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Bayesian Analysis with Python Introduction to statistical modend probabilistic programming using PyMC3 and ArviZ 2nd Edition by Osvaldo Martin ISBN 1789349665 9781789349665

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ISBN 10: 1789349665
ISBN 13: 9781789349665
Author: Osvaldo Martin

Bayesian modeling with PyMC3 and exploratory analysis of Bayesian models with ArviZ Key Features A step-by-step guide to conduct Bayesian data analyses using PyMC3 and ArviZ A modern, practical and computational approach to Bayesian statistical modeling A tutorial for Bayesian analysis and best practices with the help of sample problems and practice exercises. Book Description The second edition of Bayesian Analysis with Python is an introduction to the main concepts of applied Bayesian inference and its practical implementation in Python using PyMC3, a state-of-the-art probabilistic programming library, and ArviZ, a new library for exploratory analysis of Bayesian models. The main concepts of Bayesian statistics are covered using a practical and computational approach. Synthetic and real data sets are used to introduce several types of models, such as generalized linear models for regression and classification, mixture models, hierarchical models, and Gaussian processes, among others. By the end of the book, you will have a working knowledge of probabilistic modeling and you will be able to design and implement Bayesian models for your own data science problems. After reading the book you will be better prepared to delve into more advanced material or specialized statistical modeling if you need to. What you will learn Build probabilistic models using the Python library PyMC3 Analyze probabilistic models with the help of ArviZ Acquire the skills required to sanity check models and modify them if necessary Understand the advantages and caveats of hierarchical models Find out how different models can be used to answer different data analysis questions Compare models and choose between alternative ones Discover how different models are unified from a probabilistic perspective Think probabilistically and benefit from the flexibility of the Bayesian framework Who this book is for If you are a student, data scientist, researcher, or a developer looking to get started with Bayesian data analysis and probabilistic programming, this book is for you. The book is introductory so no previous statistical knowledge is required, although some experience in using Python and NumPy is expected.

Bayesian Analysis with Python Introduction to statistical modend probabilistic programming using PyMC3 and ArviZ 2nd Table of contents:

  1. Preface
  2. Who this book is for
  3. What this book covers
  4. To get the most out of this book
  5. Download the example code files
  6. Download the color images
  7. Conventions used
  8. Get in touch
  9. Reviews
  10. Thinking Probabilistically
  11. Statistics, models, and this book’s approach
  12. Working with data
  13. Bayesian modeling
  14. Probability theory
  15. Interpreting probabilities
  16. Defining probabilities
  17. Probability distributions
  18. Independently and identically distributed variables
  19. Bayes’ theorem
  20. Single-parameter inference
  21. The coin-flipping problem
  22. The general model
  23. Choosing the likelihood
  24. Choosing the prior
  25. Getting the posterior
  26. Computing and plotting the posterior
  27. The influence of the prior and how to choose one
  28. Communicating a Bayesian analysis
  29. Model notation and visualization
  30. Summarizing the posterior
  31. Highest-posterior density
  32. Posterior predictive checks
  33. Summary
  34. Exercises
  35. Programming Probabilistically
  36. Probabilistic programming
  37. PyMC3 primer
  38. Flipping coins the PyMC3 way
  39. Model specification
  40. Pushing the inference button
  41. Summarizing the posterior
  42. Posterior-based decisions
  43. ROPE
  44. Loss functions
  45. Gaussians all the way down
  46. Gaussian inferences
  47. Robust inferences
  48. Student’s t-distribution
  49. Groups comparison
  50. Cohen’s d
  51. Probability of superiority
  52. The tips dataset
  53. Hierarchical models
  54. Shrinkage
  55. One more example
  56. Summary
  57. Exercises
  58. Modeling with Linear Regression
  59. Simple linear regression
  60. The machine learning connection
  61. The core of the linear regression models
  62. Linear models and high autocorrelation
  63. Modifying the data before running
  64. Interpreting and visualizing the posterior
  65. Pearson correlation coefficient
  66. Pearson coefficient from a multivariate Gaussian
  67. Robust linear regression
  68. Hierarchical linear regression
  69. Correlation, causation, and the messiness of life
  70. Polynomial regression
  71. Interpreting the parameters of a polynomial regression
  72. Polynomial regression – the ultimate model?
  73. Multiple linear regression
  74. Confounding variables and redundant variables
  75. Multicollinearity or when the correlation is too high
  76. Masking effect variables
  77. Adding interactions
  78. Variable variance
  79. Summary
  80. Exercises
  81. Generalizing Linear Models
  82. Generalized linear models
  83. Logistic regression
  84. The logistic model
  85. The Iris dataset
  86. The logistic model applied to the iris dataset
  87. Multiple logistic regression
  88. The boundary decision
  89. Implementing the model
  90. Interpreting the coefficients of a logistic regression
  91. Dealing with correlated variables
  92. Dealing with unbalanced classes
  93. Softmax regression
  94. Discriminative and generative models
  95. Poisson regression
  96. Poisson distribution
  97. The zero-inflated Poisson model
  98. Poisson regression and ZIP regression
  99. Robust logistic regression
  100. The GLM module
  101. Summary
  102. Exercises
  103. Model Comparison
  104. Posterior predictive checks
  105. Occam’s razor – simplicity and accuracy
  106. Too many parameters leads to overfitting
  107. Too few parameters leads to underfitting
  108. The balance between simplicity and accuracy
  109. Predictive accuracy measures
  110. Cross-validation
  111. Information criteria
  112. Log-likelihood and deviance
  113. Akaike information criterion
  114. Widely applicable Information Criterion
  115. Pareto smoothed importance sampling leave-one-out cross-validation
  116. Other Information Criteria
  117. Model comparison with PyMC3
  118. A note on the reliability of WAIC and LOO computations
  119. Model averaging
  120. Bayes factors
  121. Some remarks
  122. Computing Bayes factors
  123. Common problems when computing Bayes factors
  124. Using Sequential Monte Carlo to compute Bayes factors
  125. Bayes factors and Information Criteria
  126. Regularizing priors
  127. WAIC in depth
  128. Entropy
  129. Kullback-Leibler divergence
  130. Summary
  131. Exercises
  132. Mixture Models
  133. Mixture models
  134. Finite mixture models
  135. The categorical distribution
  136. The Dirichlet distribution
  137. Non-identifiability of mixture models
  138. How to choose K
  139. Mixture models and clustering
  140. Non-finite mixture model
  141. Dirichlet process
  142. Continuous mixtures
  143. Beta-binomial and negative binomial
  144. The Student’s t-distribution
  145. Summary
  146. Exercises
  147. Gaussian Processes
  148. Linear models and non-linear data
  149. Modeling functions
  150. Multivariate Gaussians and functions
  151. Covariance functions and kernels
  152. Gaussian processes
  153. Gaussian process regression
  154. Regression with spatial autocorrelation
  155. Gaussian process classification
  156. Cox processes
  157. The coal-mining disasters
  158. The redwood dataset
  159. Summary
  160. Exercises
  161. Inference Engines
  162. Inference engines
  163. Non-Markovian methods
  164. Grid computing
  165. Quadratic method
  166. Variational methods
  167. Automatic differentiation variational inference
  168. Markovian methods
  169. Monte Carlo
  170. Markov chain
  171. Metropolis-Hastings
  172. Hamiltonian Monte Carlo
  173. Sequential Monte Carlo
  174. Diagnosing the samples
  175. Convergence
  176. Monte Carlo error
  177. Autocorrelation
  178. Effective sample sizes
  179. Divergences
  180. Non-centered parameterization
  181. Summary
  182. Exercises
  183. Where To Go Next?
  184. Other Books You May Enjoy
  185. Leave a review – let other readers know what you think

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Tags: Osvaldo Martin, Bayesian Analysis, statistical modend, probabilistic programming