Building Statistical Models in Python

Building Statistical Models in Python
Contributors
About the authors
About the reviewers
Preface
   Who this book is for
   What this book covers
   To get the most out of this book
   Download the example code files
   Conventions used
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Part 1:Introduction to Statistics
1
Sampling and Generalization
   Software and environment setup
   Population versus sample
   Population inference from samples
      Randomized experiments
      Observational study
   Sampling strategies – random, systematic, stratified, and clustering
      Probability sampling
      Non-probability sampling
   Summary
2
Distributions of Data
   Technical requirements
   Understanding data types
      Nominal data
      Ordinal data
      Interval data
      Ratio data
      Visualizing data types
   Measuring and describing distributions
      Measuring central tendency
      Measuring variability
      Measuring shape
   The normal distribution and central limit theorem
      The Central Limit Theorem
   Bootstrapping
      Confidence intervals
      Standard error
      Correlation coefficients (Pearson’s correlation)
   Permutations
      Permutations and combinations
      Permutation testing
   Transformations
   Summary
   References
3
Hypothesis Testing
   The goal of hypothesis testing
      Overview of a hypothesis test for the mean
      Scope of inference
      Hypothesis test steps
   Type I and Type II errors
      Type I errors
      Type II errors
   Basics of the z-test – the z-score, z-statistic, critical values, and p-values
      The z-score and z-statistic
      A z-test for means
      z-test for proportions
      Power analysis for a two-population pooled z-test
   Summary
4
Parametric Tests
   Assumptions of parametric tests
      Normally distributed population data
      Equal population variance
   T-test – a parametric hypothesis test
      T-test for means
      Two-sample t-test – pooled t-test
      Two-sample t-test – Welch’s t-test
      Paired t-test
   Tests with more than two groups and ANOVA
      Multiple tests for significance
      ANOVA
      Pearson’s correlation coefficient
      Power analysis examples
   Summary
   References
5
Non-Parametric Tests
   When parametric test assumptions are violated
      Permutation tests
   The Rank-Sum test
      The test statistic procedure
      Normal approximation
      Rank-Sum example
   The Signed-Rank test
   The Kruskal-Wallis test
   Chi-square distribution
   Chi-square goodness-of-fit
   Chi-square test of independence
   Chi-square goodness-of-fit test power analysis
   Spearman’s rank correlation coefficient
   Summary
Part 2:Regression Models
6
Simple Linear Regression
   Simple linear regression using OLS
   Coefficients of correlation and determination
      Coefficients of correlation
      Coefficients of determination
   Required model assumptions
      A linear relationship between the variables
      Normality of the residuals
      Homoscedasticity of the residuals
      Sample independence
   Testing for significance and validating models
      Model validation
   Summary
7
Multiple Linear Regression
   Multiple linear regression
      Adding categorical variables
      Evaluating model fit
      Interpreting the results
   Feature selection
      Statistical methods for feature selection
      Performance-based methods for feature selection
      Recursive feature elimination
   Shrinkage methods
      Ridge regression
      LASSO regression
      Elastic Net
   Dimension reduction
      PCA – a hands-on introduction
      PCR – a hands-on salary prediction study
   Summary
Part 3:Classification Models
8
Discrete Models
   Probit and logit models
   Multinomial logit model
   Poisson model
      The Poisson distribution
      Modeling count data
   The negative binomial regression model
      Negative binomial distribution
   Summary
9
Discriminant Analysis
   Bayes’ theorem
      Probability
      Conditional probability
      Discussing Bayes’ Theorem
   Linear Discriminant Analysis
      Supervised dimension reduction
   Quadratic Discriminant Analysis
   Summary
Part 4:Time Series Models
10
Introduction to Time Series
   What is a time series?
   Goals of time series analysis
   Statistical measurements
      Mean
      Variance
      Autocorrelation
      Cross-correlation
   The white-noise model
   Stationarity
   Summary
   References
11
ARIMA Models
   Technical requirements
   Models for stationary time series
      Autoregressive (AR) models
      Moving average (MA) models
      Autoregressive moving average (ARMA) models
   Models for non-stationary time series
      ARIMA models
   Seasonal ARIMA models
   More on model evaluation
   Summary
   References
12
Multivariate Time Series
   Multivariate time series
      Time-series cross-correlation
   ARIMAX
      Preprocessing the exogenous variables
      Fitting the model
      Assessing model performance
   VAR modeling
      Step 1 – visual inspection
      Step 2 – selecting the order of AR(p)
      Step 3 – assessing cross-correlation
      Step 4 – building the VAR(p,q) model
      Step 5 – testing the forecast
      Step 6 – building the forecast
   Summary
   References
Part 5:Survival Analysis
13
Time-to-Event Variables – An Introduction
   What is censoring?
      Left censoring
      Right censoring
      Interval censoring
      Type I and Type II censoring
   Survival data
   Survival Function, Hazard and Hazard Ratio
   Summary
14
Survival Models
   Technical requirements
   Kaplan-Meier model
      Model definition
      Model example
   Exponential model
      Model example
   Cox Proportional Hazards regression model
      Step 1
      Step 2
      Step 3
      Step 4
      Step 5
   Summary
Index
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