Independent random sampling methods. (2018)

• Record Type: Book
• Further Information: Note: Luca Martino, David Luengo, Joaquín Míguez.
• Authors: Martino, Luca; Luengo, David; Míguez, Joaquín
• Contents: Intro; Contents; List of Tables; 1 Introduction; 1.1 The Monte Carlo Method: A Brief History; 1.2 The Need for Monte Carlo; 1.2.1 Numerical Integration; 1.2.2 Importance Sampling; Bayesian Inference via IS; 1.2.3 Quasi-Monte Carlo; 1.2.4 Inverse Monte Carlo; 1.3 Random Number Generation; 1.3.1 Random, Pseudo-Random, Quasi-Random; 1.4 Pseudo-Random Number Generators; 1.4.1 Nonlinear Recursions; Invariant Sets; 1.4.2 Chaotic Pseudo-Random Number Generators; 1.4.3 The Middle-Square Generator; 1.4.4 Linear Congruential Generators; General LCGs; 1.5 Random Sampling Methods; 1.5.1 Direct Methods. 1.5.2 Accept/Reject Methods1.5.3 Markov Chain Monte Carlo (MCMC); 1.5.4 Importance Sampling; 1.5.5 Hybrid Techniques; 1.6 Goal and Organization of This Book; 1.6.1 Motivation and Goals; 1.6.2 Organization of the Book; References; 2 Direct Methods; 2.1 Introduction; 2.2 Notation; 2.2.1 Vectors, Points, and Intervals; 2.2.2 Random Variables, Distributions, and Densities; 2.2.3 Sets; 2.3 Transformations of Random Variables; 2.3.1 One-to-One Transformations; Invertible Transformations; Non-invertible Transformations; 2.3.2 Many-to-One Transformations; Scale Transformation. 2.3.3 Deconvolution Method2.3.4 Discrete Mixtures; Partition into Intervals; Pdf Expressed as an Infinite Series; 2.3.5 Continuous Mixtures: Marginalization; 2.3.6 Order Statistics; 2.4 Universal Direct Methods; 2.4.1 Inversion Method; Numerical Inversion of FX(x)=u; Truncated Random Variables; Order Statistics; Maximum of N i.i.d. Random Variates; Dependent Random Variates; Inversion for Multivariate Targets; 2.4.2 Vertical Density Representation (VDR); An Alternative Interpretation of the VDR Approach; 2.4.3 The Fundamental Theorem of Simulation; 2.4.4 Inverse-of-Density Method. IoD for Monotonic Univariate Target pdfsIoD for Generic Target pdfs; Khintchine's Method for Monotonic Target pdfs; 2.5 Tailored Techniques; 2.5.1 Recursive Methods; 2.5.2 Convex Densities; 2.6 Examples; 2.6.1 Multiplication of Independent Uniform Random Variates; 2.6.2 Sum of Independent Uniform Random Variates; 2.6.3 Polynomial Densities with Non-negative Coefficients; 2.6.4 Polynomial Densities with One or More Negative Constants; 2.7 Summary; References; 3 Accept-Reject Methods; 3.1 Introduction; 3.2 Rejection Sampling; 3.2.1 Acceptance Rate; 3.2.2 Distribution of the Rejected Samples. 3.2.3 Distribution of the Accepted and Rejected Samples with Generic L>03.2.4 Different Application Scenarios; 3.2.5 Butcher's Version of the Rejection Sampler; 3.2.6 Vaduva's Modification of the Butcher's Method; 3.2.7 Lux's Extension; 3.3 Computational Cost; 3.3.1 Further Considerations About the Acceptance Rate; 3.3.2 Squeezing; 3.3.3 Sibuya's Modified Rejection Method; 3.4 Band Rejection Method; 3.4.1 Preliminaries; 3.4.2 Generalized Band Rejection Algorithm; 3.4.3 Payne-Dagpunar's Band Rejection; 3.5 Acceptance-Complement Method; 3.6 RS with Stepwise Proposals; 3.6.1 Strip Methods.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource (xii, 280 pages), illustrations (some color)
• Subjects: 519.5/2; Statistics; Sampling (Statistics); MATHEMATICS -- Applied; MATHEMATICS -- Probability & Statistics -- General; Sampling (Statistics); Statistics; Statistics and Computing/Statistics Programs; Mathematics of Computing; Quantitative Finance; Statistical Theory and Methods; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Computers -- Data Processing; Mathematics -- Probability & Statistics -- General; Mathematical theory of computation; Finance & accounting; Probability & statistics; Mathematical statistics; Computer science; Finance; Computers -- Mathematical & Statistical Software; Mathematical & statistical software; Electronic books
• Languages: English
• ISBNs: 9783319726342
• Related ISBNs: 331972634X; 9783319726335; 3319726331
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed April 4, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.