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Sequential Bayes: Utilizing the Posterior Distribution

+ + + Source: vignettes/seq_bayes_post.Rmd +
seq_bayes_post.Rmd
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+ + + +

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:

+

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