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|a Giordano, Arthur A.
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|a Monte Carlo Integration with MATLAB and Simulink.
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|a 1st ed.
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|a Newark :
|b John Wiley & Sons, Incorporated,
|c 2026.
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|c ©2026.
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|a 1 online resource (381 pages)
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|a Presents detailed guidance on Monte Carlo integration methods for complex applications Monte Carlo integration has become an indispensable computational tool across science, engineering, mathematics, and economics, offering effective solutions where traditional numerical integration methods fall short.
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|a Description based on publisher supplied metadata and other sources.
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|a Part of the metadata in this record was created by AI, based on the text of the resource.
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|a Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- About the Software -- Abbreviations and Acronyms -- List of MATLAB® and Simulink® Programs -- About the Companion Website -- Chapter 1 Monte Carlo and Numerical Integration Methods -- Chapter 2 Numerical Integration -- 2.1 Multiple Numerical Integration Methods: Evaluate I&equals -- ∫abf(x)dx -- 2.1.1 General Formula -- 2.1.2 Rectangular Method -- 2.1.3 Trapezoidal Method -- 2.1.4 Simpson Method -- 2.1.5 MATLAB® Program Method Integral -- 2.2 Numerical Integration with Gauss Quadrature: Evaluate I&equals
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|a ∫01x3dx -- Estimates from rand in mcx3 -- Summary -- 4.2 Monte Carlo Integration of a Function I&equals -- ∫abf(x)dx, X Is an r.v. and f(x) &equals -- x exp(−x) -- 4.3 Investigation of Integral I&equals -- ∫abf(x)dx Function f(x) &equals -- x3 exp(−x) with X Having pdf U(a, b) -- 4.3.1 MATLAB Program-mcrandsum Uniform pdf Evaluate I &equals -- ∫abx3exp(−x)dx -- Problems -- Chapter 5 Monte Carlo Integration: A Binary Choice -- 5.1 Hit-or-Miss Sampling -- 5.1.1 Bound on the Error I−I^HMhttps://cse.engineering.nyu.edu/. K. Ming Leung (2000) has another description of this error.
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|a Monte Carlo method.
|7 Generated by AI.
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|a Numerical integration.
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|a Electronic books.
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|z 1-394-40704-1
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|u http://proxy.library.tamu.edu/login?url=https://onlinelibrary.wiley.com/book/10.1002/9781394407101
|z Connect to the full text of this electronic book
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|a Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- About the Software -- Abbreviations and Acronyms -- List of MATLAB® and Simulink® Programs -- About the Companion Website -- Chapter 1 Monte Carlo and Numerical Integration Methods -- Chapter 2 Numerical Integration -- 2.1 Multiple Numerical Integration Methods: Evaluate I& -- equals -- ∫abf(x)dx -- 2.1.1 General Formula -- 2.1.2 Rectangular Method -- 2.1.3 Trapezoidal Method -- 2.1.4 Simpson Method -- 2.1.5 MATLAB® Program Method Integral -- 2.2 Numerical Integration with Gauss Quadrature: Evaluate I& -- equals -- ∫abf (x)dx& -- equals -- ∑i& -- equals -- 1Nf(xi)wi -- Problems -- Chapter 3 MATLAB® Integral Programs -- 3.1 Power Spectrum Example -- 3.2 Blackbody Radiation Example -- 3.3 Probability Density Function Cauchy -- 3.4 Standard Normal Integration etest: Evaluate I& -- equals -- ∫0x12πe−t2/2dt -- 3.4.1 MATLAB Programs Integral, Trapz, Quad -- Problems -- Chapter 4 Monte Carlo Integration -- 4.1 Mean of I& -- equals -- ∫abf(x)dx Where r.v. X Has pdf U(a, b) -- 4.1.1 Monte Carlo Estimation with Large Sample Size N -- 4.1.2 Estimation of Integral I by I^ via Sums: Sample Mean Method -- 4.1.3 Evaluate I& -- equals -- ∫01x3dx -- Estimates from rand in mcx3 -- Summary -- 4.2 Monte Carlo Integration of a Function I& -- equals -- ∫abf(x)dx, X Is an r.v. and f(x) & -- equals -- x exp(−x) -- 4.3 Investigation of Integral I& -- equals -- ∫abf(x)dx Function f(x) & -- equals -- x3 exp(−x) with X Having pdf U(a, b) -- 4.3.1 MATLAB Program-mcrandsum Uniform pdf Evaluate I & -- equals -- ∫abx3exp(−x)dx -- Problems -- Chapter 5 Monte Carlo Integration: A Binary Choice -- 5.1 Hit-or-Miss Sampling -- 5.1.1 Bound on the Error I−I^HMhttps://cse.engineering.nyu.edu/. K. Ming Leung (2000) has another description of this error.
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|a 5.1.2 Example Using f(x) & -- equals -- x2 and f(x)& -- equals -- exp(−x2)cosπx2 -- 5.1.3 Convergence of the Estimate with Repeated Trials -- 5.1.4 Example Using f(x)& -- equals -- cos3π2x -- 5.1.5 Example Using an Ellipse -- 5.1.6 Example Using Sphere and Multiple Integrals -- 5.2 Monte Carlo Integration Example Evaluate I& -- equals -- ∫abf(x)dx -- Problems -- Chapter 6 Monte Carlo Integration of a Normal Probability Density Function -- 6.1 Normal Distribution erf and erfc -- 6.2 Integration of a Standard Normal pdf Compared with an Estimate of the Standard Normal -- 6.3 Integration of Standard Normal mcdist -- 6.4 Monte Carlo Routine mcfg with randn and ksdensity I& -- equals -- ∫−∞∞g(x)12πe−x22dx -- 6.5 Comparison of Monte Carlo Integration of N(0,1) I& -- equals -- ∫2b12πe−x22dx -- 6.6 Monte Carlo Routine mchm for Estimating Standard Normal Tail Using Hit-or-Miss -- Problems -- Chapter 7 Integration Using Importance Sampling1 -- 7.1 Example Using Y & -- equals -- f(X) Where X Has a Standard Normal pdf -- 7.2 Example Using Y & -- equals -- f(X) Where X Has a Uniform pdf -- 7.3 Example Integration of Standard Normal Using Importance Sampling -- Problems -- Chapter 8 Further Methods of Monte Carlo Sampling -- 8.1 Drawing Samples from a Known Distribution -- 8.2 Accept-Reject (AR) Sampling -- 8.2.1 Hit-or-Miss Revisit -- 8.2.2 Accept-Reject Programs with Uniform pdf for X and Uniform or Normal pdf for g(X) -- 8.2.3 Accept-Reject Programs with Uniform or Normal pdf for X and Uniform or Normal pdf for g(X) -- 8.2.4 Examples Comparing Hit-or-Miss with Accept-Reject Method -- 8.2.5 Validation of the Accept-Reject Method -- Problems -- Chapter 9 Metropolis-Hastings (MH) and Markov Chain Monte Carlo (MCMC) -- 9.1 Monte Carlo Sampling Methods -- 9.2 Bayes Inference -- 9.3 Bayes Theorem -- 9.4 Monte Carlo Integration.
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|a 9.5 Markov Chains -- 9.5.1 Example Markov Chain Demonstration -- 9.6 Metropolis-Hastings -- 9.6.1 Metropolis-Hastings Examples for Symmetric Conditional Distributions -- 9.6.2 Metropolis-Hastings Examples for Asymmetric Conditional Distributions -- Problems -- Chapter 10 Gibbs Sampling -- 10.1 Example Gibbs Sampler for Bivariate Normal -- 10.2 Examples of Bayes Sampling with Linear Regression -- 10.3 Example of Posterior pdf with Two Unknown Parameters μ and σ2& -- equals -- 1τ -- 10.4 Example of Posterior pdf with Three Unknown Parameters a, b, and τ& -- equals -- 1σ2 -- 10.5 Example of Gibbs Sampling with Real Data -- 10.6 Example of Gibbs Sampling for Galaxies and Hubble Constant -- 10.7 Additional Comments on Gibbs Sampling -- 10.7.1 Review of Gibbs Sampling for Random Parameters -- 10.7.2 General Description of Gibbs Sampling for Multiple Random Variables -- 10.7.3 Use of Burn-in with Gibbs Sampling -- 10.7.4 Combination of MH and Gibbs Sampling -- Problems -- Chapter 11 Slice Sampling -- 11.1 MATLAB Example of Slice SamplingChan, J., Koop, G., Poirier, D.J., and Tobias, J.L. (2020). Bayesian Economic Methods, 2e, 162-167. Cambridge University Press. -- 11.2 Example Using MATLAB Program Slicesample -- 11.3 Moment Calculations Using MATLAB Program Slicesample -- Problems -- Chapter 12 Hamiltonian Monte Carlo Sampling -- 12.1 Hamiltonian Mechanics -- 12.2 Computation of the Log of the Posterior Distribution -- 12.3 Leapfrog Integration -- 12.4 Example of Harmonic Oscillator12 -- 12.5 Example of Bivariate Normal13 -- 12.6 Example MATHWORKS® Using HMC Sampler14 -- Problems -- Chapter 13 Sequential Monte Carlo or Particle Filtering -- 13.1 Sequential Estimation: Signal Estimation in Linear Gaussian Noise with Kalman Filter -- 13.2 Sequential Estimation: State Estimation in Nonlinear Non-Gaussian Noise -- 13.2.1 Bayes Recursive Estimation.
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|a 13.2.2 Sequential Importance Sampling (SIS) -- 13.3 Examples of Linear and Nonlinear Systems in Noise -- 13.4 Comments on Particle Filters -- Problems -- Chapter 14 Numerical Integration via Simulink® -- 14.1 Example: Charged Particle in Crossed E and B Fields -- 14.2 Example: Linear Time Invariant (LTI) Systems with Complex Exponential Input -- 14.2.1 Example: RC Circuit with Step Input -- 14.2.2 Example: RLC Circuit with Step InputLathi, B.P. (1965). Signals, Systems and Communications, 207. John Wiley & -- Sons. -- 14.2.3 Example: Linear Time Invariant (LTI) System with White Noise Input -- 14.3 Cosmology: Expansion of the Universe -- 14.4 Neural Networks -- 14.4.1 Artificial Intelligence (AI) and Monte Carlo (MC) Integration -- 14.4.2 Deep Learning -- 14.4.3 BNN Examples -- 14.5 Proportional, Integral, Derivative Controller (PID Controller) -- 14.6 Mechanics: Dragster Motion and Drag Forces -- 14.7 Kalman Filtering -- 14.8 Particle Filtering -- Problems -- Chapter 15 Summary of Monte Carlo Integration Methods -- Appendix A Summary of Legendre-Gauss Quadrature Integration Method -- Appendix B Computation of Posteriori pdf for Gibbs Sampling -- B.1 Computation of Posterior pdfs -- B.2 Explanation of Terms and Notations -- B.3 Computation of Posterior Distributions -- B.4 Posterior pdf for Two Unknown Parameters μ and σ2 & -- equals -- 1/τ -- B.5 Posterior pdf for Three Unknown Parameters a, b, and τ -- B.6 Summary of Posterior pdfs -- Appendix C Hamiltonian Equations of Motion1,2 -- C.1 Celestial Mechanics Example -- Appendix D MATLAB Notes -- D.1 Integration -- D.2 Estimation of Probability Density Function (pdf) Using ksdensity -- D.3 Estimate Mean and Variance from Random Sample of Normal Variates -- D.4 Histogram -- Index -- EULA.
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