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+#' seqB method
+#'
+#' This function implements a sequential Bayesian estimation method of R0 due to
+#' Bettencourt and Riberio (PloS One, 2008). See details for important
+#' implementation notes.
+#'
+#' The method sets a uniform prior distribution on R0 with possible values
+#' between zero and \code{kappa}, discretized to a fine grid. The distribution
+#' of R0 is then updated sequentially, with one update for each new case count
+#' observation. The final estimate of R0 is \code{Rhat}, the mean of the (last)
+#' posterior distribution. The prior distribution is the initial belief of the
+#' distribution of R0, which is the uninformative uniform distribution with
+#' values between zero and \code{kappa}. Users can change the value of
+#' \code{kappa} only (i.e., the prior distribution cannot be changed from the
+#' uniform). As more case counts are observed, the influence of the prior
+#' distribution should lessen on the final estimate \code{Rhat}.
+#'
+#' This method is based on an approximation of the SIR model, which is most
+#' valid at the beginning of an epidemic. The method assumes that the mean of
+#' the serial distribution (sometimes called the serial interval) is known. The
+#' final estimate can be quite sensitive to this value, so sensitivity testing
+#' is strongly recommended. Users should be careful about units of time (e.g.,
+#' are counts observed daily or weekly?) when implementing.
+#'
+#' Our code has been modified to provide an estimate even if case counts equal
+#' to zero are present in some time intervals. This is done by grouping the
+#' counts over such periods of time. Without grouping, and in the presence of
+#' zero counts, no estimate can be provided.
+#'
+#' @param NT Vector of case counts.
+#' @param mu Mean of the serial distribution. This needs to match case counts in
+#'           time units. For example, if case counts are weekly and the serial
+#'           distribution has a mean of seven days, then \code{mu} should be set
+#'           to one. If case counts are daily and the serial distribution has a
+#'           mean of seven days, then \code{mu} should be set to seven.
+#' @param kappa Largest possible value of uniform prior (defaults to 20). This
+#'              describes the prior belief on ranges of R0, and should be set to
+#'              a higher value if R0 is believed to be larger.
+#'
+#' @return \code{seqB} returns a list containing the following components:
+#'         \code{Rhat} is the estimate of R0 (the posterior mean),
+#'         \code{posterior} is the posterior distribution of R0 from which
+#'         alternate estimates can be obtained (see examples), and \code{group}
+#'         is an indicator variable (if \code{group == TRUE}, zero values of NT
+#'         were input and grouping was done to obtain \code{Rhat}). The variable
+#'         \code{posterior} is returned as a list made up of \code{supp} (the
+#'         support of the distribution) and \code{pmf} (the probability mass
+#'         function).
+#'
+#' @examples
+#' # Weekly data.
+#' NT <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4)
+#'
+#' ## Obtain R0 when the serial distribution has a mean of five days.
+#' res1 <- seqB(NT, mu = 5 / 7)
+#' res1$Rhat
+#'
+#' ## Obtain R0 when the serial distribution has a mean of three days.
+#' res2 <- seqB(NT, mu = 3 / 7)
+#' res2$Rhat
+#'
+#' # Compute posterior mode instead of posterior mean and plot.
+#'
+#' Rpost <- res1$posterior
+#' loc <- which(Rpost$pmf == max(Rpost$pmf))
+#' Rpost$supp[loc] # Posterior mode.
+#' res1$Rhat # Compare with the posterior mean.
+#'
+#' par(mfrow = c(2, 1), mar = c(2, 2, 1, 1))
+#'
+#' plot(Rpost$supp, Rpost$pmf, col = "black", type = "l", xlab = "", ylab = "")
+#' abline(h = 1 / (20 / 0.01 + 1), col = "red")
+#' abline(v = res1$Rhat, col = "blue")
+#' abline(v = Rpost$supp[loc], col = "purple")
+#' legend("topright",
+#'   legend = c("Prior", "Posterior", "Posterior mean", "Posterior mode"),
+#'   col = c("red", "black", "blue", "purple"), lty = 1)
+#'
+#' @export
+seqB <- function(NT, mu, kappa = 20) {
+  if (length(NT) < 2)
+    print("Warning: length of NT should be at least two.")
+  else {
+    if (min(NT) > 0) {
+      times <- 1:length(NT)
+      tau <- diff(times)
+    }
+    group <- FALSE
+    if (min(NT) == 0) {
+      times <- which(NT > 0)
+      NT <- NT[times]
+      tau <- diff(times)
+      group <- TRUE
+    }
+
+    R <- seq(0, kappa, 0.01)
+    prior0 <- rep(1, kappa / 0.01 + 1)
+    prior0 <- prior0 / sum(prior0)
+    k <- length(NT) - 1
+    R0.post <- matrix(0, nrow = k, ncol = length(R))
+    prior <- prior0
+    posterior <- seq(0, length(prior0))
+    gamma <- 1 / mu
+
+    for (i in 1:k) {
+      mm1 <- NT[i]
+      mm2 <- NT[i + 1]
+      lambda <- tau[i] * gamma * (R - 1)
+      lambda <- log(mm1) + lambda
+      loglik <- mm2 * lambda - exp(lambda)
+      maxll <- max(loglik)
+      const <- 0
+
+      if (maxll > 700)
+        const <- maxll - 700
+
+      loglik <- loglik - const
+      posterior <- exp(loglik) * prior
+      posterior <- posterior / sum(posterior)
+      prior <- posterior
+    }
+
+    Rhat <- sum(R * posterior)
+
+    return(list(Rhat = Rhat,
+                posterior = list(supp = R, pmf = posterior),
+                group = group))
+  }
+}