Digital Signal Processing (DSP) with Python Programming

Inbunden, Engelska, 2017

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The parameter estimation and hypothesis testing are the basic tools in statistical inference. These techniques occur in many applications of data processing., and methods of Monte Carlo have become an essential tool to assess performance. For pedagogical purposes the book includes several computational problems and exercices. To prevent students from getting stuck on exercises, detailed corrections are provided.

Produktinformation

Utgivningsdatum2017-01-13
Mått69 x 104 x 20 mm
Vikt499 g
FormatInbunden
SpråkEngelska
Antal sidor304
FörlagISTE Ltd and John Wiley & Sons Inc
ISBN9781786301260

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Preface ixNotations and Abbreviations xiA Few Functions of Python® xiiiChapter 1 Useful Maths 11.1. Basic concepts on probability 11.2. Conditional expectation 101.3. Projection theorem 111.3.1. Conditional expectation 141.4. Gaussianity 141.4.1. Gaussian random variable 141.4.2. Gaussian random vectors 151.4.3. Gaussian conditional distribution 161.5. Random variable transformation 181.5.1. General expression 181.5.2. Law of the sum of two random variables 191.5.3. δ-method 201.6. Fundamental theorems of statistics 221.7. A few probability distributions 24Chapter 2 Statistical Inferences 292.1. First step: visualizing data 292.1.1. Scatter plot 292.1.2. Histogram/boxplot 302.1.3. Q-Q plot 322.2. Reduction of dataset dimensionality 342.2.1. PCA 342.2.2. LDA 362.3. Some vocabulary 402.3.1. Statistical inference 402.4. Statistical model 412.4.1. Notation 422.5. Hypothesis testing 432.5.1. Simple hypotheses 452.5.2. Generalized likelihood ratio test (GLRT) 502.5.3. χ 2 goodness-of-fit test 572.6. Statistical estimation 582.6.1. General principles 582.6.2. Least squares method 622.6.3. Least squares method for the linear model 642.6.4. Method of moments 812.6.5. Maximum likelihood approach 842.6.6. Logistic regression 1002.6.7. Non-parametric estimation of probability distribution 1032.6.8. Bootstrap and others 107Chapter 3 Inferences on HMM 1133.1. Hidden Markov models (HMM) 1133.2. Inferences on HMM 1163.3. Filtering: general case 1173.4. Gaussian linear case: Kalman algorithm 1183.4.1. Kalman filter 1183.4.2. RTS smoother 1273.5. Discrete finite Markov case 1293.5.1. Forward-backward formulas 1303.5.2. Smoothing formula at one instant 1333.5.3. Smoothing formula at two successive instants 1343.5.4. HMM learning using the EM algorithm 1353.5.5. The Viterbi algorithm 137Chapter 4 Monte-Carlo Methods 1414.1. Fundamental theorems 1414.2. Stating the problem 1414.3. Generating random variables 1444.3.1. The cumulative function inversion method 1444.3.2. The variable transformation method 1474.3.3. Acceptance-rejection method 1494.3.4. Sequential methods 1514.4. Variance reduction 1564.4.1. Importance sampling 1564.4.2. Stratification 1604.4.3. Antithetic variates 164Chapter 5 Hints and Solutions 1675.1. Useful maths 1675.2. Statistical inferences 1705.3. Inferences on HMM 2265.4. Monte-Carlo methods 251Bibliography 261Index 263