Muutke küpsiste eelistusi

E-raamat: Statistical Computing in Nuclear Imaging

Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 59,79 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Statistical Computing in Nuclear ImagingSuurem pilt
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

Sitek presents students, academics, researchers, mathematicians, physicists, engineers, computer scientiests, and professionals working in a variety of other contexts with an exploration of aspects of Bayesian computing used in duclear imaging. The author has organized the main body of his text into six chapters, covering basic statistical concepts, elements of decision theory, counting statistics, Monte Carlo methods in posterior analysis, the basics of nuclear imaging, and statistical computing. Additional material examines probability distributions, elements of set theory, multinomial distribution of single-voxel imaging, and other subjects. Arkadiusz Sitek is a faculty member of Massachusetts General Hospital. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

Statistical Computing in Nuclear Imaging introduces aspects of Bayesian computing in nuclear imaging. The book provides an introduction to Bayesian statistics and concepts and is highly focused on the computational aspects of Bayesian data analysis of photon-limited data acquired in tomographic measurements.

Basic statistical concepts, elements of decision theory, and counting statistics, including models of photon-limited data and Poisson approximations, are discussed in the first chapters. Monte Carlo methods and Markov chains in posterior analysis are discussed next along with an introduction to nuclear imaging and applications such as PET and SPECT.

The final chapter includes illustrative examples of statistical computing, based on Poisson-multinomial statistics. Examples include calculation of Bayes factors and risks as well as Bayesian decision making and hypothesis testing. Appendices cover probability distributions, elements of set theory, multinomial distribution of single-voxel imaging, and derivations of sampling distribution ratios. C++ code used in the final chapter is also provided.

The text can be used as a textbook that provides an introduction to Bayesian statistics and advanced computing in medical imaging for physicists, mathematicians, engineers, and computer scientists. It is also a valuable resource for a wide spectrum of practitioners of nuclear imaging data analysis, including seasoned scientists and researchers who have not been exposed to Bayesian paradigms.

List of Figures xi
List of Tables xvi
About the Series xviii
Preface xxi
About the Author xxiii
Chapter 1 Basic statistical concepts 1(36)
1.1 Introduction
1(1)
1.2 Before- and after-the-experiment concepts
2(4)
1.3 Definition of probability
6(4)
1.3.1 Countable and uncountable quantities
8(2)
1.4 Joint and conditional probabilities
10(3)
1.5 Statistical model
13(4)
1.6 Likelihood
17(2)
1.7 Pre-posterior and posterior
19(6)
1.7.1 Reduction of pre-posterior to posterior
19(1)
1.7.2 Posterior through Bayes theorem
19(1)
1.7.3 Prior selection
20(2)
1.7.4 Examples
22(1)
1.7.5 Designs of experiments
23(2)
1.8 Extension to multi-dimensions
25(4)
1.8.1 Chain rule and marginalization
26(1)
1.8.2 Nuisance quantities
27(2)
1.9 Unconditional and conditional independence
29(5)
1.10 Summary
34(3)
Chapter 2 Elements of decision theory 37(30)
2.1 Introduction
37(2)
2.2 Loss function and expected loss
39(3)
2.3 After-the-experiment decision making
42(14)
2.3.1 Point estimation
43(5)
2.3.2 Interval estimation
48(2)
2.3.3 Multiple-alternative decisions
50(2)
2.3.4 Binary hypothesis testing/detection
52(4)
2.4 Before-the-experiment decision making
56(8)
2.4.1 Bayes risk
58(4)
2.4.2 Other methods
62(2)
2.5 Robustness of the analysis
64(3)
Chapter 3 Counting statistics 67(32)
3.1 Introduction to statistical models
67(2)
3.2 Fundamental statistical law
69(2)
3.3 General models of photon-limited data
71(17)
3.3.1 Binomial statistics of nuclear decay
71(1)
3.3.2 Multinomial statistics of detection
72(5)
3.3.3 Statistics of complete data
77(7)
3.3.4 Poisson-multinomial distribution of nuclear data
84(4)
3.4 Poisson approximation
88(5)
3.4.1 Poisson statistics of nuclear decay
88(2)
3.4.2 Poisson approximation of nuclear data
90(3)
3.5 Normal distribution approximation
93(6)
3.5.1 Approximation of binomial law
94(1)
3.5.2 Central limit theorem
95(4)
Chapter 4 Monte Carlo methods in posterior analysis 99(30)
4.1 Monte Carlo approximations of distributions
99(8)
4.1.1 Continuous distributions
99(5)
4.1.2 Discrete distributions
104(3)
4.2 Monte Carlo integrations
107(3)
4.3 Monte Carlo summations
110(1)
4.4 Markov chains
111(18)
4.4.1 Markov processes
113(1)
4.4.2 Detailed balance
114(2)
4.4.3 Design of Markov chain
116(2)
4.4.4 Metropolis-Hastings sampler
118(2)
4.4.5 Equilibrium
120(6)
4.4.6 Resampling methods (bootstrap)
126(3)
Chapter 5 Basics of nuclear imaging 129(50)
5.1 Nuclear radiation
130(11)
5.1.1 Basics of nuclear physics
130(6)
5.1.1.1 Atoms and chemical reactions
130(1)
5.1.1.2 Nucleus and nuclear reactions
131(2)
5.1.1.3 Types of nuclear decay
133(3)
5.1.2 Interaction of radiation with matter
136(5)
5.1.2.1 Inelastic scattering
137(1)
5.1.2.2 Photoelectric effect
138(1)
5.1.2.3 Photon attenuation
138(3)
5.2 Radiation detection in nuclear imaging
141(6)
5.2.1 Semiconductor detectors
142(1)
5.2.2 Scintillation detectors
143(4)
5.2.2.1 Photomultiplier tubes
144(1)
5.2.2.2 Solid-state photomultipliers
145(2)
5.3 Nuclear imaging
147(21)
5.3.1 Photon-limited data
150(2)
5.3.2 Region of response (ROR)
152(1)
5.3.3 Imaging with gamma camera
153(6)
5.3.3.1 Gamma camera
153(4)
5.3.3.2 SPECT
157(2)
5.3.4 Positron emission tomography (PET)
159(7)
5.3.4.1 PET nuclear imaging scanner
159(2)
5.3.4.2 Coincidence detection
161(1)
5.3.4.3 ROR for PET and TOF-PET
162(3)
5.3.4.4 Quantitation of PET
165(1)
5.3.5 Compton imaging
166(2)
5.4 Dynamic imaging and kinetic modeling
168(5)
5.4.1 Compartmental model
169(2)
5.4.2 Dynamic measurements
171(2)
5.5 Applications of nuclear imaging
173(6)
5.5.1 Clinical applications
173(1)
5.5.2 Other applications
174(5)
Chapter 6 Statistical computing 179(30)
6.1 Computing using Poisson-multinomial distribution (PMD)
179(14)
6.1.1 Sampling the posterior
180(2)
6.1.2 Computationally efficient priors
182(4)
6.1.3 Generation of Markov chain
186(1)
6.1.4 Metropolis-Hastings algorithm
187(3)
6.1.5 Origin ensemble algorithms
190(3)
6.2 Examples of statistical computing
193(16)
6.2.1 Simple tomographic system (STS)
194(1)
6.2.2 Image reconstruction
195(3)
6.2.3 Bayes factors
198(2)
6.2.4 Evaluation of data quality
200(3)
6.2.5 Detection-Bayesian decision making
203(2)
6.2.6 Bayes risk
205(4)
Appendix A Probability distributions 209(4)
A.1 Univariate distributions
209(2)
A.1.1 Binomial distribution
209(1)
A.1.2 Gamma distribution
209(1)
A.1.3 Negative binomial distribution
209(1)
A.1.4 Poisson-binomial distribution
210(1)
A.1.5 Poisson distribution
210(1)
A.1.6 Uniform distribution
210(1)
A.1.7 Univariate normal distribution
210(1)
A.2 Multivariate distributions
211(2)
A.2.1 Multinomial distribution
211(1)
A.2.2 Multivariate normal distribution
211(1)
A.2.3 Poisson-multinomial distribution
211(2)
Appendix B Elements of set theory 213(4)
Appendix C Multinomial distribution of single-voxel imaging 217(4)
Appendix D Derivations of sampling distribution ratios 221(2)
Appendix E Equation (6.11) 223(2)
Appendix F C++ OE code for STS 225(6)
References 231(8)
Index 239
Arkadiusz Sitek is an associate physicist at Massachusetts General Hospital in Boston and an assistant professor at Harvard Medical School. He received his doctorate from the University of British Columbia in Canada and since 2001 has worked as a nuclear imaging scientist in the Lawrence Berkeley National Laboratory, Beth Israel Medical Center, and Brigham and Womens Hospital before joining Massachusetts General Hospital. He has authored more than 100 scientific journal and proceedings papers, book chapters, and patents, and served as a principal investigator on nuclear imaging research projects. Dr. Sitek is a practitioner of the Bayesian school of thought and a member of the International Society for Bayesian Analysis.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97814987293072e.html
Märksõnad: