Acknowledgements; Contents; 1 Introduction; 1.1 On Dynamic Mixtures; 1.2 General Conventions; 2 Basic Models; 2.1 Regression Model; 2.1.1 Estimation; 2.1.2 Point Estimates; 2.1.3 Prediction; 2.2 Categorical Model; 2.2.1 Estimation; 2.2.2 Point Estimates; 2.2.3 Prediction; 2.3 State-Space Model; 2.3.1 State Estimation; 3 Statistical Analysis of Dynamic Mixtures; 3.1 Dynamic Mixture; 3.2 Unified Approach to Mixture Estimation; 3.2.1 The Component Part; 3.2.2 The Pointer Part; 3.2.3 Main Subtasks of Mixture Estimation; 3.2.4 General Algorithm; 3.3 Mixture Prediction; 3.3.1 Pointer Prediction

3.3.2 Data Prediction4 Dynamic Mixture Estimation; 4.1 Normal Regression Components; 4.1.1 Algorithm; 4.1.2 Simple Program; 4.1.3 Comments; 4.2 Categorical Components; 4.2.1 Algorithm; 4.2.2 Simple Program; 4.2.3 Comments; 4.3 State-Space Components; 4.3.1 Algorithm; 4.3.2 Simple Program; 4.3.3 Comments; 5 Program Codes; 5.1 Main Program; 5.1.1 Comments; 5.2 Subroutines; 5.2.1 Initialization of Estimation; 5.2.2 Computation of Proximities; 5.2.3 Update of Component Statistics; 5.3 Collection of Programs; 6 Experiments; 6.1 Mixture with Regression Components; 6.1.1 Well-Separated Components

6.1.2 Weak Components6.1.3 Reduced Number of Components; 6.1.4 High-Dimensional Output; 6.1.5 Big Noise; 6.2 Mixture with Categorical Components; 6.3 Mixture with State-Space Components; 6.4 Case Studies; 6.4.1 Static Normal Components; 6.4.2 Dynamic Normal Components; 7 Appendix A (Supporting Notions); 7.1 Useful Matrix Formulas ; 7.2 Matrix Trace ; 7.3 Dirac and Kronecker Functions ; 7.4 Gamma and Beta Functions ; 7.5 The Bayes Rule ; 7.6 The Chain Rule; 7.7 The Natural Conditions of Control ; 7.8 Conjugate Dirichlet Distribution; 7.8.1 The Normalization Constant of Dirichlet Distribution

7.8.2 Statistics Update with the Conjugate Dirichlet Distribution7.8.3 The Parameter Point Estimate of the Categorical Model; 7.8.4 Data Prediction with Dirichlet Distribution; 7.9 Conjugate Gauss-Inverse-Wishart Distribution ; 7.9.1 Statistics Update for the Normal Regression Model; 7.9.2 The Parameter Point Estimate of the Regression Model ; 7.9.3 The Proximity Evaluation; 8 Appendix B (Supporting Programs); 8.1 Simulation Programs; 8.1.1 The Simulation of Pointer Values; 8.1.2 The Simulation of Mixture with Regression Components; 8.1.3 The Simulation of Mixture with Discrete Components

8.1.4 The Simulation of Mixture with State-Space Components8.2 Supporting Subroutines; 8.2.1 Scilab Start Settings; 8.2.2 The Point Estimation of a Normal Regression Model; 8.2.3 The Value of a Normal Multivariate Distribution; 8.2.4 Discrete Regression Vector Coding; 8.2.5 Kalman Filter; 8.2.6 Matrix Upper
Lower Factorization; 8.2.7 Transition Table Normalization; 8.2.8 The Approximation of Normal Pdfs by a Single Pdf; Appendix References