Statistical Computing in Nuclear Imaging (Hardcover)

Statistical Computing in Nuclear Imaging introduces aspects of Bayesian computing in nuclear imaging. The book provides an introduction to Bayesian statistics and concepts and is highly focused on the computational aspects of Bayesian data analysis of photon-limited data acquired in tomographic measurements.

Basic statistical concepts, elements of decision theory, and counting statistics, including models of photon-limited data and Poisson approximations, are discussed in the first chapters. Monte Carlo methods and Markov chains in posterior analysis are discussed next along with an introduction to nuclear imaging and applications such as PET and SPECT.

The final chapter includes illustrative examples of statistical computing, based on Poisson-multinomial statistics. Examples include calculation of Bayes factors and risks as well as Bayesian decision making and hypothesis testing. Appendices cover probability distributions, elements of set theory, multinomial distribution of single-voxel imaging, and derivations of sampling distribution ratios. C++ code used in the final chapter is also provided.

The text can be used as a textbook that provides an introduction to Bayesian statistics and advanced computing in medical imaging for physicists, mathematicians, engineers, and computer scientists. It is also a valuable resource for a wide spectrum of practitioners of nuclear imaging data analysis, including seasoned scientists and researchers who have not been exposed to Bayesian paradigms.

《核醫學中的統計計算》介紹了在核醫學中的貝葉斯計算方面的知識。本書介紹了貝葉斯統計和概念，並且重點關注於在斷層測量中獲得的光子有限數據的貝葉斯數據分析的計算方面。

第一章討論了基本的統計概念、決策理論的要素以及計數統計學，包括光子有限數據和泊松近似的模型。接下來討論了後驗分析中的蒙特卡羅方法和馬爾可夫鏈，以及核醫學和PET、SPECT等應用的介紹。

最後一章包括了基於泊松-多項式統計的統計計算的實例。這些實例包括貝葉斯因子和風險的計算，以及貝葉斯決策和假設檢驗。附錄涵蓋了概率分布、集合論的要素、單像素成像的多項式分布，以及抽樣分布比率的推導。最後一章提供了C++代碼。

本書可作為物理學家、數學家、工程師和計算機科學家的教科書，介紹貝葉斯統計和醫學影像中的高級計算。對於核醫學數據分析的廣泛從業人員，包括經驗豐富的科學家和研究人員，本書也是一個寶貴的資源，使他們接觸到貝葉斯範式。