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E-raamat: Bayesian Models for Astrophysical Data: Using R, JAGS, Python, and Stan

(Jet Propulsion Laboratory, California Institute of Technology), (Eötvös Loránd University, Budapest),
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  • Ilmumisaeg: 27-Apr-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108216142
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 27-Apr-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108216142

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This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. A must-have for astronomers, its concrete focus on modeling, analysis, and interpretation will also be attractive to researchers in the sciences more broadly.

This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.

Arvustused

'This volume is a very welcome addition to the small but growing library of resources for advanced analysis of astronomical data. Astronomers are often confronted with complex constrained regression problems, situations that benefit from computationally intensive Bayesian approaches. The authors provide a unique and sophisticated guide with tutorials in methodology and software implementation. The worked examples are impressive. Many astronomers use Python and will benefit from the less familiar capabilities of R, Stan, and JAGS for Bayesian analysis. I suspect the work will also be useful to scientists in other fields who venture into the world of Bayesian computational statistics.' Eric D. Feigelson, Pennsylvania State University, author of Modern Statistical Methods for Astronomy 'Encyclopaedic in scope, a treasure trove of ready code for the hands-on practitioner.' Ben Wandelt, Paris Institute of Astrophysics, Institut Lagrange de Paris, Université Paris-Sorbonne 'This informative book is a valuable resource for astronomers, astrophysicists, and cosmologists at all levels of their career. From students starting out in the field to researchers at the frontiers of data analysis, everyone will find insightful techniques accompanied by helpful examples of code. With this book, Hilbe, de Souza, and Ishida are firmly taking astrostatistics into the twenty-first century.' Roberto Trotta, Imperial College London, author of The Edge of the Sky ' the focus of the book is not on providing a full understanding of how the distributions arise, but to give guidelines on how to write code for applications, including building multi-level models, and here it succeeds well, and is an excellent resource in conjunction with powerful packages such as STAN and JAGS.' Alan Heavens, The Observatory

Muu info

A hands-on guide to Bayesian models with R, JAGS, Python, and Stan code, for a wide range of astronomical data types.
Preface xiii
1 Astrostatistics 1(8)
1.1 The Nature and Scope of Astrostatistics
1(3)
1.2 The Recent Development of Astrostatistics
4(2)
1.3 What is a Statistical Model?
6(1)
1.4 Classification of Statistical Models
7(2)
2 Prerequisites 9(14)
2.1 Software
9(1)
2.2 R
10(2)
2.3 JAGS
12(2)
2.4 Python
14(3)
2.5 Stan
17(6)
3 Frequentist vs. Bayesian Methods 23(23)
3.1 Frequentist Statistics
23(4)
3.1.1 Fitting a Linear Regression in R
25(1)
3.1.2 Fitting a Linear Regression in Python
26(1)
3.2 Basic Theory of Bayesian Modeling
27(16)
3.2.1 Example: Calculating a Beta Prior and Posterior Analytically
32(6)
3.2.2 Fitting a Simple Bayesian Normal Model using R
38(3)
3.2.3 Fitting a Simple Bayesian Normal Model using Python
41(2)
3.3 Selecting Between Frequentist and Bayesian Modeling
43(3)
4 Normal Linear Models 46(22)
4.1 The Gaussian or Normal Model
46(12)
4.1.1 Bayesian Synthetic Normal Model in R using JAGS
48(6)
4.1.2 Bayesian Synthetic Normal Model in R using JAGS and the Zero Trick
54(2)
4.1.3 Bayesian Synthetic Normal Model in Python using Stan
56(1)
4.1.4 Bayesian Synthetic Normal Model using Stan with a Customized Likelihood
57(1)
4.2 Multivariate Normal Model
58(3)
4.2.1 Multivariate Linear Regression in R using JAGS
58(2)
4.2.2 Multivariate Linear Regression in Python using Stan
60(1)
4.3 Bayesian Errors-in-Measurements Modeling
61(7)
4.3.1 Generating Data with Errors using R
62(1)
4.3.2 Build Model ignoring Errors in R using JAGS
62(1)
4.3.3 Build Model including Errors in R using JAGS
63(2)
4.3.4 Bayesian Errors-in-Measurements Modeling in Python using Stan
65(3)
5 GLMs Part I - Continuous and Binomial Models 68(67)
5.1 Brief Overview of Generalized Linear Models
68(6)
5.2 Bayesian Continuous Response Models
74(24)
5.2.1 Bayesian Lognormal Model
75(7)
5.2.2 Bayesian Gamma Models
82(5)
5.2.3 Bayesian Inverse Gaussian Models
87(5)
5.2.4 Bayesian Beta Model
92(6)
5.3 Bayesian Binomial Models
98(37)
5.3.1 Bayesian Bernoulli Logit Models
99(11)
5.3.2 Bayesian Bernoulli Probit Models
110(7)
5.3.3 Bayesian Grouped Logit or Binomial Model
117(7)
5.3.4 Bayesian Grouped Probit Model
124(1)
5.3.5 Bayesian Beta-Binomial Models
125(10)
6 GLMs Part II - Count Models 135(49)
6.1 Bayesian Poisson Models
135(13)
6.1.1 Poisson Models with R
142(1)
6.1.2 Poisson Models with JAGS
143(1)
6.1.3 Poisson Models in Python
144(3)
6.1.4 Poisson Models in Python using Stan
147(1)
6.2 Bayesian Negative Binomial Models
148(16)
6.2.1 Modeling the Negative Binomial using JAGS
154(7)
6.2.2 Negative Binomial Models in Python using pymc3
161(2)
6.2.3 Modeling the Negative Binomial in Python using Stan
163(1)
6.3 Bayesian Generalized Poisson Model
164(5)
6.3.1 Generalized Poisson Model using JAGS
166(2)
6.3.2 Generalized Poisson Model using Stan
168(1)
6.4 Bayesian Zero-Truncated Models
169(10)
6.4.1 Bayesian Zero-Truncated Poisson Model
170(4)
6.4.2 Zero-Truncated Poisson in Python using Stan
174(2)
6.4.3 Bayesian Zero-Truncated Negative Binomial Model
176(3)
6.5 Bayesian Three-Parameter NB Model (NB-P)
179(5)
6.5.1 Three-Parameter NB-P Model using JAGS
180(2)
6.5.2 Three-Parameter NB-P Models in Python using Stan
182(2)
7 GLMs Part III - Zero-Inflated and Hurdle Models 184(31)
7.1 Bayesian Zero-Inflated Models
184(12)
7.1.1 Bayesian Zero-Inflated Poisson Model
184(6)
7.1.2 Bayesian Zero-Inflated Negative Binomial Model
190(6)
7.2 Bayesian Hurdle Models
196(19)
7.2.1 Bayesian Poisson-Logit Hurdle Model
197(5)
7.2.2 Bayesian Negative Binomial-Logit Hurdle Model
202(4)
7.2.3 Bayesian Gamma-Logit Hurdle Model
206(4)
7.2.4 Bayesian Lognormal-Logit Hurdle Model
210(5)
8 Hierarchical GLMMs 215(47)
8.1 Overview of Bayesian Hierarchical Models/GLMMs
215(4)
8.2 Bayesian Gaussian or Normal GLMMs
219(9)
8.2.1 Random Intercept Gaussian Data
219(1)
8.2.2 Bayesian Random Intercept Gaussian Model in R using JAGS
220(2)
8.2.3 Bayesian Random Intercept Normal Model in R using JAGS
222(4)
8.2.4 Bayesian Random Intercept Normal Model in Python using Stan
226(2)
8.3 Bayesian Binary Logistic GLMMs
228(7)
8.3.1 Random Intercept Binary Logistic Data
228(1)
8.3.2 Bayesian Random Intercept Binary Logistic Model with R
229(1)
8.3.3 Bayesian Random Intercept Binary Logistic Model with Python
230(2)
8.3.4 Bayesian Random Intercept Binary Logistic Model in R using JAGS
232(2)
8.3.5 Bayesian Random Intercept Binary Logistic Model in Python using Stan
234(1)
8.4 Bayesian Binomial Logistic GLMMs
235(5)
8.4.1 Random Intercept Binomial Logistic Data
236(1)
8.4.2 Bayesian Random Intercept Binomial Logistic Model in R using JAGS
237(1)
8.4.3 Bayesian Random Intercept Binomial Logistic Model in Python using Stan
238(2)
8.5 Bayesian Poisson GLMMs
240(12)
8.5.1 Random Intercept Poisson Data
241(1)
8.5.2 Bayesian Random Intercept Poisson Model with R
241(1)
8.5.3 Bayesian Random Intercept Poisson Model in Python
242(2)
8.5.4 Bayesian Random Intercept Poisson Model in R using JAGS
244(2)
8.5.5 Bayesian Random Intercept Poisson Model in Python using Stan
246(2)
8.5.6 Bayesian Random-Intercept-Random-Slopes Poisson Model
248(4)
8.6 Bayesian Negative Binomial GLMMs
252(10)
8.6.1 Random Intercept Negative Binomial Data
253(1)
8.6.2 Random Intercept Negative Binomial MLE Model using R
254(1)
8.6.3 Bayesian Random Intercept Negative Binomial Model using Python
255(2)
8.6.4 Bayesian Random Intercept Negative Binomial Model in R using JAGS
257(2)
8.6.5 Bayesian Random Intercept Negative Binomial Model in Python using Stan
259(3)
9 Model Selection 262(14)
9.1 Information Criteria Tests for Model Selection
262(4)
9.1.1 Frequentist and Bayesian Information Criteria
262(2)
9.1.2 Bayesian Deviance Statistic s
264(1)
9.1.3 pD and Deviance Information Criteria (DIC)
265(1)
9.2 Model Selection with Indicator Functions
266(8)
9.3 Bayesian LASSO
274(2)
10 Astronomical Applications 276(88)
10.1 Normal Model, Black Hole Mass, and Bulge Velocity Dispersion
277(6)
10.1.1 Data
278(1)
10.1.2 The Statistical Model Formulation
278(1)
10.1.3 Running the Model in R using JAGS
279(1)
10.1.4 Running the Model in Python using Stan
280(3)
10.2 Gaussian Mixed Models, Type Ia Supernovae, and Hubble Residuals
283(7)
10.2.1 Data
284(1)
10.2.2 Statistical Model Formulation
284(1)
10.2.3 Running the Model in R using JAGS
285(3)
10.2.4 Running the Model in Python using Stan
288(2)
10.3 Multivariate Normal Mixed Model and Early-Type Contact Binaries
290(7)
10.3.1 Data
292(1)
10.3.2 The Statistical Model Formulation
292(1)
10.3.3 Running the Model in R using JAGS
293(3)
10.3.4 Running the Model in Python using Stan
296(1)
10.4 Lognormal Distribution and the Initial Mass Function
297(5)
10.4.1 Data
298(1)
10.4.2 Statistical Model Formulation
298(1)
10.4.3 Running the Model in R using JAGS
299(2)
10.4.4 Running the Model in Python using Stan
301(1)
10.5 Beta Model and the Baryon Content of Low Mass Galaxies
302(5)
10.5.1 Data
303(1)
10.5.2 The Statistical Model Formulation
303(1)
10.5.3 Running the Model in R using JAGS
304(2)
10.5.4 Running the Model in Python using Stan
306(1)
10.6 Bernoulli Model and the Fraction of Red Spirals
307(6)
10.6.1 Data
308(1)
10.6.2 The Statistical Model Formulation
308(1)
10.6.3 Running the Model in R using JAGS
309(2)
10.6.4 Running the Model in Python using Stan
311(2)
10.7 Count Models, Globular Cluster Population, and Host Galaxy Brightness
313(10)
10.7.1 Data
313(1)
10.7.2 The Statistical Poisson Model Formulation
314(1)
10.7.3 Running the Poisson Model in R using JAGS
315(2)
10.7.4 The Statistical Negative Binomial Model Formulation
317(1)
10.7.5 Running the Negative Binomial Model in R using JAGS
318(2)
10.7.6 The Statistical NB-P Model Formulation
320(1)
10.7.7 Running the NB-P Model in R using JAGS
321(2)
10.7.8 Running the NB-P Model in Python using Stan
323(9)
10.8 Bernoulli Mixed Model, AGNs, and Cluster Environment
325(1)
10.8.1 Data
326(1)
10.8.2 Statistical Model Formulation
327(1)
10.8.3 Running the Model in R using JAGS
328(1)
10.8.4 Running the Model in Python using Stan
329(3)
10.9 Lognormal-Logit Hurdle Model and the Halo-Stellar-Mass Relation
332(8)
10.9.1 Data
333(1)
10.9.2 The Statistical Model Formulation
333(1)
10.9.3 Running the Model in R using JAGS
334(3)
10.9.4 Running the Model in Python using Stan
337(3)
10.10 Count Time Series and Sunspot Data
340(7)
10.10.1 Data
341(1)
10.10.2 Running the Normal AR(1) Model in R using JAGS
341(3)
10.10.3 Running the Negative Binomial AR Model in R using JAGS
344(2)
10.10.4 Running the Negative Binomial AR Model in Python using Stan
346(1)
10.11 Gaussian Model, ODEs, and Type Ia Supernova Cosmology
347(8)
10.11.1 Data
348(1)
10.11.2 The Statistical Model Formulation
348(1)
10.11.3 Running the Model in R using Stan
349(4)
10.11.4 Errors in Measurements
353(2)
10.12 Approximate Bayesian Computation
355(8)
10.12.1 Distance
356(1)
10.12.2 Population Monte Carlo ABC
357(1)
10.12.3 Toy Model
357(2)
10.12.4 CosmoABC
359(4)
10.13 Remarks on Applications
363(1)
11 The Future of Astrostatistics 364(2)
Appendix A Bayesian Modeling using INLA 366(3)
Appendix B Count Models with Offsets 369(8)
Appendix C Predicted Values, Residuals, and Diagnostics 377(3)
References 380(11)
Index 391
Joseph M. Hilbe is Solar System Ambassador with NASA's Jet Propulsion Laboratory, California Institute of Technology, Adjunct Professor of Statistics at Arizona State University, and Professor Emeritus at the University of Hawaii. He is currently President of the International Astrostatistics Association (IAA) and was awarded the IAA's 2016 Outstanding Contributions to Astrostatistics medal, the association's top award. Hilbe is an elected Fellow of both the American Statistical Association and the IAA and is a full member of the American Astronomical Society. He has authored nineteen books on statistical modeling, including leading texts on modeling count and binomial data. His book, Modeling Count Data (Cambridge, 2014) received the 2015 PROSE honorable mention for books in mathematics. Rafael S. de Souza is a researcher at Eötvos Loránd University, Budapest. He is currently Vice-President for development of the International Astrostatistics Association (IAA) and was awarded the IAA's 2016 Outstanding Publication in Astrostatistics award. He has authored dozens of scientific papers, serving as the leading author for over twenty of them. Emille E. O. Ishida is a researcher at the Université Clermont-Auvergne (Université Blaise Pascal), France. She is cochair of the Cosmostatistics Initiative and coordinator of its Python-related projects. She is a specialist in machine learning applications to astronomy with special interests in type Ia supernovae spectral characterization, classification, and cosmology. She has been the lead author of numerous articles in prominent astrophysics journals and currently serves as chair of the IAA public relations committee.