R/PM_MCMChospAdmissions2.R

In JMacDonaldPhD/COVID19UK:

PM_MCMCCOVIDLancs2.ADAPTIVE <- function(totalHospAdmissions, 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, 3)
  V0 <- diag(1, n)

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

  while(logPostCurr == -Inf){
    if(runParallel){
      cl <- parallel::makePSOCKcluster(parallel::detectCores() - 1)
      doParallel::registerDoParallel(cl)
      sims <-
        foreach(1:noSims) %dopar% {
          simulator(param = c(thetaCurr[1:2], fixedParam, thetaCurr[3]), kernelParam)$dailyNoCases
          }
    } else{
      sims <- replicate(noSims, simulator(param = c(thetaCurr[1:2], fixedParam, thetaCurr[3]), kernelParam)$dailyNoCases,
                        simplify = F)
    }

    logPCurr <- sapply(X = sims, function(X) totalHospLikelihood(colSums(X), totalHospAdmissions,
                                                                 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)

    if(runParallel){
      cl <- parallel::makePSOCKcluster(parallel::detectCores() - 1)
      doParallel::registerDoParallel(cl)
      sims <-
        foreach(1:noSims) %dopar% {
          simulator(param = c(thetaProp[1:2], fixedParam, thetaProp[3]), kernelParam)$dailyNoCases
        }
    } else{
      sims <- replicate(noSims, simulator(param = c(thetaProp[1:2], fixedParam, thetaProp[3]), kernelParam)$dailyNoCases,
                        simplify = F)
    }

    logPProp <- sapply(X = sims, function(X) totalHospLikelihood(colSums(X), totalHospAdmissions,
                                                                 thetaProp[3]))
    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_MCMCCOVIDLancs2 <- function(totalHospAdmissions, fixedParam, theta0, priors, kernelParam, simulator, lambda, V, noSims, noIts,
                              burnIn, runParallel = TRUE){

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

  while(logPostCurr == -Inf){
    if(runParallel){
      cl <- parallel::makePSOCKcluster(parallel::detectCores() - 1)
      doParallel::registerDoParallel(cl)
      sims <-
        foreach(1:noSims) %dopar% {
          simulator(param = c(thetaCurr[1:2], fixedParam, thetaCurr[3]), kernelParam)$dailyNoCases
        }
    } else{
      sims <- replicate(noSims, simulator(param = c(thetaCurr[1:2], fixedParam, thetaCurr[3]), kernelParam)$dailyNoCases,
                        simplify = F)
    }

    logPCurr <- sapply(X = sims, function(X) totalHospLikelihood(colSums(X), totalHospAdmissions,
                                                                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
    thetaProp <- RWMProposalMixed(thetaCurr, lambda, V, type)


    if(runParallel){
      cl <- parallel::makePSOCKcluster(parallel::detectCores() - 1)
      doParallel::registerDoParallel(cl)
      sims <-
        foreach(1:noSims) %dopar% {
          simulator(param = c(thetaProp[1:2], fixedParam, thetaProp[3]), kernelParam)$dailyNoCases
        }
    } else{
      sims <- replicate(noSims, simulator(param = c(thetaProp[1:2], fixedParam, thetaProp[3]), kernelParam)$dailyNoCases,
                        simplify = F)
    }

    logPProp <- sapply(X = sims, function(X) totalHospLikelihood(colSums(X), totalHospAdmissions,
                                                                thetaProp[3]))
    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))
}