1.2A Preview of the Book
Chapter 2 describes the foundation of Bayesian statistics. First, Bayesian theorem is given for both discrete and continuous measurements. This necessitates an explanation of the components of Bayes theorem, namely prior information, the posterior distribution of the unknown parameters, and the predictive distribution of future observations. Also provided in this chapter are many examples that illustrate Bayes theorem, among then the standard populations, such as the binomial, the normal, the Poisson, the multivariate normal, and the multinomial, and the Dirichlet.
Chapter 3 explicates the biology and evolutionary behavior of infectious diseases, including viral and bacterial manifestations of the contagion. Next to be explained is that of the immune response via antibodies that attack the invading pathogens. The immune response involves various blood cells (white, red, and platelets) that defend against the disease. Next to be described are drugs that attempt to destroy the components of the disease. A good example of this is quinine and related drugs that control the malaria virus, and drugs that can nearly eradicate the HIV virus of AIDS patients. Although drugs have been very successful in controlling diseases, drug resistance can become a serious issue. This was the case for streptomycin, the breakthrough drug that controlled tuberculosis, but later developed a resistance. Of course, vaccines were a giant advance in medical theory, and one first thinks of the smallpox vaccine against polio. Of course, there are many examples of vaccines, such as those against measles, mumps, and diphtheria. It should be noted that for some viruses, a vaccine is yet to be developed. AIDS and Ebola do not have vaccines, but a very successful treatment for AIDS is successful, but not for Ebola. Of course, transmission of the disease from animals to humans plays an important role in the biology of emerging diseases. It is thought that the coronavirus first appeared in animals (birds, pigs, etc.) in China and was later transmitted to humans in the latter months in 2019. Ebola is believed to have been transmitted by nonhuman African primates to human.
Chapter 4 lays the foundation for Bayesian inference of discrete time Markov chain. The concepts of limiting distributions, transient and recurrent states, ergodic chains, and the period of a chain are defined and explai...
