# 1 - Computational Statistics Stat 227...

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Computational Statistics: Stat 227 May 25, 2005 Contents 1 Logistics 1.1 Prerequisites 1.2 Text 1.3 Assignments 1.4 Projects 1.5 Office Hours 1.6 Course Web Site 1.7 Startup computer labs Sequoia 201 1.8 Outline 1.9 Statistical Methods 1.10 Algorithms 1.11 Software 2 Homeworks 3 Numerical Analysis for Statisticians 3.1 If you missed some lectures: 3.2 Real numbers: Floating Point Arithmetic 3.3 Matrices, and their decompositions 3.4 The linear equation solving problem 3.4.1 Square systems 3.4.2 Rectangular system: QR decomposition and least squares 3.4.3 Examples 3.4.4 Givens Rotations 3.4.5 R examples handout 3.4.6 Backsubstitution 3.5 Householder Functions 3.5.1 Householder Multiplication-Row 3.6 QR decomposition in R 3.7 Singular value decompostion and pc regression 3.7.1 Ridge Regression 3.7.2 Principal Components Regression 3.7.3 Principal Components 3.8 More than I said on the Singular Value Decomposition 3.8.1 Generalized Inverses 3.9 Principal Components 3.9.1 Eigenvalue Analysis 4 EM algorithm Computational Statistics: Stat 227 http://www-stat.stanford.edu/~susan/courses/s227... 1 of 57 03/11/2010 11:26 PM

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4.0.2 Implementation 4.0.3 Estimating Mixture Proportions 4.0.4 EM for exponential families 5 Monte Carlo Simulations 5.1 Monte Carlo methods 5.1.1 Antithetic Resampling 5.1.2 Importance Sampling 5.2 Random Number Generation- Uniform[0 , 1] 5.2.1 Congruential Methods 5.2.2 Other `Better?' Methods 5.2.3 Random Number Generation- other than Uniform 5.2.4 Inversion Method 5.2.5 Rejection Methods 5.2.6 Table Lookup 5.3 Specialized Methods 5.3.1 Polar methods for the Normal 5.4 Importance Sampling 6 The Bootstrap, Permutation Tests, Simulation 6.1 Motivation 6.2 The bootstrap : the univariate context 6.3 In practice 6.4 S examples for simple bootstraps 6.5 Parametric bootstrap 6.6 Smoothed Bootstrap 6.7 Di�erent Uses for bootstrapping 6.7.1 Quality of Estimates 6.8 Enhancements 6.9 Bootstrap-t : Studentizing 6.10 R functions 6.11 Preliminary Transformations of the Estimate 6.12 Pre-pivoting or Double Bootstrap 6.13 Balanced Bootstrap : saving computations 6.14 Antithetic Sampling : more on saving computations 6.15 Bootstrap and Randomization Tests 6.15.1 An example : Infants walking 6.15.2 More generally 6.16 Finding out how good a parametric bootstrap procedure is through a simulation experience : 6.17 Maximum Likelihood Estimation 6.17.1 Maximum Likelihood of Multinomial Cell Probabilities 6.17.2 The Hardy Weinberg Example 7 Density Estimation 8 References Chapter 1 Logistics Computational Statistics: Stat 227 http://www-stat.stanford.edu/~susan/courses/s227... 2 of 57 03/11/2010 11:26 PM
Time and Place: MW 11.-12.15, Hewlett 101, please do not arrive late and distract your colleagues 1.1 Prerequisites Computer Science 106(Introd. to Computer Programming) or equivalent Stat 116 (Probability) or equivalent Math 113 (Matrix Algebra) or equivalent 1.2 Text Computational Statistics, Geof Givens and Jennifer Hoeting. Wiley 2005 1.3 Assignments There will be four homeworks/labs to hand in 40 % and one big project ( final) 60 % 1.4 Projects Projects Pick a paper from the projects below or on the website on the course webpage at http://www-stat.stanford.edu/~susan/courses/s227/ .

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