Bayesian Analysis with Python

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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.;Annotation 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 analysisModel 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 readingExercises 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 autocorrelationModifying 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 variablesAdding 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.