R0 - Sequential Bayesian Method (SB) Clause Samples

R0 - Sequential Bayesian Method (SB). The Bayesian statistical method proposed by ▇▇▇▇▇▇▇▇▇▇▇ and ▇▇▇▇▇▇▇, is used estimate R. [23] The infectiousness at a future time which can be the next day is assumed Poisson distributed with a certain mean. The expression for the mean has the term R that is to be estimated and the number of incidences at the present time. Starting from a gamma distributed prior for R the Poisson posterior distribution is updated by applying Bayes theorem as each new incident data is included. This updated posterior becomes the prior distribution for the next update of the posterior for the following day. As more and more incidence data is taken into account R tends to decrease. This model implicitly uses an exponential distribution for the generation time and in addition it also assumes that there is random mixing in the population. This method will fail when there are gaps in the incidence data, that is periods during which the number of observations is 0. Because of the continuous update made to the prior distribution, it can take into account the impact of intervention on a real-time basis. [23] This method is similar to the method described for the EpiEstim package (shown below) except for the fact that the posterior distribution updates and becomes the prior distribution for the computation of the reproduction number for following day.[13, 23] The analysis begins with a non-informative prior on the conditional distribution of R. The conditional distribution of R given a set of number of incidences up to time t, the prior distribution R used on each new day is the posterior distribution from the previous day [23] 𝑃 𝑅 N0, N1, … . , N𝑡 = 𝑃 N𝑡 R, N0, N1, … . , N𝑡–1 𝑃 𝑅 N0, N1, … . , N𝑡–1 (2) 𝑃(N0, N1, … . , N𝑡) More details are available on the mathematical derivation in the ▇▇▇▇▇▇▇▇▇▇▇ and ▇▇▇▇▇▇▇ paper. [23]