R/PM_MCMCdailyHospAds2.R

In JMacDonaldPhD/COVID19UK:

PM_MCMCCOVIDdailyHospAds2.ADAPTIVE <- function(dailyHospAdmissions, fixedParam, theta0, priors, kernelParam, simulator, noSims,
                                       noIts, burnIn, lambda0, delta, runParallel = TRUE){

  start <- as.numeric(Sys.time())
  # Adaptive Step

  n <- length(theta0)
  thetaCurr <- theta0
  type <- c(2, 2, 2, 3)
  V0 <- diag(1, n)

  lambda <- lambda0
  # Likelihood Function
  logPostCurr <- -Inf

  while(logPostCurr == -Inf){

    sims <- replicate(noSims, simulator(param = c(thetaCurr[1:2], fixedParam, thetaCurr[3]), kernelParam)$dailyNoCases,
                     simplify = F)
    logPCurr <- sapply(X = sims, function(X) dailyHospLikelihood(X, dailyHospAdmissions,
                                                                thetaCurr[3]))
    logPCurr <- log(mean(exp(logPCurr)))
    logPostCurr <- logPCurr + sum(evalPrior(thetaCurr, priors))
  }

  draws <- matrix(nrow = noIts + 1, ncol = n + 1)
  draws[1, ] <- c(thetaCurr, logPostCurr)
  noAccept <- 0

  print("Sampling Progress")
  pb <- progress::progress_bar$new(total = noIts)
  for(i in 1:noIts){
    pb$tick()
    # Proposal

    u.delta <- runif(1, 0, 1)
    if(u.delta > delta & noAccept >= 10){
      V <- var(draws[,1:n], na.rm = T)
      thetaProp <- RWMProposalMixed(thetaCurr, lambda, V, type)
    } else{
      thetaProp <- RWMProposalMixed(thetaCurr, lambda0, V0, type)
    }
    #print(thetaProp)
    sims <- replicate(noSims, simulator(P0,
                                       epiParam = c(thetaProp[1:2], fixedParam[1], thetaProp[4], fixedParam[2])),
                     simplify = F)
    logPProp <- sapply(X = sims, function(X) dailyHospLikelihood(X$dailyNoCases, dailyHospAdmissions,
                                                                thetaProp[4]))
    logPProp <- log(mean(exp(logPProp)))
    logPostProp <- logPProp + sum(evalPrior(thetaProp, priors))
    acceptProb <- logPostProp - logPostCurr
    #print(acceptProb)

    u1 <- runif(1)
    if(log(u1) < acceptProb){
      noAccept <- noAccept + 1
      logPostCurr <- logPostProp
      thetaCurr <- thetaProp
      if(u.delta > delta){
        lambda <- lambda + 0.93*(lambda/sqrt(i))
      }
    } else{
      if(u.delta > delta){
        lambda <- lambda - 0.07*(lambda/sqrt((i)))
      }
    }
    #print(thetaCurr)
    draws[i+1, ] <- c(thetaCurr, logPostCurr)
  }
  timeTaken <- as.numeric(Sys.time()) - start

  # Calculate Effective Sample Sizes (and Per Second) and Acceptance Rates
  ESS <- min(coda::effectiveSize(draws[, 1:n]))
  ESS.sec <- ESS/timeTaken
  acceptRate <-  noAccept/noIts


  print(c("Accept Rate:", acceptRate))

  return(list(draws = draws, lambda = lambda, V = V, noSims = noSims, ESS.sec = ESS.sec))
}

PM_MCMCCOVIDdailyHospAds2 <- function(dailyHospAdmissions, P0, fixedParam, theta0, priors, simulator, lambda, V, noSims, noIts,
                              burnIn){

  start <- as.numeric(Sys.time())
  # Adaptive Step
  n <- length(theta0)
  thetaCurr <- theta0
  type <- c(2, 2, 2, 3)
  # Likelihood Function
  logPostCurr <- -Inf

  while(logPostCurr == -Inf){
    sims <- replicate(noSims, simulator(P0,
                                       epiParam = c(thetaCurr[1:3], fixedParam[1], thetaCurr[4], fixedParam[2])),
                     simplify = F)
    logPCurr <- sapply(X = sims, function(X) dailyHospLikelihood(X$dailyNoCases, dailyHospAdmissions,
                                                                thetaCurr[4]))
    logPCurr <- log(mean(exp(logPCurr)))
    logPostCurr <- logPCurr + sum(evalPrior(thetaCurr, priors))
  }

  draws <- matrix(nrow = noIts + 1, ncol = n + 1)
  draws[1, ] <- c(thetaCurr, logPostCurr)
  noAccept <- 0

  print("Sampling Progress")
  pb <- progress::progress_bar$new(total = noIts)
  for(i in 1:noIts){
    pb$tick()
    # Proposal
    thetaProp <- RWMProposalMixed(thetaCurr, lambda, V, type)

    sims <- replicate(noSims, simulator(P0,
                                       epiParam = c(thetaProp[1:3], fixedParam[1], thetaProp[4], fixedParam[2])),
                     simplify = F)
    logPProp <- sapply(X = sims, function(X) dailyHospLikelihood(X$dailyNoCases, dailyHospAdmissions,
                                                                thetaProp[4]))
    logPProp <- log(mean(exp(logPProp)))
    logPostProp <- logPProp + sum(evalPrior(thetaProp, priors))
    acceptProb <- logPostProp - logPostCurr
    #print(acceptProb)

    u1 <- runif(1)
    if(log(u1) < acceptProb){
      noAccept <- noAccept + 1
      logPostCurr <- logPostProp
      thetaCurr <- thetaProp
    }

    draws[i+1, ] <- c(thetaCurr, logPostCurr)
  }
  timeTaken <- as.numeric(Sys.time()) - start

  # Calculate Effective Sample Sizes (and Per Second) and Acceptance Rates
  ESS <- min(coda::effectiveSize(draws[, 1:n]))
  ESS.sec <- ESS/timeTaken
  acceptRate <-  noAccept/noIts


  print(c("Accept Rate:", acceptRate))

  return(list(draws = draws, ESS.sec = ESS.sec, acceptRate = acceptRate))
}