Chain Binomial Model

The chain binomial model arises from chains of binomial probability mass functions, where each function is conditioned on previous function. Products of these probability mass functions give the probabilities of particular sequences of binomial realizations. This chain structure allows for detailed analysis of physical phenomena that can be represented by chain binomials. The simple chain structure allows for statistical inference based on likelihood theory. The chain binomial model forms the statistical underpinnings of the life table. In addition, the chain binomial model has been important in the analysis of infectious disease spread in small groups such as households. For example, the Reed–Frost model is a chain binomial model where the number of new infectives at some time t depends on the number of infectives and susceptibles at time t − 1. This model has been used to estimate epidemiological parameters for the spread of such diseases as measles, smallpox, and influenza. Keywords: binomial; epidemic model; inference; life table; Markov chain; random mixing; secondary attack rate; stochastic process