Random Closed Sets and Capacity Functionals -- Expectations of Random Sets -- Minkowski Addition -- Unions of Random Sets -- Random Sets and Random Functions. Appendices: Topological Spaces -- Linear Spaces -- Space of Closed Sets -- Compact Sets and the Hausdorff Metric -- Multifunctions and Continuity -- Measures and Probabilities -- Capacities -- Convex Sets -- Semigroups and Harmonic Analys…
Modèles micro-macro pour les solides -- Techniques d’homogénéisation -- Simulation moléculaire -- Modèles micro-macro pour les fluides -- Cinétique chimique -- Vers une unité des approches.Systèmes multi-échelles est une introduction à la problématique des systémes multi-échelles du point de vue du mathématicien appliqué. Il se compose d'une mosaique d'exemples dont le seul lie…
to Survival Analysis -- Kaplan-Meier Survival Curves and the Log-Rank Test -- The Cox Proportional Hazards Model and Its Characteristics -- Evaluating the Proportional Hazards Assumption -- The Stratified Cox Procedure -- Extension of the Cox Proportional Hazards Model for Time-Dependent Variables -- Parametric Survival Models -- Recurrent Event Survival Analysis -- Competing Risks Survival Ana…
Kinetic theory -- Related Markov processes -- Stochastic weighted particle method -- Numerical experiments.Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes a…
Basics -- Introduction -- Linear Programming Prerequisites -- Nonlinear Programming Prerequisites -- Single-stage SLP Models -- Introduction -- Models involving Probability Functions -- Quantile Functions, Value at Risk -- Models Based on Expectation -- Models Built with Deviation Measures -- Modeling Risk and Opportunity -- Risk Measures -- Multi-stage SLP Models -- The General SLP with Recour…
Dependence Properties of Meta-Elliptical Distributions -- The Statistical Significance of Palm Beach County -- Bayesian Functional Estimation of Hazard Rates for Randomly Right Censored Data Using Fourier Series Methods -- Conditions for the Validity of F-Ratio Tests for Treatment and Carryover Effects in Crossover Designs -- Bias in Estimating the Variance of K-Fold Cross-Validation -- Effecti…
Inverse Problems and Interpretation of Measurements -- Classical Regularization Methods -- Statistical Inversion Theory -- Nonstationary Inverse Problems -- Classical Methods Revisited -- Model Problems -- Case Studies.The book develops the statistical approach to inverse problems with an emphasis on modeling and computations. The framework is the Bayesian paradigm, where all variables are mode…
Introduction -- 1. Stochastic Differential Equations -- 2. One-Sided Classification of Isolated Singular Points -- 3. Two-Sided Classification of Isolated Singular Points -- 4. Classification at Infinity and Global Solutions -- 5. Several Special Cases -- Appendix A: Some Known Facts -- Appendix B: Some Auxiliary Lemmas -- Rferences -- Index of Notation -- Index of Terms.The authors introduce, …
Processus de Lévy: R.A. Doney: Tanaka's construction for random walks and Lévy processes -- R.A. Doney: Some excursion calculations for spectrally one-sided Lévy processes -- A.E. Kyprianou, Z. Palmowski: A martingale review of some fluctuation theory for spectrally megative Lévy processes -- M.R. Pistorius: A potential-theoretical review of some exit problems of spectrally negative Lévy p…
Exploratory and Descriptive Methods -- Basic Statistical Methods -- Linear Regression -- Predictor Selection -- Logistic Regression -- Survival Analysis -- Repeated Measures and Longitudinal Data Analysis -- Generalized Linear Models -- Complex Surveys -- Summary.This new book provides a unified, in-depth, readable introduction to the multipredictor regression methods most widely used in biosta…