# Sequential Bayes: Utilizing the Posterior Distribution

In the Sequential Bayes method, the probability distribution of R0 is updated sequentially from one case count to the next, starting from a (discretized) uniform prior. By default, the function `seq_bayes()` returns the mean of the last updated posterior distribution as its estimate of R0. However, by setting the parameter `post` to `TRUE`, it is possible to return the final distribution itself:

    # Daily case counts.
    cases <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4)

    posterior <- seq_bayes(cases, mu = 8, kappa = 7, post = TRUE)

First, the distribution can be used to retrieve the original estimate (had `post` been left to its default value of `FALSE`) by calculating its mean:

    # `supp` is the support of the distribution, and `pmf` is its probability mass
    # function.
    post_mean <- sum(posterior$supp * posterior$pmf)
    post_mean
    #> [1] 1.476652

    # Verify that the following is true:
    post_mean == seq_bayes(cases, mu = 8, kappa = 7)
    #> [1] TRUE

Another use of the posterior is to obtain an alternative estimate of R0. For instance, the following extracts the posterior mode rather than the mean:

    post_mode <- posterior$supp[which.max(posterior$pmf)]
    post_mode
    #> [1] 1.36

Returning the posterior is suitable for visualization purposes. Below is a graph containing the uniform prior, final posterior distribution, posterior mean and posterior mode: