STANDS | Monte Carlo simulation | Fittings | Correlation | Computer simulation | Methodology | Efficiency | Computation | Bias | Burrs

Method of Percentiles | Method of Moments | Primary 62E17, 62F40, 62G05, 62G09, 62H05, 62H10, 62H12, 62H20; Secondary 65C05 | Monte Carlo Simulation | 62G05 | 62H05 | Primary 62E17 | Secondary 65C05 | 62G09 | STATISTICS & PROBABILITY | RELIABILITY | 62F40 | 62H20 | 62H10 | 62H12 | STANDS | Monte Carlo simulation | Fittings | Correlation | Computer simulation | Methodology | Efficiency | Computation | Bias | Burrs

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 6/2012, Volume 22, Issue 3, pp. 1167 - 1214

Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with...

Algorithms | Approximation | Local maximum | Covariance | Cost estimates | Polynomials | Mathematical moments | Design efficiency | Random variables | Estimators | High-level excursions | Monte Carlo | Gaussian random fields | Efficiency | Tail distributions | high-level excursions | efficiency | STATISTICS | tail distributions | STATISTICS & PROBABILITY | MICROWAVE BACKGROUND MAPS | Mathematics - Probability | 60G60 | 62G32 | 65C05 | 60G15

Algorithms | Approximation | Local maximum | Covariance | Cost estimates | Polynomials | Mathematical moments | Design efficiency | Random variables | Estimators | High-level excursions | Monte Carlo | Gaussian random fields | Efficiency | Tail distributions | high-level excursions | efficiency | STATISTICS | tail distributions | STATISTICS & PROBABILITY | MICROWAVE BACKGROUND MAPS | Mathematics - Probability | 60G60 | 62G32 | 65C05 | 60G15

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 03/2019, Volume 48, Issue 5, pp. 1166 - 1176

This paper investigates a class of location invariant non-positive moment-type estimators of extreme value index, which is highly flexible due to the tuning...

Bootstrap methodology | Primary 60G70 | Extreme value statistics | Secondary 65C05 | Extreme value index | Location-invariant moment-type estimation

Bootstrap methodology | Primary 60G70 | Extreme value statistics | Secondary 65C05 | Extreme value index | Location-invariant moment-type estimation

Journal Article

European Journal of Applied Mathematics, ISSN 0956-7925, 12/2017, Volume 28, Issue 6, pp. 949 - 972

The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored...

2010 AMS Subject Classification: Primary: 65C05 65C30 Secondary: 65N55 60H35 91-XX 35CXX | MATHEMATICS, APPLIED | Probabilistic Domain Decomposition | high-performance parallel computing | STOCHASTIC DIFFERENTIAL-EQUATIONS | APPROXIMATION | Marked branching diffusions | hybrid non-linear PDE solvers | BSDES | DOMAIN DECOMPOSITION | NUMERICAL ALGORITHM | MONTE-CARLO | Monte Carlo methods | DIFFUSION | BACKWARD SDES | SCHEMES | Algorithms | Computer simulation | Numerical methods | Parallel computers | Parallel processing | Solvers | Mathematical models | Probabilistic methods | Domain decomposition

2010 AMS Subject Classification: Primary: 65C05 65C30 Secondary: 65N55 60H35 91-XX 35CXX | MATHEMATICS, APPLIED | Probabilistic Domain Decomposition | high-performance parallel computing | STOCHASTIC DIFFERENTIAL-EQUATIONS | APPROXIMATION | Marked branching diffusions | hybrid non-linear PDE solvers | BSDES | DOMAIN DECOMPOSITION | NUMERICAL ALGORITHM | MONTE-CARLO | Monte Carlo methods | DIFFUSION | BACKWARD SDES | SCHEMES | Algorithms | Computer simulation | Numerical methods | Parallel computers | Parallel processing | Solvers | Mathematical models | Probabilistic methods | Domain decomposition

Journal Article

Communications in Statistics - Simulation and Computation, ISSN 0361-0918, 05/2017, Volume 46, Issue 5, pp. 3990 - 4003

The log-Birnbaum-Saunders regression model introduced by Rieck and Nedelman ( 1991 ) is useful for modeling lifetimes of materials and equipments subject to...

Bootstrap Bartlett correction | RESET test | Likelihood ratio test | Bootstrap | Secondary 65C05, 62F40 | Log-Birnbaum-Saunders model | Monte Carlo simulation | Primary 62F03, 62J02 | 62J02 | Secondary 65C05 | STATISTICS & PROBABILITY | MODELS | 62F40 | Primary 62F03 | DIAGNOSTICS | Economic models | Null hypothesis | Regression models | Computer simulation | Likelihood ratio | Mathematical models

Bootstrap Bartlett correction | RESET test | Likelihood ratio test | Bootstrap | Secondary 65C05, 62F40 | Log-Birnbaum-Saunders model | Monte Carlo simulation | Primary 62F03, 62J02 | 62J02 | Secondary 65C05 | STATISTICS & PROBABILITY | MODELS | 62F40 | Primary 62F03 | DIAGNOSTICS | Economic models | Null hypothesis | Regression models | Computer simulation | Likelihood ratio | Mathematical models

Journal Article

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General Error Estimates for the Longstaff–Schwartz Least-Squares Monte Carlo Algorithm

Mathematics of Operations Research, ISSN 0364-765X, 11/2019

Journal Article

The Annals of Statistics, ISSN 0090-5364, 2/2007, Volume 35, Issue 1, pp. 420 - 448

In the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performance of a given...

Statistical variance | Monte Carlo methods | Technical reports | Approximation | Infinity | Importance Sampling | Random walk | Markov chains | Mathematical functions | Estimators | Perceptron convergence procedure | Rao-Blackwellization | MCMC algorithm | Population Monte Carlo | Bayesian statistics | Kullback divergence | Proposal distribution | LLN | DISTRIBUTIONS | proposal distribution | STATISTICS & PROBABILITY | METROPOLIS ALGORITHM | population Monte Carlo | CHAIN MONTE-CARLO | 62L12 | 65-04 | 65C60 | 65C40 | 65C05 | Rao–Blackwellization | 60F05

Statistical variance | Monte Carlo methods | Technical reports | Approximation | Infinity | Importance Sampling | Random walk | Markov chains | Mathematical functions | Estimators | Perceptron convergence procedure | Rao-Blackwellization | MCMC algorithm | Population Monte Carlo | Bayesian statistics | Kullback divergence | Proposal distribution | LLN | DISTRIBUTIONS | proposal distribution | STATISTICS & PROBABILITY | METROPOLIS ALGORITHM | population Monte Carlo | CHAIN MONTE-CARLO | 62L12 | 65-04 | 65C60 | 65C40 | 65C05 | Rao–Blackwellization | 60F05

Journal Article

The Annals of Statistics, ISSN 0090-5364, 4/2010, Volume 38, Issue 2, pp. 1244 - 1278

We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor...

Approximation | Approximation algorithms | Mathematics | Credit risk | Logarithms | Random variables | Estimators | Martingales | Distribution functions | Truncation | Stochastic approximation | Law of iterated logarithm | Robbins-monro | Adaptive importance sampling | Quantile estimation | law of iterated logarithm | CONVERGENCE | STATISTICS & PROBABILITY | STOCHASTIC-APPROXIMATION | stochastic approximation | adaptive importance sampling | Robbins-Monro | 65C05 | 65C60 | Robbins–Monro | 62L20

Approximation | Approximation algorithms | Mathematics | Credit risk | Logarithms | Random variables | Estimators | Martingales | Distribution functions | Truncation | Stochastic approximation | Law of iterated logarithm | Robbins-monro | Adaptive importance sampling | Quantile estimation | law of iterated logarithm | CONVERGENCE | STATISTICS & PROBABILITY | STOCHASTIC-APPROXIMATION | stochastic approximation | adaptive importance sampling | Robbins-Monro | 65C05 | 65C60 | Robbins–Monro | 62L20

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2007, Volume 45, Issue 5, pp. 2141 - 2176

In this paper, we give explicit constructions of point sets in the s-dimensional unit cube yielding quasi-Monte Carlo algorithms which achieve the optimal rate...

Integers | Numerical quadratures | Real numbers | Natural numbers | Mathematical lattices | Walsh function | Hilbert spaces | Mathematical vectors | Mathematical functions | Matrices | Digital net | Digital sequence | Lattice rule | Numerical integration | Quasi-Monte Carlo method | digital net | MATHEMATICS, APPLIED | numerical integration | WEIGHTED SOBOLEV SPACES | SEQUENCES | LATTICE RULES | DIGITAL NETS | DISCREPANCY | quasi-Monte Carlo method | digital sequence | lattice rule | POINT SETS | Mathematics - Numerical Analysis

Integers | Numerical quadratures | Real numbers | Natural numbers | Mathematical lattices | Walsh function | Hilbert spaces | Mathematical vectors | Mathematical functions | Matrices | Digital net | Digital sequence | Lattice rule | Numerical integration | Quasi-Monte Carlo method | digital net | MATHEMATICS, APPLIED | numerical integration | WEIGHTED SOBOLEV SPACES | SEQUENCES | LATTICE RULES | DIGITAL NETS | DISCREPANCY | quasi-Monte Carlo method | digital sequence | lattice rule | POINT SETS | Mathematics - Numerical Analysis

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 8/2007, Volume 17, Issue 4, pp. 1306 - 1346

Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of...

Saddle points | Heuristics | Boundary conditions | Markov chains | Mathematical moments | Queueing networks | Random variables | Estimators | Consistent estimators | Term weighting | Sub-solutions | Asymptotic optimality | Isaacs equation | Importance sampling | Tandem queueing networks | QUEUES | subsolutions | EXCESSIVE BACKLOGS | STATISTICS & PROBABILITY | asymptotic optimality | importance sampling | SIMULATION | tandem queueing networks | LARGE DEVIATIONS | Mathematics - Probability | 60F10 | 49N90 | 65C05

Saddle points | Heuristics | Boundary conditions | Markov chains | Mathematical moments | Queueing networks | Random variables | Estimators | Consistent estimators | Term weighting | Sub-solutions | Asymptotic optimality | Isaacs equation | Importance sampling | Tandem queueing networks | QUEUES | subsolutions | EXCESSIVE BACKLOGS | STATISTICS & PROBABILITY | asymptotic optimality | importance sampling | SIMULATION | tandem queueing networks | LARGE DEVIATIONS | Mathematics - Probability | 60F10 | 49N90 | 65C05

Journal Article

Communications in Statistics: Simulation and Computation, ISSN 0361-0918, 2019, pp. 1 - 19

Journal Article

The Annals of Statistics, ISSN 0090-5364, 10/2009, Volume 37, Issue 5B, pp. 2626 - 2654

Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305-320] as a general...

Monte Carlo methods | Approximation | Algorithms | Markov chains | Mathematical functions | Mathematical vectors | Bayesian networks | Data smoothing | Estimators | Perceptron convergence procedure | Stochastic approximation Monte Carlo | Reversible jump | Model selection | Smoothing | Markov chain Monte Carlo | REGRESSION | reversible jump | ALGORITHM | STATISTICS & PROBABILITY | STOCHASTIC-APPROXIMATION | INFERENCE | CHAIN MONTE-CARLO | stochastic approximation Monte Carlo | CONVERGENCE | OPTIMIZATION | smoothing | COMPUTATION | SIMULATIONS | 65C05 | 60J22

Monte Carlo methods | Approximation | Algorithms | Markov chains | Mathematical functions | Mathematical vectors | Bayesian networks | Data smoothing | Estimators | Perceptron convergence procedure | Stochastic approximation Monte Carlo | Reversible jump | Model selection | Smoothing | Markov chain Monte Carlo | REGRESSION | reversible jump | ALGORITHM | STATISTICS & PROBABILITY | STOCHASTIC-APPROXIMATION | INFERENCE | CHAIN MONTE-CARLO | stochastic approximation Monte Carlo | CONVERGENCE | OPTIMIZATION | smoothing | COMPUTATION | SIMULATIONS | 65C05 | 60J22

Journal Article

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