Statistical Computing in Nuclear Imaging

Content: Basic Statistical Concepts  Introduction  Before- and After-the-Experiment Concepts Definition of Probability Joint and Conditional Probabilities Statistical Model  Likelihood  Pre-Posterior and Posterior  Extension to Multi-Dimensions  Unconditional and Conditional Independence Summary  Elements of Decision Theory  Introduction  Loss Function and Expected Loss  After-the-Experiment Decision Making  Before-the-Experiment Decision Making Robustness of the Analysis   Counting Statistics  Introduction to Statistical Models  Fundamental Statistical Law  Exact Models of Photon-Limited Data Poisson Approximation  Normal Distribution Approximation   Monte Carlo Methods in Posterior Analysis Monte Carlo Approximations of Distributions  Monte Carlo Integrations  Monte Carlo Summations  Markov Chains   Basics of Nuclear Imaging Nuclear Radiation  Radiation Detection in Nuclear Imaging  Nuclear Imaging  Dynamic Imaging and Kinetic Modeling  Applications of Nuclear Imaging  Statistical Computing  Computing Using Poisson-Multinomial Statistics Examples of Statistical Computing   Appendix A Probability Distributions  Appendix B Elements of Set Theory  Appendix C Multinomial Distribution of Single-Voxel Imaging Appendix D Derivations of Sampling Distribution Ratios  Appendix E Equation (6.11)  Appendix F C++ Code of the OE Algorithm for STS References