Censoring/Truncation in JAGS

Question

I have a question on how to fit a censoring problem in JAGS.

I observe a bivariate mixture normal where the X values have measurement error. I would like to model the true underlying 'means' of the observed censored values.

\begin{align*} \lceil x_{true}+\epsilon \rceil = x_{observed} \ \epsilon \sim N(0,sd=.5) \end{align*}

Here is what I have now:

 for (i in 1:n){
   x[i,1:2]~dmnorm(mu[z[i],1:2], tau[z[i],1:2,1:2])
   z[i]~dcat(prob[ ])
 }

Y also has measurement error. What I want to do is something like this:

 for (i in 1:n){
   x_obs[i] ~ dnorm(x_true[i],prec_x)I(x_true[i],)
   y_obs[i] ~ dnorm(y_true[i],prec_y)
   c(x_true[i]:y_true[i])~dmnorm(mu[ z [ i ],1:2], tau[z[i],1:2,1:2])
   z[i]~dcat(prob[ ])
 }

 #priors for measurement error
 e_x~dunif(.1,.9)
 prec_x<-1/pow(e_x,2)
 e_y~dunif(2,4)
 prec_y<-1/pow(e_y,2)

Obviously the c command is not valid in JAGS.

Thanks in advance.

To truncate, use T(-,-), but read the users manual for info on censuring and truncationq — David LeBauer, Feb 04 '11 at 04:06

David LeBauer · Answer 1 · 2011-02-21T18:21:36.643

11

Perhaps this is what you are looking for:

x_obs[i] ~ dnorm(x_true[i],prec_x)T(x_true[i], )

JAGS has options for both censoring and truncation. It sounds like you want truncation, since you know a-priori that the observation lies within a particular range

Read the user's manual for more details about how jags uses truncation and censoring.

edited Feb 21 '11 at 18:21

answered Feb 04 '11 at 04:14

David LeBauer

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score 3 · Accepted Answer · answered Feb 21 '11 at 18:53

Thanks for the tips David. I posted this question on the JAGS support forum and got a useful answer. The key was to use a two dimensional array for the 'true' values.

for (j in 1:n){ 
  x_obs[j] ~ dnorm(xy_true[j,1], prec_x)T(xy_true[j,1],) 
  y_obs[j] ~ dnorm(xy_true[j,2], prec_y)
  xy_true[j, ] ~ dmnorm(mu[ z [j],1:2], tau[z[j],1:2,1:2]) 
  z[j]~dcat(prob[ ]) 
}

 #priors for measurement error 
 e_x~dunif(.1,.9)
 prec_x<-1/pow(e_x,2)
 e_y~dunif(2,4)
 prec_y<-1/pow(e_y,2)

Censoring/Truncation in JAGS

2 Answers2