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  • Chapter 1: Introduction and Data Sets
  • Chapter 2: Fast Computation and Massive Datasets
  • Chapter 3: Probability and Statistical Distributions
    • Overview of Probability and Random Variables
    • Descriptive Statistics
    • Univariate Distribution Functions
    • The Central Limit Theorem
    • Bivariate and multivariate distribution functions
  • Chapter 4: Classical Statistical Inference
    • Maximum Likelihood Estimation (MLE)
    • MLE applied to Gaussian mixtures
    • Confidence Estimates: The Bootstrap and The Jackknife
    • Hypothesis Testing
    • Comparison of distributions
    • Nonparametric modeling and selection effects
  • Chapter 5: Bayesian Statistical Inference
    • Parameter Estimation for a Gaussian Distribution
    • Parameter Estimation for a Binomial Distribution
    • Parameter estimation for the Cauchy (Lorentzian) distribution
    • Approximate Bayesian Computation Example
    • Hierarchical Bayes Example
  • Chapter 6: Searching for Structure in Point Data
    • Density Estimation for SDSS “Great Wall”
    • Searching for Structure in Point Data
    • Gaussian Mixture Models Example
    • Extreme Deconvolution
  • Chapter 7: Dimensionality and its Reduction
    • Dimensionality reduction
  • Chapter 8: Regression and Model Fitting
    • Measurement Errors in Linear Regression
    • Measurement errors in both dependent and independent variables
  • Chapter 9: Classification
    • Classification
    • Deep Learning: Classifying Astronomical Images
  • Chapter 10: Time Series Analysis
    • Modeling Toolkit For Time Series Analysis
    • Wavelets
    • Digital Filtering
    • Temporally localized signals
    • Analysis of Stochastic Processes
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Chapter 4: Classical Statistical Inference

Chapter 4: Classical Statistical Inference#

This chapter develops the classical or “frequentist” approach to statistics.

  • Maximum Likelihood Estimation (MLE)
  • MLE applied to Gaussian mixtures
  • Confidence Estimates: The Bootstrap and The Jackknife
  • Hypothesis Testing
  • Comparison of distributions
  • Nonparametric modeling and selection effects

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Bivariate and multivariate distribution functions

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Maximum Likelihood Estimation (MLE)

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