Dirichlet sampler

[diegoro...@gmail.com]

Hi all,
Thank you for your time in advance.
I have quite a complex model that has mixing problems. Chain 2 is getting stuck in extreme values producing strange results.  
In the model there is a time-dependent 6x6 transition matrix, where the first row is as follows:
    {S0[1, t], S0[2, t], S0[3, t], S0[4, t], S0[5, t], 0} # transition probability from state 1 to 1:6
in here:
    S0[1:5, t]  ~ ddirch(D_Alpha[1:5, t]) # prior
  D_Alpha[1:5, t]<-c(1/5, 1/5, 1/5, 1/5, 1/5) 

I examined the correlation of the samples for each chain and found that 2 variables are highly correlated over time.

To be more specific, for chain two:
    cor(S0[3,t=16], S0[5,t=16]) =-0.993

 
The picture below presents a plot of the correlation matrix at different time points, each plot represents a chain 1 to 3 (left to right)
Since NIMBLE recognizes a Dirichlet distribution, it assigns a RW_dirichlet sampler to all the S0 variables.

is it possible to block this sampling in order to reduce the correlation? I try to remove the sampler and add a "RW_block" for each time point but does not seem to sample since the outcome has 0 variability.
If not, how else can I reduce this strong correlation?

Thank you for your time, any comments or ideas will be very helpful.
--

Diego

[Matthijs Hollanders]

Hi Diego,

If you're looking for a vague prior on S0[1:5,t] I think you want D_alpha[1:5,t] <- 1. I don't think the 1/5 prior on each element of that vector gives you the vague prior. So every element should be a 1 if you want something analogous to dbeta(1, 1).

Cheers,

Matt

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[diegoro...@gmail.com]

Hello Matt, 

Thank you for the quick response.  One of my tries was also, as you suggested: D_alpha[1:5,t] <- 1

But the results were similar. I did also try to add improper prior and also D_alpha[1:5,t] <- 1/N, where N is population size. and still no change.

Have a nice day!

--

Diego

[Chris Paciorek]

Given the very large magnitude correlation only occurs for one chain, I am wondering if it represents that your chain, at least for those two elements, has wandered off into some low-probability part of the parameter space. If so, you might look at your starting values.

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