Numerical Analysis for Statisticians

Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.

Contenu

Recurrence Relations.- Power Series Expansions.- Continued Fraction Expansions.- Asymptotic Expansions.- Solution of Nonlinear Equations.- Vector and Matrix Norms.- Linear Regression and Matrix Inversion.- Eigenvalues and Eigenvectors.- Splines.- The EM Algorithm.- Newton's Method and Scoring.- Variations on the EM Theme.- Convergence of Optimization Algorithms.- Constrained Optimization.- Concrete Hilbert Spaces.- Quadrature Methods.- The Fourier Transform.- The Finite Fourier Transform.- Wavelets.- Generating Random Deviates.- Independent Monte Carlo.- Bootstrap Calculations.- Finite-State Markov Chains.- Markov Chain Monte Carlo.