我认为您遇到问题有几个原因。首先,您提供给模型的数据(即y
)不是正态分布的混合。因此,模型本身无需混合。我会改为生成如下数据:
set.seed(320)
# number of samples
n <- 10
# Because it is a mixture of 2 we can just use an indicator variable.
# here, pick (in the long run), would be '1' 30% of the time.
pick <- rbinom(n, 1, p[1])
# generate the data. b is in terms of precision so we are converting this
# to standard deviations (which is what R wants).
y_det <- pick * rnorm(n, a[1], sqrt(1/b[1])) + (1 - pick) * rnorm(n, a[2], sqrt(1/b[2]))
# add a small amount of noise, can change to be more as necessary.
y <- rnorm(n, y_det, 1)
这些数据看起来更像是您想要提供给混合模型的数据。
在此之后,我将以与数据生成过程类似的方式对模型进行编码。我想要一些指标变量在两个正态分布之间跳转。因此,mu
对于 中的每个标量,可能会发生变化y
。
mod_str = "model{
# Likelihood
for (i in 1:n){
y[i] ~ dnorm(mu[i], 10)
mu[i] <- mu_ind[i] * a_mu + (1 - mu_ind[i]) * b_mu
mu_ind[i] ~ dbern(p[1])
}
a_mu ~ dnorm(a[1], b[1])
b_mu ~ dnorm(a[2], b[2])
}"
model = jags.model(textConnection(mod_str), data = list(y = y, n=n, a=a, b=b, p=p), n.chains=1)
update(model, 10000)
res = coda.samples(model, variable.names = c('mu_ind', 'a_mu', 'b_mu'), n.iter = 10000)
summary(res)
2.5% 25% 50% 75% 97.5%
a_mu -100.4 -100.3 -100.2 -100.1 -100
b_mu 199.9 200.0 200.0 200.0 200
mu_ind[1] 0.0 0.0 0.0 0.0 0
mu_ind[2] 1.0 1.0 1.0 1.0 1
mu_ind[3] 0.0 0.0 0.0 0.0 0
mu_ind[4] 1.0 1.0 1.0 1.0 1
mu_ind[5] 0.0 0.0 0.0 0.0 0
mu_ind[6] 0.0 0.0 0.0 0.0 0
mu_ind[7] 1.0 1.0 1.0 1.0 1
mu_ind[8] 0.0 0.0 0.0 0.0 0
mu_ind[9] 0.0 0.0 0.0 0.0 0
mu_ind[10] 1.0 1.0 1.0 1.0 1
如果您提供了更多数据,您将(从长远来看)让指标变量mu_ind
在 30% 的时间里取值 1。如果您有超过 2 个发行版,则可以改用dcat
. 因此,另一种更通用的方法是(我从 John Kruschke 的这篇文章中大量借用):
mod_str = "model {
# Likelihood:
for( i in 1 : n ) {
y[i] ~ dnorm( mu[i] , 10 )
mu[i] <- muOfpick[ pick[i] ]
pick[i] ~ dcat( p[1:2] )
}
# Prior:
for ( i in 1:2 ) {
muOfpick[i] ~ dnorm( a[i] , b[i] )
}
}"
model = jags.model(textConnection(mod_str), data = list(y = y, n=n, a=a, b=b, p=p), n.chains=1)
update(model, 10000)
res = coda.samples(model, variable.names = c('pick', 'muOfpick'), n.iter = 10000)
summary(res)
2.5% 25% 50% 75% 97.5%
muOfpick[1] -100.4 -100.3 -100.2 -100.1 -100
muOfpick[2] 199.9 200.0 200.0 200.0 200
pick[1] 2.0 2.0 2.0 2.0 2
pick[2] 1.0 1.0 1.0 1.0 1
pick[3] 2.0 2.0 2.0 2.0 2
pick[4] 1.0 1.0 1.0 1.0 1
pick[5] 2.0 2.0 2.0 2.0 2
pick[6] 2.0 2.0 2.0 2.0 2
pick[7] 1.0 1.0 1.0 1.0 1
pick[8] 2.0 2.0 2.0 2.0 2
pick[9] 2.0 2.0 2.0 2.0 2
pick[10] 1.0 1.0 1.0 1.0 1
上面的链接包括更多的先验(例如,关于合并到分类分布中的概率的狄利克雷先验)。