Journal of Mechanical Design, Transactions of the ASME, ISSN 1050-0472, 2015, Volume 137, Issue 3, pp. 31405 - np

A new reliability analysis method is proposed for time-dependent problems with explicit in time limit-state functions of input random variables and input random processes using the total probability...

SYSTEMS | SUBSET SIMULATION | DESIGN | ENGINEERING, MECHANICAL | Monte Carlo method | Usage | Blades | Analysis | Limit theorems (Probability theory) | Event history analysis | Design and construction | Turbines | Theorems | Computer simulation | Mathematical analysis | Limit states | Reliability analysis | Mathematical models | Random processes | Standards

SYSTEMS | SUBSET SIMULATION | DESIGN | ENGINEERING, MECHANICAL | Monte Carlo method | Usage | Blades | Analysis | Limit theorems (Probability theory) | Event history analysis | Design and construction | Turbines | Theorems | Computer simulation | Mathematical analysis | Limit states | Reliability analysis | Mathematical models | Random processes | Standards

Journal Article

2004, ISBN 9780521829717, xvi, 124

This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability is a mode of judgment...

Probabilities | Judgment

Probabilities | Judgment

Book

Stochastic Processes and their Applications, ISSN 0304-4149, 02/2013, Volume 123, Issue 2, pp. 651 - 674

...]. More precisely, we prove, without additional assumptions, that the sequence {Fn} actually converges in total variation and that the law of F...

Wiener chaos | Convergence in distribution | Malliavin calculus | Convergence in total variation | Multiple Wiener–Itô integral | MultipleWiener-Itô integral | CENTRAL LIMIT-THEOREMS | Multiple Wiener-Ito integral | STATISTICS & PROBABILITY | MULTIPLE STOCHASTIC INTEGRALS | Probability | Mathematics

Wiener chaos | Convergence in distribution | Malliavin calculus | Convergence in total variation | Multiple Wiener–Itô integral | MultipleWiener-Itô integral | CENTRAL LIMIT-THEOREMS | Multiple Wiener-Ito integral | STATISTICS & PROBABILITY | MULTIPLE STOCHASTIC INTEGRALS | Probability | Mathematics

Journal Article

2000, 1. Aufl., Wiley series in probability and statistics., ISBN 047149464X, xiv, 586

This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on...

Bayesian statistical decision theory | statistical models | Mathematics | Statistical decision

Bayesian statistical decision theory | statistical models | Mathematics | Statistical decision

Book

ANNALS OF PROBABILITY, ISSN 0091-1798, 11/2019, Volume 47, Issue 6, pp. 3762 - 3811

The goal of this paper is to estimate the total variation distance between two general stochastic polynomials...

CENTRAL LIMIT-THEOREMS | UNIVERSALITY | SEQUENCES | invariance principles | U-statistics | quadratic central limit theorem | STATISTICS & PROBABILITY | Stochastic polynomials | abstract Malliavin calculus | Mathematics - Probability | Probability | Mathematics

CENTRAL LIMIT-THEOREMS | UNIVERSALITY | SEQUENCES | invariance principles | U-statistics | quadratic central limit theorem | STATISTICS & PROBABILITY | Stochastic polynomials | abstract Malliavin calculus | Mathematics - Probability | Probability | Mathematics

Journal Article

2003, 1. Aufl., Wiley series in probability and statistics, ISBN 9780471486954, 478

The use of Bayesian statistics has grown significantly in recent years, and will undoubtedly continue to do so. Applied Bayesian Modellingis the follow-up to...

Bayesian statistical decision theory | Mathematical statistics | Mathematics

Bayesian statistical decision theory | Mathematical statistics | Mathematics

eBook

2000, ISBN 9789810243227, xiv, 177

Book

1977, 4th ed. --, Graduate texts in mathematics, ISBN 9780387902104, Volume 45-46, 2 v.

Book

BMC medical research methodology, ISSN 1471-2288, 2017, Volume 17, Issue 1, pp. 128 - 10

... to summarize the benefit of patient-specific instrumentation on the alignment of total knee replacement from previously published evidence...

Direct probability | Cumulative | Posterior probability | Bayesian statistics | Predictive probability | Meta-analysis | Superiority | SURGERY | RANDOMIZED CONTROLLED-TRIALS | MULTICENTER | METAANALYSIS | BIAS | PATIENT-SPECIFIC INSTRUMENTS | TOTAL KNEE ARTHROPLASTY | COMPUTED-TOMOGRAPHY | COMPONENT ALIGNMENT | CLINICAL-TRIALS | HEALTH CARE SCIENCES & SERVICES | Treatment Outcome | Likelihood Functions | Clinical Trials as Topic | Bias | Humans | Bayes Theorem | Bayesian statistical decision theory | Studies | Clinical trials | Probability | Research | Joint surgery | Random variables | Information sources | Life Sciences | Human health and pathology | Santé publique et épidémiologie | Surgery

Direct probability | Cumulative | Posterior probability | Bayesian statistics | Predictive probability | Meta-analysis | Superiority | SURGERY | RANDOMIZED CONTROLLED-TRIALS | MULTICENTER | METAANALYSIS | BIAS | PATIENT-SPECIFIC INSTRUMENTS | TOTAL KNEE ARTHROPLASTY | COMPUTED-TOMOGRAPHY | COMPONENT ALIGNMENT | CLINICAL-TRIALS | HEALTH CARE SCIENCES & SERVICES | Treatment Outcome | Likelihood Functions | Clinical Trials as Topic | Bias | Humans | Bayes Theorem | Bayesian statistical decision theory | Studies | Clinical trials | Probability | Research | Joint surgery | Random variables | Information sources | Life Sciences | Human health and pathology | Santé publique et épidémiologie | Surgery

Journal Article

1988, 2nd ed. --, Springer texts in statistics., ISBN 0387966951, xviii, 467

Book

2011, Mathematical surveys and monographs, ISBN 9780821852859, Volume 171, xiv, 632

Book

1990, 2nd ed., The Duxbury series in statistics and decision sciences., ISBN 9780534916541, xxii, 810

Book

2009, 1. Aufl., ISBN 9780470772690, viii, 268

In a probabilistic model, a rare event is an event with a very small probability of occurrence...

Mathematics | Limit theorems (Probability theory) | Monte Carlo method | Data processing | System analysis | Digital computer simulation

Mathematics | Limit theorems (Probability theory) | Monte Carlo method | Data processing | System analysis | Digital computer simulation

Book

Bernoulli, ISSN 1350-7265, 08/2016, Volume 22, Issue 3, pp. 1839 - 1893

Given random samples drawn i.i.d. from a probability measure P (defined on say, R-d), it is well-known that the empirical estimator is an optimal estimator of P in weak topology but not even a consistent estimator of its density...

Reproducing kernel Hilbert space | U-processes | Uniform central limit theorem | Exponential inequality | Kernel density estimator | Bounded Lipschitz metric | Smoothed empirical processes | Adaptive estimation | Two-sample test | Rademacher chaos | Total variation distance | uniform central limit theorem | EMPIRICAL PROCESSES | WAVELET | STATISTICS & PROBABILITY | bounded Lipschitz metric | DENSITY | SPACE | LIMIT-THEOREMS | ADAPTATION | CONVERGENCE | reproducing kernel Hilbert space | kernel density estimator | smoothed empirical processes | exponential inequality | two-sample test | adaptive estimation | total variation distance

Reproducing kernel Hilbert space | U-processes | Uniform central limit theorem | Exponential inequality | Kernel density estimator | Bounded Lipschitz metric | Smoothed empirical processes | Adaptive estimation | Two-sample test | Rademacher chaos | Total variation distance | uniform central limit theorem | EMPIRICAL PROCESSES | WAVELET | STATISTICS & PROBABILITY | bounded Lipschitz metric | DENSITY | SPACE | LIMIT-THEOREMS | ADAPTATION | CONVERGENCE | reproducing kernel Hilbert space | kernel density estimator | smoothed empirical processes | exponential inequality | two-sample test | adaptive estimation | total variation distance

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 06/2015, Volume 125, Issue 6, pp. 2190 - 2205

.... An old and celebrated result of Prohorov (1952) asserts that Sn converges in total variation to the standard Gaussian distribution if and only if Sn0 has an absolutely continuous component for some integer n0≥1...

Invariance principle | Absolute continuity | Convergence in law | Convergence in total variation | INEQUALITIES | CONVERGENCE | STATISTICS & PROBABILITY | CENTRAL-LIMIT-THEOREM | Probability | Mathematics

Invariance principle | Absolute continuity | Convergence in law | Convergence in total variation | INEQUALITIES | CONVERGENCE | STATISTICS & PROBABILITY | CENTRAL-LIMIT-THEOREM | Probability | Mathematics

Journal Article

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