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Random Process Analysis With R [Kõva köide]

(Senior Researcher, Institute of Applied Physics, National Research Council, Italy), (Professor, Department of Physics and Matter Technologies, Na), (Professor, Department of Agricultural and Food Sciences, University of Bologna, Italy)
  • Formaat: Hardback, 512 pages, kõrgus x laius x paksus: 253x174x28 mm, kaal: 1108 g, 212 line drawings and 11 colour images
  • Ilmumisaeg: 13-Oct-2022
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198862512
  • ISBN-13: 9780198862512
Teised raamatud teemal:
Random Process Analysis With RSuurem pilt
  • Formaat: Hardback, 512 pages, kõrgus x laius x paksus: 253x174x28 mm, kaal: 1108 g, 212 line drawings and 11 colour images
  • Ilmumisaeg: 13-Oct-2022
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198862512
  • ISBN-13: 9780198862512
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780198862512.html
Märksõnad:
Random process analysis (RPA) is used as a mathematical model in physics, chemistry, biology, computer science, information theory, economics, environmental science, and many other disciplines. Over time, it has become more and more important for the provision of computer code and data sets. This book presents the key concepts, theory, and computer code written in R, helping readers with limited initial knowledge of random processes to become confident in their understanding and application of these principles in their own research. Consistent with modern trends in university education, the authors make readers active learners with hands-on computer experiments in R code directing them through RPA methods and helping them understand the underlying logic.

Each subject is illustrated with real data collected in experiments performed by the authors or taken from key literature. As a result, the reader can promptly apply the analysis to their own data, making this book an invaluable resource for undergraduate and graduate students, as well as professionals, in physics, engineering, biophysical and environmental sciences, economics, and social sciences.
1 Introduction
1(3)
1.1 Introduction
1(3)
2 Historical Background
4(8)
2.1 The Philosopher and the Gambler
4(4)
2.2 Comments
8(3)
2.3 Exercises
11(1)
3 Introduction to Stochastic Processes
12(95)
3.1 Basic notion
12(13)
3.2 Markov processes
25(6)
3.3 Predicting the future
31(29)
3.4 Continuous-time Markov chain
60(26)
3.5 Ehrenfest urn model
86(19)
3.6 Exercises
105(2)
4 Poisson Processes
107(33)
4.1 Counting process
108(2)
4.2 Poisson process from counting process
110(1)
4.3 Poisson process from Bernoulli process
111(9)
4.4 Poisson process through the inter-arrival time
120(1)
4.5 Poisson processes simulations
121(14)
4.6 Nonhomogeneous Poisson process
135(4)
4.7 Exercises
139(1)
5 Random Walk
140(47)
5.1 Definitions and examples
140(33)
5.2 Some topics on Brownian motion
173(11)
5.3 Exercises
184(3)
6 ARMA Processes
187(45)
6.1 White noise and other useful definitions
187(4)
6.2 Moving-average processes
191(5)
6.3 Autoregressive processes
196(8)
6.4 Autoregressive moving-average processes (ARMA)
204(4)
6.5 An introduction to non stationary and seasonal time series
208(9)
6.6 A physical application
217(11)
6.7 Exercises
228(4)
7 Spectrum Analysis
232(37)
7.1 Spectrum of stochastic signals
237(9)
7.2 Noise spectrum
246(3)
7.3 Applications of spectrum analysis
249(4)
7.4 Singular Spectrum Analysis
253(12)
7.5 Exercises
265(4)
8 Markov Chain Monte Carlo
269(25)
8.1 Mother Nature's minimization algorithm
269(2)
8.2 From physical birth to statistical development
271(13)
8.3 The travelling salesman problem
284(8)
8.4 Exercises
292(2)
9 Bayesian Inference and Stochastic Processes
294(41)
9.1 Application of MCMC in a regression problem with auto-correlated errors
297(12)
9.2 Bayesian spectral analysis applied to RADAR target detection
309(12)
9.3 Bayesian analysis of a Poisson process: the waiting-time paradox
321(5)
9.4 Bayesian analysis applied to a lighthouse
326(6)
9.5 Exercises
332(3)
10 Genetic algorithms: an evolutionary-based global random search
335(40)
10.1 Introduction
335(1)
10.2 Terminology and basics of GA
336(3)
10.3 Simple genetic algorithm
339(10)
10.4 A simple application: non linear fitting
349(8)
10.5 Advanced genetic algorithms
357(4)
10.6 Parameter estimation of ARMA models
361(6)
10.7 Solving the travelling salesman problem
367(6)
10.8 Concluding remarks
373(1)
10.9 Exercises
373(2)
11 The Problem of Accuracy
375(27)
11.1 Estimating accuracy
375(1)
11.2 Averaging time series
376(5)
11.3 The batch means method
381(6)
11.4 The moving block bootstrap method
387(9)
11.5 Convergence diagnostic with the MBB method
396(4)
11.6 Exercises
400(2)
12 Spatial Analysis
402(44)
12.1 Geostatistical perspective
402(4)
12.2 Correlation coefficient and correlogram
406(7)
12.3 Semivariogram
413(17)
12.4 Spacetime analysis
430(9)
12.5 On the optimization of the spatio-temporal variogram
439(5)
12.6 Exercises
444(2)
13 How Random is a Random Process?
446(21)
13.1 Random hints about randomness
446(2)
13.2 Characterizing mathematical randomness
448(6)
13.3 Entropy
454(11)
13.4 A final note
465(2)
Appendix A Bootstrap
467(9)
A.1 Bootstrap standard error
469(3)
A.2 Parametric bootstrap
472(4)
Appendix B JAGS
476(7)
List of Symbols 483(2)
List of R Codes 485(3)
References 488(10)
Index 498
Marco Bittelli received a degree in Agricultural Sciences from the University of Bologna, Italy, in 1994 and an M.S. and a Ph.D. in Soil Physics from Washington State University, USA, in 2001. He teaches Soil and Environmental Physics, Statistics and Philosophy of Science courses at the University of Bologna.



Roberto Olmi received a degree in Physics from the University of Firenze, Italy, in 1983. Since 1984 he has been a researcher at the Institute of Research on Electromagnetic Waves of the National Research Council in Firenze.



Rodolfo Rosa received a degree in Physics in 1968 and in Philosophy in 1977 from the University of Bologna. From 1969 to 1992, he was a researcher at the National Research Council-Institute of Microelectronics and Microsystems, Bologna. From 1992 to 2014 he was a Professor at the Faculty of Statistics at the University of Bologna, where he taught courses on Statistics for Experimental Research, Chaos and Complexity, and Probability and Stochastic Processes.