Bayesian analysis with Python : unleash the power and flexibility of the Bayesian framework

Key Features* Simplify the Bayes process for solving complex statistical problems using Python; * Tutorial guide that will take the you through the journey of Bayesian analysis with the help of sample problems and practice exercises; * Learn how and when to use Bayesian analysis in your applications with this guide. Book DescriptionThe 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 the Bayesian framework and the main advantages of this approach from a practical point of view. Moving on, we will explore the power and flexibility of generalized linear models and how to adapt them to a wide array of problems, including regression and classification. We will also look into mixture models and clustering data, and we will finish with advanced topics like non-parametrics models and Gaussian processes. With the help of Python and PyMC3 you will learn to implement, check and expand Bayesian models to solve data analysis problems. What you will learn* Understand the essentials Bayesian concepts from a practical point of view * Learn how to build probabilistic models using the Python library PyMC3 * Acquire the skills to sanity-check your models and modify them if necessary * Add structure to your models and get the advantages of hierarchical models * Find out how different models can be used to answer different data analysis questions * When in doubt, learn to choose between alternative models. * Predict continuous target outcomes using regression analysis or assign classes using logistic and softmax regression. * Learn how to think probabilistically and unleash the power and flexibility of the Bayesian framework About the Author**Osvaldo Martin** is a researcher at The National Scientific and Technical Research Council (CONICET), the main organization in charge of the promotion of science and technology in Argentina. He has worked on structural bioinformatics and computational biology problems, especially on how to validate structural protein models. He has experience in using Markov Chain Monte Carlo methods to simulate molecules and loves to use Python to solve data analysis problems. He has taught courses about structural bioinformatics, Python programming, and, more recently, Bayesian data analysis. Python and Bayesian statistics have transformed the way he looks at science and thinks about problems in general. Osvaldo was really motivated to write this book to help others in developing probabilistic models with Python, regardless of their mathematical background. He is an active member of the PyMOL community (a C/Python-based molecular viewer), and recently he has been making small contributions to the probabilistic programming library PyMC3. Table of Contents1. Thinking Probabilistically - A Bayesian Inference Primer 2. Programming Probabilistically – A PyMC3 Primer 3. Juggling with Multi-Parametric and Hierarchical Models 4. Understanding and Predicting Data with Linear Regression Models 5. Classifying Outcomes with Logistic Regression 6. Model Comparison 7. Mixture Models 8. Gaussian Processes Bayesian Analysis with Python Credits About the Author About the Reviewer www.PacktPub.com eBooks, discount offers, and more Why subscribe? Preface What this book covers What you need for this book Who this book is for Conventions Reader feedback Customer support Downloading the example code Downloading the color images of this book Errata Piracy Questions 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 2. Programming Probabilistically – A PyMC3 Primer Probabilistic programming Inference engines Non-Markovian methods Grid computing Quadratic method Variational methods Markovian methods Monte Carlo Markov chain Metropolis-Hastings Hamiltonian Monte Carlo/NUTS Other MCMC methods PyMC3 introduction Coin-flipping, the computational approach Model specification Pushing the inference button Diagnosing the sampling process Convergence Autocorrelation Effective size Summarizing the posterior Posterior-based decisions ROPE Loss functions Summary Keep reading Exercises 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 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 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 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 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 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

Unleash the power and flexibility of the Bayesian framework

About This Book

• Simplify the Bayes process for solving complex statistical problems using Python;
• Tutorial guide that will take the you through the journey of Bayesian analysis with the help of sample problems and practice exercises;
• Learn how and when to use Bayesian analysis in your applications with this guide.

Who This Book Is For

Students, researchers and data scientists who wish to learn Bayesian data analysis with Python and implement probabilistic models in their day to day projects. Programming experience with Python is essential. No previous statistical knowledge is assumed.

What You Will Learn

• Understand the essentials Bayesian concepts from a practical point of view
• Learn how to build probabilistic models using the Python library PyMC3
• Acquire the skills to sanity-check your models and modify them if necessary
• Add structure to your models and get the advantages of hierarchical models
• Find out how different models can be used to answer different data analysis questions
• When in doubt, learn to choose between alternative models.
• Predict continuous target outcomes using regression analysis or assign classes using logistic and softmax regression.
• Learn how to think probabilistically and unleash the power and flexibility of the Bayesian framework

In Detail

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 the Bayesian framework and the main advantages of this approach from a practical point of view. Moving on, we will explore the power and flexibility of generalized linear models and how to adapt them to a wide array of problems, including regression and classification. We will also look into mixture models and clustering data, and we will finish with advanced topics like non-parametrics models and Gaussian processes. With the help of Python and PyMC3 you will learn to implement, check and expand Bayesian models to solve data analysis problems.

Style and approach

Bayes algorithms are widely used in statistics, machine learning, artificial intelligence, and data mining. This will be a practical guide allowing the readers to use Bayesian methods for statistical modelling and analysis using Python.

Unleash the power and flexibility of the Bayesian framework About This Book Simplify the Bayes process for solving complex statistical problems using Python; Tutorial guide that will take the you through the journey of Bayesian analysis with the help of sample problems and practice exercises; Learn how and when to use Bayesian analysis in your applications with this guide. Who This Book Is For Students, researchers and data scientists who wish to learn Bayesian data analysis with Python and implement probabilistic models in their day to day projects. Programming experience with Python is essential. No previous statistical knowledge is assumed. What You Will Learn Understand the essentials Bayesian concepts from a practical point of view Learn how to build probabilistic models using the Python library PyMC3 Acquire the skills to sanity-check your models and modify them if necessary Add structure to your models and get the advantages of hierarchical models Find out how different models can be used to answer different data analysis questions When in doubt, learn to choose between alternative models. Predict continuous target outcomes using regression analysis or assign classes using logistic and softmax regression. Learn how to think probabilistically and unleash the power and flexibility of the Bayesian framework In Detail 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 the Bayesian framework and the main advantages of this approach from a practical point of view. Moving on, we will explore the power and flexibility of generalized linear models and how to adapt them to a wide array of problems, including regression and classification. We will also look into mixture models and clustering data, and we will finish with advanced topics like non-parametrics models and Gaussian processes. With the help of Python and PyMC3 you will learn to implement, check and expand Bayesian models to solve data analysis problems. Style and approach Bayes algorithms are widely used in statistics, machine learning, artificial intelligence, and data mining. This will be a practical guide allowing the readers to use Bayesian methods for statistical modelling and analysis using Python. Downloading the example code for this b.. Annotation Unleash the power and flexibility of the Bayesian frameworkAbout This Book Simplify the Bayes process for solving complex statistical problems using Python; Tutorial guide that will take the you through the journey of Bayesian analysis with the help of sample problems and practice exercises; Learn how and when to use Bayesian analysis in your applications with this guide. Who This Book Is ForStudents, researchers and data scientists who wish to learn Bayesian data analysis with Python and implement probabilistic models in their day to day projects. Programming experience with Python is essential. No previous statistical knowledge is assumed. What You Will Learn Understand the essentials Bayesian concepts from a practical point of view Learn how to build probabilistic models using the Python library PyMC3 Acquire the skills to sanity-check your models and modify them if necessary Add structure to your models and get the advantages of hierarchical models Find out how different models can be used to answer different data analysis questions When in doubt, learn to choose between alternative models. Predict continuous target outcomes using regression analysis or assign classes using logistic and softmax regression. Learn how to think probabilistically and unleash the power and flexibility of the Bayesian frameworkIn DetailThe 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 the Bayesian framework and the main advantages of this approach from a practical point of view. Moving on, we will explore the power and flexibility of generalized linear models and how to adapt them to a wide array of problems, including regression and classification. We will also look into mixture models and clustering data, and we will finish with advanced topics like non-parametrics models and Gaussian processes. With the help of Python and PyMC3 you will learn to implement, check and expand Bayesian models to solve data analysis problems. Style and approachBayes algorithms are widely used in statistics, machine learning, artificial intelligence, and data mining. This will be a practical guide allowing the readers to use Bayesian methods for statistical modelling and analysis using Python About This BookSimplify the Bayes process for solving complex statistical problems using Python;Tutorial guide that will take the you through the journey of Bayesian analysis with the help of sample problems and practice exercises;Learn how and when to use Bayesian analysis in your applications with this guide.Who This Book Is ForStudents, researchers and data scientists who wish to learn Bayesian data analysis with Python and implement probabilistic models in their day to day projects. Programming experience with Python is essential. No previous statistical knowledge is assumed.What You Will LearnUnderstand the essential Bayesian concepts from a practical point of viewLearn how to build probabilistic models using the Python library PyMC3Acquire the skills to sanity-check your models and modify them if necessaryAdd structure to your models and get the advantages of hierarchical modelsFind out how different models can be used to answer different data analysis questionsWhen in doubt, learn to choose between alternative modelsPredict continuous target outcomes using regression analysis or assign classes using logistic and softmax regressionLearn how to think probabilistically and unleash the power and flexibility of the Bayesian frameworkIn DetailThis book covers the main concepts of Bayesian statistics and how to apply them to data analysis. It is intended for readers without any previous statistical knowledge, but with some experience using Python. The basic elements of Bayesian modeling are introduced using a computational and practical approach. Synthetic and simple real data sets are used to explain each topic and explore the main features of the Bayesian framework. Among the explored models in the book we find the generalized linear models for regression and classification. Mixture models and hierarchical models are also explained. Model selection is discussed in its own chapter and the book ends with a short introduction to non-parametrics models and Gaussian processes. All Bayesian models are implemented using PyMC3, a Python library for probabilistic programming. Many of the main features of PyMC3 are exemplified throughout the text. With this book and the help of Python and PyMC3 you will learn to implement, check and expand Bayesian statistical models to solve a wide array of data analysis problems.