Bayesian analysis with Python unleash the power and flexibility of the Bayesian framework
The purpose of this book is to teach the main concepts of Bayesian data analysis. We will learn how to effectively use PyMC3, a Python library for probabilistic programming, to perform Bayesian parameter estimation, to check models and validate them. This book begins presenting the key concepts of t...
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| Main Author | |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Birmingham
PACKT Publishing
2016
Packt Publishing Packt Publishing, Limited Packt Publishing Limited |
| Edition | 1st ed. |
| Subjects | |
| Online Access | Get full text |
| ISBN | 1785889850 1785883801 9781785889851 9781785883804 |
| DOI | 10.0000/9781785889851 |
Cover
Table of Contents:
- Bayesian analysis with Python : unleash the power and flexibility of the Bayesian framework -- Credits -- About the Author -- About the Reviewer -- www.PacktPub.com -- Table of Contents -- Preface -- Chapter 1: Thinking Probabilistically - A Bayesian Inference Primer -- Chapter 2: Programming Probabilistically – A PyMC3 Primer -- Chapter 3: Juggling with Multi-Parametric and Hierarchical Models -- Chapter 4: Understanding and Predicting Data with Linear Regression Models -- Chapter 5: Classifying Outcomes with Logistic Regression -- Chapter 6: Model Comparison -- Chapter 7: Mixture Models -- Chapter 8: Gaussian Processes -- Index.
- Cover -- Copyright -- Credits -- About the Author -- About the Reviewer -- www.PacktPub.com -- Table of Contents -- Preface -- Chapter 1: Thinking Probabilistically - A Bayesian Inference Primer -- Statistics as a form of modeling -- Exploratory data analysis -- Inferential statistics -- Probabilities and uncertainty -- Probability distributions -- Bayes' theorem and statistical inference -- Single parameter inference -- The coin-flipping problem -- The general model -- Choosing the likelihood -- Choosing the prior -- Getting the posterior -- Computing and plotting the posterior -- Influence of the prior and how to choose one -- Communicating a Bayesian analysis -- Model notation and visualization -- Summarizing the posterior -- Highest posterior density -- Posterior predictive checks -- Installing the necessary Python packages -- Summary -- Exercises -- Chapter 2: Programming Probabilistically - A PyMC3 Primer -- Probabilistic programming -- Inference engines -- Non-Markovian methods -- Markovian methods -- PyMC3 introduction -- Coin-flipping, the computational approach -- Model specification -- Pushing the inference button -- Diagnosing the sampling process -- Summarizing the posterior -- Posterior-based decisions -- ROPE -- Loss functions -- Summary -- Keep reading -- Exercises -- Chapter 3: Juggling with Multi-Parametric and Hierarchical Models -- Nuisance parameters and marginalized distributions -- Gaussians, Gaussians, Gaussians everywhere -- Gaussian inferences -- Robust inferences -- Student's t-distribution -- Comparing groups -- The tips dataset -- Cohen's d -- Probability of superiority -- Hierarchical models -- Shrinkage -- Summary -- Keep reading -- Exercises -- Chapter 4: Understanding and Predicting Data with Linear Regression Models -- Simple linear regression -- The machine learning connection
- The core of linear regression models -- Linear models and high autocorrelation -- Modifying the data before running -- Changing the sampling method -- Interpreting and visualizing the posterior -- Pearson correlation coefficient -- Pearson coefficient from a multivariate Gaussian -- Robust linear regression -- Hierarchical linear regression -- Correlation, causation, and the messiness of life -- Polynomial regression -- Interpreting the parameters of a polynomial regression -- Polynomial regression - the ultimate model? -- Multiple linear regression -- Confounding variables and redundant variables -- Multicollinearity or when the correlation is too high -- Masking effect variables -- Adding interactions -- The GLM module -- Summary -- Keep reading -- Exercises -- Chapter 5: Classifying Outcomes with Logistic Regression -- Logistic regression -- The logistic model -- The iris dataset -- The logistic model applied to the iris dataset -- Making predictions -- Multiple logistic regression -- The boundary decision -- Implementing the model -- Dealing with correlated variables -- Dealing with unbalanced classes -- How do we solve this problem? -- Interpreting the coefficients of a logistic regression -- Generalized linear models -- Softmax regression or multinomial logistic regression -- Discriminative and generative models -- Summary -- Keep reading -- Exercises -- Chapter 6: Model Comparison -- Occam's razor - simplicity and accuracy -- Too many parameters leads to overfitting -- Too few parameters leads to underfitting -- The balance between simplicity and accuracy -- Regularizing priors -- Regularizing priors and hierarchical models -- Predictive accuracy measures -- Cross-validation -- Information criteria -- The log-likelihood and the deviance -- Akaike information criterion -- Deviance information criterion
- Widely available information criterion -- Pareto smoothed importance sampling leave-one-out cross-validation -- Bayesian information criterion -- Computing information criteria with PyMC3 -- A note on the reliability of WAIC and LOO computations -- Interpreting and using information criteria measures -- Posterior predictive checks -- Bayes factors -- Analogy with information criteria -- Computing Bayes factors -- Common problems computing Bayes factors -- Bayes factors and information criteria -- Summary -- Keep reading -- Exercises -- Chapter 7: Mixture Models -- Mixture models -- How to build mixture models -- Marginalized Gaussian mixture model -- Mixture models and count data -- The Poisson distribution -- The Zero-Inflated Poisson model -- Poisson regression and ZIP regression -- Robust logistic regression -- Model-based clustering -- Fixed component clustering -- Non-fixed component clustering -- Continuous mixtures -- Beta-binomial and negative binomial -- The Student's t-distribution -- Summary -- Keep reading -- Exercises -- Chapter 8: Gaussian Processes -- Non-parametric statistics -- Kernel-based models -- The Gaussian kernel -- Kernelized linear regression -- Overfitting and priors -- Gaussian processes -- Building the covariance matrix -- Sampling from a GP prior -- Using a parameterized kernel -- Making predictions from a GP -- Implementing a GP using PyMC3 -- Posterior predictive checks -- Periodic kernel -- Summary -- Keep reading -- Exercises -- Index
- Bayesian Analysis with Python: Unleash the power and flexibility of the Bayesian framework