- 1.0 FOUNDATIONAL CONCEPTS
- 1.1 Random Variables and Probability
- 1.1.1 Random Experiments, Random Walks, and Random Variables – An Introduction to the Foundational Concepts of Statistical Science
- 1.1.2 An Introduction to Conditional Probability and the Bayes’ Theorem [upcoming]
- 1.1.3 Convergence of Random Variables
- 1.1.3.1 Statistical Convergence and its Consequences [upcoming]
- 1.2 The Limit Theorems of Statistics
- 1.2.1 An Introduction to Markov’s Inequality and Chebyshev’s Inequality
- 1.2.2 The Weak Law of Large Numbers
- 1.2.2 Inverse Probability and the Central Limit Theorem
- 1.2.2.1 Understanding the Central Limit Theorem
- 1.2.2.2 The Fascinating History of the Law of Large Numbers and the Central Limit Theorem
- 1.2.2.2.1 On Jacob Bernoulli, the Law of Large Numbers, and the Origins of the Central Limit Theorem
- 1.2.2.2.2 Abraham De Moivre, His Famous Theorem, and the Birth of the Normal Curve [upcoming]
- 1.2.2.2.3 Pierre-Simon Laplace, Inverse Probability, and the Discovery of the Central Limit Theorem [upcoming]
- 1.2.2.3 A Proof of the Central Limit Theorem [upcoming]
- 1.3 Statistical Estimation
- 1.3.1 The Science Of Statistical Expectation
- 1.3.2 Properties Of The Statistical Estimator
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- 1.3.2.1 Bias
- 1.3.2.1.1 Omitted Variable Bias [upcoming]
- 1.3.2.1.2 Nonresponse Bias [upcoming]
- 1.3.1.1.3 The Bias-Variance Tradeoff
- 1.3.2.1 Bias
- 1.3.1.2 Estimator Consistency And Its Connection With The Bienaymé–Chebyshev Inequality
- 1.3.1.3 An Introduction To The Fisher Information: Gaining The Intuition Into A Complex Concept
- 1.3.1.4 Estimator Efficiency And The Cramér–Rao Bound On Variance
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- 1.3.3 Estimating The Range Of A Population Parameter: A Guide To Interval Estimation
- 1.4 Correlation
- 1.1 Random Variables and Probability
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- 1.5 Variance And Covariance
- 1.6 Random Processes
- 1.6.1 The Poisson Process
- 1.6.2 The Markov Process
- 1.6.2.1 The Discrete Time Markov Process
- 2.0 DATA TRANSFORMATIONS
- 3.0 REGRESSION MODELS
- 3.1 The Basics
- 3.2 Linear Regression Models
- 3.2.1 The Assumptions Of Linear Regression, And How To Test Them
- 3.2.2 An Overview Of The Variance-Covariance Matrices Used In Linear Regression
- 3.2.3 A Deep Dive Into The Variance-Covariance Matrices Used In Linear Regression
- 3.2.4 The Consequences of Omitting Important Variables From A Linear Regression Model
- 3.2.5 The Consequences of Including Irrelevant Variables In Linear Regression Models
- 3.2.6 The Effect Of Measurement Errors On A Linear Regression Model
- 3.2.6 Heteroscedasticity
- 3.2.6.1 Introduction To Heteroskedasticity
- 3.2.6.2 Introducing the White’s Heteroskedasticity Consistent Estimator
- 3.2.6.3 A Tutorial on White’s Heteroskedasticity Consistent Estimator Using Python And Statsmodels
- 3.2.6.4 Building Robust Linear Models For Nonlinear, Heteroscedastic Data
- 3.2.6.5 A Deep-Dive Into Generalized Least Squares Estimation
- 3.2.6.6 A Tutorial On Generalized Least Squares Estimation Using Python And Statsmodels
- 3.2.7 What Are Dummy Variables And How To Use Them In A Regression Model
- 3.2.8 Introduction To The Difference In Differences Regression Model
- 3.2.9 A Guide To Building Linear Models For Discontinuous Data
- 3.2.10 Introduction To The Quantile Regression Model
- 3.2.11 How To Use Proxy Variables In A Regression Model
- 3.2.12 Instrumental Variables Regression
- 3.2.13 Systems of Regression Equations
- 3.3 Regression Models For Counts Data Sets
- 3.4 Generalized Linear Models
- 3.5 Time Series Regression Models
- 3.5.1 Exponential Smoothing Models
- 3.5.2 ARIMA, SARIMA And SARIMAX models
- 3.5.3 Hidden Markov Models For Time Series Data Sets
- 3.5.4 Models For Integer Valued Time Series Data Sets
- 3.5.5 Time Series Models for Panel Data Sets
- 3.6 Models for Survival Data
- 3.7 Less Commonly Used (But Important) Nonlinear Regression Models
- 4.0 MODEL EVALUATION AND GOODNESS OF FIT
- 4.1 Analysis of Residual Errors
- 4.2 Goodness of Fit Measures
- 4.3 Model Selection Tests
- 4.4 Model Evaluation Techniques for Survival Models
- 5.0 BIO-STATISTICS
- 5.1 Vaccine Efficacy
- 5.0 BIBLIOGRAPHY AND REFERENCES