Degrees Of Mixture Degrees Of Freedom

Finite Mixture Models

An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.

Mixture Models

Equations for Isentropic and Plane Shock Flows of Mixtures of Undissociated Planetary Gases

Equations for aerodynamic quantities of interest in equilibrium isentropic one-dimensional flows and for properties across plane showck waves in arbitrary of planetary gases are derived under the assumption that the gases obey the perfect gas law. This assumption restricts the range of applicability of the equations to conditions for which the onset of chemical dissociation or ionization has not been reached although no requirement for the gases to be calorically perfect is imposed. Analytic functions used to specify the variation of specific heats with temperature are consistent with the assumption that molecular vibrations behave like harmonic oscillators and are independent of rotational degrees of freedom. Simplified equations giving approximate results over more limited ranges of the variables are also presented. Sample comparisons of the aerodynamic behavior of a number of pure gases are made. It is shown that while some of the flow quantities characterizing aerodynamic flows are very sensitive to gas composition, the stagnation pressure coefficients for a number of gases differ by only a few percent from one gas to another.