How to override priors?

Modeling
1

If I write the following:

parameters {
  vector[5] beta;
} 

model {
  //priors
  beta ~ normal(0,1);
  beta[3] ~ normal(1,1);
}

Does this put a prior of N(0,1) on beta coefficients 1,2,4,5 and N(1,1) on beta coefficient 3?

In other words, does the final line override the prior specified for beta[3] in the penultimate line?

1 Like
2

Technically, the sampling statements

  beta ~ normal(0,1);
  beta[3] ~ normal(1,1);

are largely equivalent to

  target += normal_lpdf(beta | 0,1);
  target += normal_lpdf(beta[3] | 1,1);

with the exception that the former statements drop constant terms in the target log probability density.

So, no, there’s no overriding. target is incremented by both normal_lpdf(beta[3] | 0,1) and normal_lpdf(beta[3] | 1,1).

3 Likes
3

It seems that it is not doing what you are looking for:

edit: @jjramsey explains why it does not work like this.

parameters {
  vector[5] beta;
  real beta3_I_want;
} 

model {
  //priors
  beta ~ normal(0,1);
  beta[3] ~ normal(1,1);
  beta3_I_want ~ normal(1,1);
}

Rplot
Rplot.jpeg696×479 35.7 KB

Maybe you can use an index?

in this case index <- c(1,2,4,5).

data {
int P;
int index[P];
}
parameters {
  vector[5] beta;
  real beta3_I_want;
} 

model {
  //priors
  beta[index] ~ normal(0,1);
  beta[3] ~ normal(1,1);
  beta3_I_want ~ normal(1,1);
}

Rplot02
Rplot02.jpeg696×479 32.6 KB

1 Like
4

Really helpful responses, thanks.

I will work with @tiagocc solution for now. One follow up, there is no way to directly write the indices in stan rather than pass them as data in the data block? Something like this:

model {
  beta[1,2,4,5] ~ normal(0,1)
  beta[3] ~ normal(1,1)
}

(I’ve tried that particular solution and it generates a syntax error)

I would like to avoid writing something like this:

model {
  beta[1] ~ normal(0,1)
  beta[2] ~ normal(0,1) 
  beta[3] ~ normal(1,1)
  beta[4] ~ normal(0,1)
  beta[5] ~ normal(0,1)
}

What about this?:

model {
  beta[1:2] ~ normal(0,1)
  beta[3] ~ normal(1,1)
  beta[4:5] ~ normal(0,1)
}