Question

我正在拟合一个混合模型，以估计3个种群中每个种群的性状平均值。我有一个标签切换问题，我正在尝试计算每个群体中每种基因型个体的观察数与预期数之间的距离，以重新标记群体簇。下面是一个可重现的示例。

由于某些原因，JAGS不能正确计算距离的平方值。以下代码中的相应行是：pow(DistNumPerClust[k,j], 2))

因此，输出矩阵results$mean$dist与矩阵results$mean$DistNumPerClust^2的计算是后验的。有人知道解决这个问题的方法吗？

library(R2jags)
library(runjags)
library(dirmult)
set.seed(123)

############################
## Simulation of the data ## 
############################ 

npop=3
ngeno=2
freqbalance=1
nsamplesizeperpop <- 100
freqMLG <- t(rdirichlet(n=npop, alpha=rep(freqbalance, ngeno)))

samplesizegenoperpop <- sweep(freqMLG, 1, nsamplesizeperpop, "*") 

## Compute membership (probability that a genotype comes from pop 1, 2 or 3)
## Genotype as rows and populations as columns
membership <- sweep(freqMLG, 1, rowSums(freqMLG), "/")

# Parameters for simulations
nind=90
N = npop*nind # nb of observations

clust <- rep(1:npop, each=N/npop)

geno <- c()
for (i in 1:N){
  geno <- c(geno, sum(rmultinom(n=1, size=1, prob=freqMLG[, clust[i]])*1:ngeno))
}

numgeno <- as.numeric(table(geno))
## Multiply membership probabilities by sample size for each genotype
ExpNumPerClust <- sweep(membership, 1, numgeno, "*")

muOfClustsim <- c(1, 20, 50) # vector of population means
sigma <- 1.5 # residual sd
(tausim <- 1/(sigma*sigma)) # precision

# parameters are treated as data for the simulation step
data <- list(N=N, npop=npop, ngeno=ngeno, geno=geno, muOfClustsim=muOfClustsim, tausim=tausim, samplesizegenoperpop=samplesizegenoperpop)


## JAG model

txtstring <- "
data{
  # Likelihood:
  for (i in 1:N){
  ysim[i] ~ dnorm(eta[i], tausim) # tau is precision (1 / variance)
  eta[i] <- muOfClustsim[clust[i]]
  clust[i] ~ dcat( pClust[geno[i], 1:npop] )
  }
  for (k in 1:ngeno){
   pClust[k, 1:npop] ~ ddirch( samplesizegenoperpop[k,] )
  }
}

model{
fake <- 0
}
"

# Simulate with jags
out <- run.jags(txtstring, data = data, monitor=c("ysim"), sample=1, n.chains=1, summarise=FALSE)

# reformat the outputs
ysim <- coda::as.mcmc(out)[1:N]

## Estimation model
bayes.mod <- function(){

  # Likelihood:
  for (i in 1:N){
    ysim[i] ~ dnorm(eta[i], tau) # tau is precision (1 / variance)
    eta[i] <- beta[clust[i]]
    clust[i] ~ dcat( pClust[geno[i], 1:npop] )

  }
  for (k in 1:ngeno){
    ## pClust membership estimates 
   pClust[k, 1:npop] ~ ddirch( samplesizegenoperpop[k,] )
  }


    for (k in 1:ngeno){
      for (j in 1:npop){
        # problem of label switching: try to compute the distance between ObsNumPerClust and ExpNumPerClust (i.e. between observed and expected number of individuals of each genotype in each population)
        ObsNumPerClust[k,j] <- pClust[k, j] * numgeno[k] 
        DistNumPerClust[k,j] <- ObsNumPerClust[k,j] - ExpNumPerClust[k,j]
        dist[k,j] <- pow(DistNumPerClust[k,j], 2)
      }
    }


  # Priors
  beta ~ dmnorm(mu, sigma.inv)
  mu ~ dmnorm(m, V)
  sigma.inv ~  dwish(R, K)
  tau ~ dgamma(0.01, 0.01)
  # parameters transformations
  sig <- sqrt(1/ tau)
}

m = rep(1, npop)
V = diag(rep(0.01, npop))
R = diag(rep(0.1, npop))
K = npop

## Input variables
sim.dat.jags<-list("ysim","N","npop", "ngeno", "geno","m","V","R", "K", "samplesizegenoperpop","numgeno","ExpNumPerClust")

## Variables to monitor
bayes.mod.params <- c("beta","tau","sig","DistNumPerClust","dist")

## Starting values
init1 <- list(beta = c(0, 100, 1000), tau = 1)
bayes.mod.inits <-  list(init1)

## Run model
bayes.mod.fit<-jags(data = sim.dat.jags, inits = bayes.mod.inits, parameters.to.save = bayes.mod.params, n.chains=1, n.iter=101000, n.burnin=1000, n.thin=200, model.file = bayes.mod)

results <- print(bayes.mod.fit)

results$mean$dist
results$mean$DistNumPerClust^2

Answer 1

似乎您希望转换后的一组值的平均值将得到与转换同一组值的平均值相同的结果。事实并非如此-例如：

values <- c(1,2,3,6,8,20)
mean(values)^2
mean(values^2)

不是同一回事。

模型中正在发生等效情况-您将dist [k，j]计算为DistNumPerClust [k，j]的平方，然后求和为dist的均值，并期望与dist的平方相同DistNumPerClust [k，j]的平均值。或更简单的例子：

library('runjags')

X <- 1:100
Y <- rnorm(length(X), 2*X + 10, 1)

model <- "model { 
for(i in 1 : N){ 
    Y[i] ~ dnorm(true.y[i], precision);
    true.y[i] <- (m * X[i]) + c
} 
m ~ dunif(-1000,1000)
c ~ dunif(-1000,1000) 
precision ~ dexp(1)
p2 <- precision^2

}"

data <- list(X=X, Y=Y, N=length(X))

results <- run.jags(model=model, monitor=c("m", "c", "precision", "p2"), 
data=data, n.chains=2)
results

更具体地说，不应期望它们是相同的：

summary(results)['p2','Mean']
summary(results)['precision','Mean']^2

如果要计算同一事物，则可以将整个值链提取为MCMC对象，然后对这些值进行转换：

p <- combine.mcmc(results,vars='precision')
p2 <- combine.mcmc(results,vars='p2')

mean(p^2)
mean(p2)

mean(p)
mean(sqrt(p2))

现在一切都等同了。

马特

JAGS-pow功能在带有标签切换的混合模型中无法正常工作

1 个答案: