Contents
Preface vii Mathematical notation xi Contents xiii 1 Introduction 1
1.1 1.2
1.3 1.4 1.5
Example:PolynomialCurveFitting................. 4
ProbabilityTheory .......................... 12 1.2.1 Probabilitydensities ..................... 17 1.2.2 Expectationsandcovariances ................ 19 1.2.3 Bayesianprobabilities .................... 21 1.2.4 TheGaussiandistribution .................. 24 1.2.5 Curvefittingre-visited .................... 28 1.2.6 Bayesiancurvefitting .................... 30
ModelSelection ........................... 32 TheCurseofDimensionality..................... 33 DecisionTheory ........................... 38
1.5.1 Minimizing the misclassification rate . . . . . . . . . . . . 39
1.5.2 Minimizingtheexpectedloss ................ 41
1.5.3 Therejectoption ....................... 42
1.5.4 Inferenceanddecision .................... 42
1.5.5 Loss functions for regression . . . . . . . InformationTheory................
.......... 46 .......... 48 .......... 55
1.6
Exercises .................................. 58
