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Stan vs PYMC3 for Discrete Mixture Models

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1

I am studying zero-inflated count temporal data. I have built a stan model that deals with this zero-inflated data with an if statement in the model block. This is as they advise in the Stan Reference Guide. e.g.,

model 
 for (n in 1:N) theta), bernoulli_lpmf(0 

This if statement is clearly necessary as Stan uses NUTS as the sampler which does not deal with discrete variables (and thus we are marginalising over this discrete random variable instead of sampling from it). I have not had very much experience with pymc3 but my understanding is that it can deal with a Gibbs update step (to sample from the discrete bernoulli likelihood). Then conditioned on the zero-inflated value, it could perform a Metropolis or NUTS update for the parameters that depend on the Poisson likelihood.

My question is: Can (and if so how can) pymc3 be used in such a way to sample from the discrete zero-inflated variable with the updates to the continuous variable being performed with a NUTS update? If it can, is the performance significantly improved over the above implementation in stan (which marginalises out the discrete random variable)? Further, if pymc3 can only support a Gibbs + Metropolis update, is this change away from NUTS worth considering?

bayesian pymc3 mcmc stan pystan

share|improve this question

edited Mar 24 at 13:04

nick

asked Mar 24 at 10:47

nicknick

629313

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  
  Yes, PyMC3 can block update continuous and discrete parameters to provide discrete sampling. The only problem is that it will be slower and less accurate and less robust. Marginalizing is almost always a win for efficiency/mixing due to the Rao-Blackwell theorem and for accuracy by working in expectation. This is explained with an example in the Stan user's guide chapter on latent discrete parameters (the change-point model is also available in PyMC3). So if you can marginalize in PyMC3 (or BUGS or JAGS), that'll be a big win for efficiency and accuracy.
  
  – Bob Carpenter
  Mar 25 at 15:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thanks very much Bob. I was not aware of the ties to Rao-Blackwell. I'll work though that to understand more.
  
  – nick
  Mar 26 at 8:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Roughly speaking, the theorem says that working in expectation is more efficient. By marginalizing out the discrete parameters, you work in expectation.
  
  – Bob Carpenter
  Mar 27 at 17:28
  
  

  
  
  
  

add a comment | 

1

I am studying zero-inflated count temporal data. I have built a stan model that deals with this zero-inflated data with an if statement in the model block. This is as they advise in the Stan Reference Guide. e.g.,

model 
 for (n in 1:N) theta), bernoulli_lpmf(0 

This if statement is clearly necessary as Stan uses NUTS as the sampler which does not deal with discrete variables (and thus we are marginalising over this discrete random variable instead of sampling from it). I have not had very much experience with pymc3 but my understanding is that it can deal with a Gibbs update step (to sample from the discrete bernoulli likelihood). Then conditioned on the zero-inflated value, it could perform a Metropolis or NUTS update for the parameters that depend on the Poisson likelihood.

My question is: Can (and if so how can) pymc3 be used in such a way to sample from the discrete zero-inflated variable with the updates to the continuous variable being performed with a NUTS update? If it can, is the performance significantly improved over the above implementation in stan (which marginalises out the discrete random variable)? Further, if pymc3 can only support a Gibbs + Metropolis update, is this change away from NUTS worth considering?

bayesian pymc3 mcmc stan pystan

share|improve this question

edited Mar 24 at 13:04

nick

asked Mar 24 at 10:47

nicknick

629313

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  
  Yes, PyMC3 can block update continuous and discrete parameters to provide discrete sampling. The only problem is that it will be slower and less accurate and less robust. Marginalizing is almost always a win for efficiency/mixing due to the Rao-Blackwell theorem and for accuracy by working in expectation. This is explained with an example in the Stan user's guide chapter on latent discrete parameters (the change-point model is also available in PyMC3). So if you can marginalize in PyMC3 (or BUGS or JAGS), that'll be a big win for efficiency and accuracy.
  
  – Bob Carpenter
  Mar 25 at 15:28
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thanks very much Bob. I was not aware of the ties to Rao-Blackwell. I'll work though that to understand more.
  
  – nick
  Mar 26 at 8:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Roughly speaking, the theorem says that working in expectation is more efficient. By marginalizing out the discrete parameters, you work in expectation.
  
  – Bob Carpenter
  Mar 27 at 17:28
  
  

  
  
  
  

add a comment | 

I am studying zero-inflated count temporal data. I have built a stan model that deals with this zero-inflated data with an if statement in the model block. This is as they advise in the Stan Reference Guide. e.g.,

model 
 for (n in 1:N) theta), bernoulli_lpmf(0 

This if statement is clearly necessary as Stan uses NUTS as the sampler which does not deal with discrete variables (and thus we are marginalising over this discrete random variable instead of sampling from it). I have not had very much experience with pymc3 but my understanding is that it can deal with a Gibbs update step (to sample from the discrete bernoulli likelihood). Then conditioned on the zero-inflated value, it could perform a Metropolis or NUTS update for the parameters that depend on the Poisson likelihood.

My question is: Can (and if so how can) pymc3 be used in such a way to sample from the discrete zero-inflated variable with the updates to the continuous variable being performed with a NUTS update? If it can, is the performance significantly improved over the above implementation in stan (which marginalises out the discrete random variable)? Further, if pymc3 can only support a Gibbs + Metropolis update, is this change away from NUTS worth considering?

bayesian pymc3 mcmc stan pystan

share|improve this question

edited Mar 24 at 13:04

nick

asked Mar 24 at 10:47

nicknick

629313

model 
 for (n in 1:N) theta), bernoulli_lpmf(0 

share|improve this question

edited Mar 24 at 13:04

nick

asked Mar 24 at 10:47

nicknick

629313

share|improve this question

edited Mar 24 at 13:04

nick

asked Mar 24 at 10:47

nicknick

629313

asked Mar 24 at 10:47

nicknick

629313

asked Mar 24 at 10:47

nicknick

629313