Statistical foundations, reasoning and inference : for science and data science / / by Göran Kauermann, Helmut Küchenhoff, Christian Heumann

• Autore: Kauermann Göran
• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (361 pages)
• Disciplina: 519.5
• Soggetto topico: Mathematical statistics; Estadística matemàtica
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): KüchenhoffHelmut; HeumannChristian <1962->
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Introduction -- 1.1 General Ideas -- 1.2 Databases, Samples and Biases -- 2 Background in Probability -- 2.1 Random Variables and Probability Models -- 2.1.1 Definitions of Probability -- 2.1.2 Independence, Conditional Probability, BayesTheorem -- 2.1.3 Random Variables -- 2.1.4 Common Distributions -- 2.1.5 Exponential Family Distributions -- 2.1.6 Random Vectors and Multivariate Distributions -- 2.2 Limit Theorems -- 2.3 Kullback-Leibler Divergence -- 2.4 Exercises -- 3 Parametric Statistical Models -- 3.1 Likelihood and Bayes -- 3.2 Parameter Estimation -- 3.2.1 Bayes Estimation -- 3.2.2 Maximum Likelihood Estimation -- 3.2.3 Method of Moments -- 3.2.4 Loss Function Approach -- 3.2.5 Kullback-Leibler Loss -- 3.3 Sufficiency and Consistency, Efficiency -- 3.3.1 Sufficiency -- 3.3.2 Consistency -- 3.3.3 Cramer-Rao Bound -- 3.4 Interval Estimates -- 3.4.1 Confidence Intervals -- 3.4.2 Credibility Interval -- 3.5 Exercises -- 4 Maximum Likelihood Inference -- 4.1 Score Function and Fisher Information -- 4.2 Asymptotic Normality -- 4.3 Numerical Calculation of ML Estimate -- 4.4 Likelihood-Ratio -- 4.5 Exercises -- 5 Bayesian Statistics -- 5.1 Bayesian Principles -- 5.2 Selecting a Prior Distribution -- 5.2.1 Jeffrey's Prior -- 5.2.2 Empirical Bayes -- 5.2.3 Hierarchical Prior -- 5.3 Integration Methods for the Posterior -- 5.3.1 Numerical Integration -- 5.3.2 Laplace Approximation -- 5.3.3 Monte Carlo Approximation -- 5.4 Markov Chain Monte Carlo (MCMC) -- 5.5 Variational Bayes -- 5.6 Exercises -- 6 Statistical Decisions -- 6.1 The Idea of Testing -- 6.2 Classical Tests -- 6.2.1 t-Test -- 6.2.2 Wald Test -- 6.2.3 Score Test -- 6.2.4 Likelihood-Ratio Test -- 6.3 Power of a Test and Neyman-Pearson Test -- 6.4 Goodness-of-Fit Tests -- 6.4.1 Chi-Squared Goodness-of-Fit Test -- 6.4.2 Kolmogorov-Smirnov Test. ; 6.5 Tests on Independence -- 6.5.1 Chi-Squared Test of Independence -- 6.5.2 Fisher's Exact Test -- 6.5.3 Correlation-Based Tests -- 6.6 p-Value, Confidence Intervals and Test -- 6.6.1 The p-Value -- 6.6.2 Confidence Intervals and Tests -- 6.7 Bayes Factor -- 6.8 Multiple Testing -- 6.9 Significance and Relevance -- 6.9.1 Significance in Large Samples -- 6.9.2 Receiver Operating Characteristics -- 6.10 Exercises -- 7 Regression -- 7.1 Linear Model -- 7.1.1 Simple Linear Model -- 7.1.2 Multiple Linear Model -- 7.1.3 Bayesian Inference in the Linear Model -- 7.2 Weighted Regression -- 7.3 Quantile Regression -- 7.4 Nonparametric Smooth Models -- 7.5 Generalised Linear Models -- 7.6 Case Study in Generalised Additive Models -- 7.7 Exercises -- 8 Bootstrapping -- 8.1 Nonparametric Bootstrap -- 8.1.1 Motivation -- 8.1.2 Empirical Distribution Function and the Plug-In Principle -- 8.1.3 Bootstrap Estimate of a Standard Error -- 8.1.4 Bootstrap Estimate of a Bias -- 8.2 Parametric Bootstrap -- 8.3 Bootstrap in Regression Models -- 8.4 Theory and Extension of Bootstrapping -- 8.4.1 Theory of the Bootstrap -- 8.4.2 Extensions of the Bootstrap -- 8.4.3 Subsampling -- 8.5 Bootstrapping the Prediction Error -- 8.5.1 Prediction Error -- 8.5.2 Cross Validation Estimate of the Prediction Error -- 8.5.3 Bootstrapping the Prediction Error -- 8.6 Bootstrap Confidence Intervals and Hypothesis Testing -- 8.6.1 Bootstrap Confidence Intervals -- 8.6.2 Testing -- 8.7 Sampling from Data -- 8.8 Exercises -- 9 Model Selection and Model Averaging -- 9.1 Akaike Information Criterion -- 9.1.1 Maximum Likelihood in Misspecified Models -- 9.1.2 Derivation of AIC -- 9.1.3 AIC for Model Comparison -- 9.1.4 Extensions and Modifications -- Bias-Corrected AIC -- The Bayesian Information Criterion -- Deviance Information Criterion -- Cross Validation -- 9.2 AIC/BIC Model Averaging. ; 9.3 Inference After Model Selection -- 9.4 Model Selection with Lasso -- 9.5 The Bayesian Model Selection -- 9.6 Exercises -- 10 Multivariate and Extreme Value Distributions -- 10.1 Multivariate Normal Distribution -- 10.1.1 Parameterisation -- 10.1.2 Graphical Models -- 10.1.3 Principal Component Analysis -- 10.2 Copulas -- 10.2.1 Copula Construction -- 10.2.2 Common Copula Models -- Gaussian and Elliptical Copulas -- Archimedean Copula -- Pair Copula -- 10.2.3 Tail Dependence -- 10.3 Statistics of Extremes -- 10.4 Exercises -- 11 Missing and Deficient Data -- 11.1 Missing Data -- 11.1.1 Missing Data Mechanisms -- 11.1.2 EM Algorithm -- 11.1.3 Multiple Imputation -- 11.1.4 Censored Observations -- 11.1.5 Omitting Variables (Simpson's Paradox) -- 11.2 Biased Data -- 11.3 Quality Versus Quantity -- 11.4 Measurement and Measurement Error -- 11.4.1 Theory of Measurement -- 11.4.2 Effect of Measurement Error in Regression -- 11.4.3 Correction for Measurement Error in LinearRegression -- 11.4.4 General Strategies for Measurement Error Correction -- 11.5 Exercises -- 12 Experiments and Causality -- 12.1 Design of Experiments -- 12.1.1 Experiment Versus Observational Data -- 12.1.2 ANOVA -- 12.1.3 Block Designs -- 12.1.4 More Complex Designs -- 12.2 Instrumental Variables -- 12.3 Propensity Score Matching -- 12.4 Directed Acyclic Graphs (DAGs) -- 12.5 Exercises -- References -- Index.
• Titolo autorizzato: Statistical foundations, reasoning and inference
• ISBN: 3-030-69827-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466409003316
• Lo trovi qui: Univ. di Salerno
• Serie: Springer series in statistics.