图书简介

Prologue; I Talking Probability; 1 1 The Eminence of Models; 1.A For brave eyes only; 2 Building Vocabulary; 2.1 Probability; 2.1.1 Basic rules; 2.2 Conditional probability; 2.2.1 Independence; 2.2.2 Law of total probability; 2.2.3 Bayes law; 2.3 Random variables; 2.3.1 Summation and integration; 2.3.2 Expectations and variances; 2.3.3 Two simple distributions; 2.4 The bell curve; 3 Gaining Fluency; 3.1 Multiple random quantities; 3.1.1 Higher-dimensional problems; 3.2 Two hard problems; 3.2.1 Functions of random variables; 3.2.2 Compound distributions; 3A Sums of independent random variables; 3.A.1 Convolutions; 3.A.2 Moment generating functions; 3.A.3 Formulae for expectations and variances; II Doing Statistics; 4 An Overview of Statistics; 4.1 Frequentist approach; 4.1.1 Functions of random variables; 4.2 Bayesian approach; 4.2.1 Compound distributions; 4.3 Two more distributions; 4.3.1 Poisson distribution; 4.3.2 Gamma distribution; 4.A Expectation and variance of the Poisson; 4.B Waiting time in Poisson process; 5 The Frequentist Approach; 5.1 Maximum likelihood estimation; 5.1.1 Random variables that are i.i.d.; 5.1.2 Problems with covariates; 5.2 Statistical properties of estimators; 5.3 Some advanced techniques; 5.3.1 EM algorithm; 5.3.2 Latent variables; 5.A Finite mixture models; 6 The Bayesian Approach; 6.1 Basics; 6.2 Empirical Bayes; 6.3 Hierarchical Bayes; 6.A General sampling algorithms; 6.A.1 Metropolis algorithm; 6.A.2 Some theory; 6.A.3 Metropolis-Hastings algorithm; III Facing Uncertainty; 7 Interval Estimation; 7.1 Uncertainty quantification; 7.1.1 Bayesian version; 7.1.2 Frequentist version; 7.2 Main difficulty; 7.3 Two useful methods; 7.3.1 Likelihood ratio; 7.3.2 Bootstrap; 8 Tests of Significance; 8.1 Basics; 8.1.1 Relation to interval estimation; 8.1.2 The p-value; 8.2 Some challenges; 8.2.1 Multiple testing; 8.2.2 Six degrees of separation; 8.A Intuition of Benjamini-Hockberg; IV Appendices; A Some Further Topics; A.1 Graphical models; A.2 Regression models; A.3 Data collection; Epilogue; Bibliography; Index

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