```
#' ABC SMC
#'
#' A function which returns an ABC SMC algorithm function given an initial tolerance, a
#' model simulator, a vector of observation times, a distance calculator function which contains
#' the observed data information and a prior distribution for both the rates and states.
#'
#' @importFrom parallel mclapply
#' @importFrom mvtnorm rmvnorm
#' @param epsilon1 The initial tolerance value for the ABC SMC algorithm
#' @param simulator A model simulator
#' @param times A vector of observation times of the data
#' @param distance A metric function
#' @param prior A function which gives returns prior samples of the states and rate parameters
#' @return A function which runs the ABC SMC algorithm for a desired accepted sample size, over a desired number of populations for a given adaptive tolerance selected as the alpha ntile of the distribution of distances
#' @export
abcSmc = function(epsilon1, simulator, times, distance,prior){
## wraps up the simulator using the ABC wrapper function
simfunction = abcSimulatorWrapper(distance,simulator,times)
priorfunction = prior
sim = simfunction(epsilon1)
return(function(nSamples,nDist,alpha){
message("running abc smc")
for(population in 1:nDist){
samples = 0
batch = 10000
## empty matrix to store results
out = c()
while(samples < nSamples){
## simulate forward and keep any non null in a matrix
out = rbind(do.call(rbind, Filter(Negate(is.null),mclapply(priorfunction(batch),sim))),out)
## if none are retained in a batch set samples = 0
samples = ifelse(!is.null(nrow(out)),nrow(out),0)
message(paste(population,"\t",samples,sep = ""))
}
## the number of parameters is one less since kept samples have attached their distance
pars = ncol(out) - 1
message("updating weights")
if(population == 1){
weights = rep(1/samples,samples) ## normalised weights
}else{
## construct a new weight calculator function based on current samples and weigths
weightCalc = weightCalculator(weights,post,sigma)
weights = weightCalc(out[,1:pars])
weights = weights/sum(weights)
}
post = out
## work out desired new tolerance
tol = quantile(out[,pars+1],alpha)
## the samples which beat new tolerance
indicies = which(out[,pars+1] < tol)
good = out[indicies,]
goodweights = weights[indicies]
goodweights = goodweights/sum(goodweights) ## normalise
## calculate tuning parameters for innovations
message("Calculating new proposal covariance")
sigma = matrix(0,nrow = pars, ncol = pars)
for(i in 1:samples){
for(j in 1:length(indicies)){
v = good[j,1:pars] - out[i,1:pars]
v = v %*% t(v)
sigma = sigma + weights[i]*goodweights[j]*v
}
}
## if ess < nSamples/2 resample
message("checking ESS")
s = sum(weights)
if(s*s/sum(weights*weights) < samples/2){
message("resampling")
index = sample(1:samples,nSamples,weights,replace = TRUE)
weights = weights[index]
post = out[index,]
}
if(population == 1){
df = cbind(post[,1],population)
colnames(df) <- c("th1","population")
df = as.data.frame(df)
}
else{
x = cbind(post[,1],population)
colnames(x) <- c("th1","population")
df = rbind(df,x)
}
## construct new abc simulator based on new tolerance
sim = simfunction(tol)
message(paste("New tolerance = ",tol,sep = ""))
## construct a new "prior" function based on proposals from current samples
priorfunction = function(N){
x = x_prior(N)
i = sample(1:dim(post)[1],N,weights,replace=TRUE)
th = post[i,pars] + rmvnorm(N,sigma = sigma)
return(lapply(1:N,function(i){c(x[i,],th[i,])}))
}
}
## final sample
i = sample(1:nrow(post),nSamples,weights,replace=TRUE)
return(list("post" = post, "df" = df))
})
}
```

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