Metropolis proposal dist

Questions
1

Hi
Does anyone have an example of using the proposal_dist argument in the metropolis sampler ?
I’d like to use some domain knowledge and provide random samples from a different pdf (there is a good reason to do this) as jump proposals in this chain. It’s not clear to me if this is possible here ?
Thanks
Rhys

2

You can do something like the following:

import pymc3 as pm
from pymc3.step_methods.metropolis import Proposal


class MyCustomProposal(Proposal):
    def __call__(self):
        # do whatever you need. Notice self.s has the state of the
        # proposal instance


with pm.Model():
    # define variables
    proposal_state = # something appropriate
    step = pm.Metropolis(vars, proposal_dist=MyCustomProposal(proposal_state))

You can checkout the source code of Metropolis to see how the default NormalProposal or MultivariateNormalProposal are constructed to gain more intuition.

2 Likes
4

Hi Thanks for the reply !
So i’d effectively like to make the proposal independent of the current position, I notice in the metropolis sampler it is effectively:
new_proposal = current point + proposal_dist()

Do you think the best way to avoid this to to hack Metropolis step so that we have:
new_proposal = proposal_dist() ?

or can i do something in MyCustomProposal(Proposal) like :
def __call__self() :
return my_proposal - current_pos

This could then be supplied to the metropolis step as the current_pos would cancel out.

Thanks
Rhys

5

What you do is likely resulting quite poor proposal and, more importantly, invalid proposal as detail balance is not guaranteed (unless the proposal is uniform).

6

Hi
This proposal will be based around some domain knowledge for the parameter space, I’m also aware that I will need to carefully balance the jump probability.
I suppose my current question is mostly based around whether or not a proposal_dist can take current position as an argument ? or whether I’m better off adjusting the metropolis step function ?
Thanks again
Rhys

7

In that case, I dont think you can use the metropolis kernel directly, as the proposal distribution does not take current value. You will need to build your own sampler - I think you can copy the code from Metropolis and do new_proposal = proposal_dist()

8

Great thanks for your help !