Add delayed rejection metropolis hastings class by dawsoneliasen · Pull Request #136 · bangerth/SampleFlow · GitHub

This PR adds a new producer for delayed rejection metropolis hastings sampling.

Close. I think it would be useful to also have a test that samples from either a uniform or a Gaussian distribution, and computes the mean and standard deviation to make sure we're at least in the ballpark of what one would analytically expect.

I think you should update the description of this parameter for the DR case.

@bangerth Would you please elaborate? Are you referring to log_likelihood or perturb? I'm not sure what needs to be changed about the description.

Close. I think it would be useful to also have a test that samples from either a uniform or a Gaussian distribution, and computes the mean and standard deviation to make sure we're at least in the ballpark of what one would analytically expect.

@bangerth Good idea, I copied the metropolis_hasting_producer_04 test which gets a mean value of about 2, but when executed with the new class, the mean value is 1. Is this be a sign that something is going wrong? The test was pushed to this branch so you can take a look at what is happening exactly.

It may be a problem. Knowing that the mean value should be 2 is really only a statement about having a very large number of samples. What happens if you look a many more samples?

Suggested change

      
            std::pair<SampleType,double> perturb (const SampleType &x, const std::vector<SampleType> y)
          
            std::pair<SampleType,double> perturb (const SampleType &x, const std::vector<SampleType> &y)

I'm not sure this is right. The fact that the function lies about what the ratio of probabilities are, makes it probably so that it doesn't quite lead to correct results. It may be better to sample from something like a Gaussian, and compute the mean of that.

Or you can leave the test as is and just go with it. Returning a ratio of 1 means that the delayed rejection simply always accepts the very first sample. That's not wrong, and in some sense just checks a specific part of the algorithm. So maybe it does make sense to just keep the test.

Yes, that looks wrong :-(

@bangerth see this commit. I tried with max_delays=0 just like you said and observed different results from the vanilla MH. I went through the vanilla MH to see what could possibly be different and this was missing. I thought that including this likelihood check was redundant but I guess I was wrong (let's talk about this more next week). With this included, the max_delays=0 DRMH produces samples with a mean of 1.99.

However, when I increase the number of delay stages to 5, the resulting mean is 1.69. This makes me very suspicous that there is something wrong with the delayed rejection process. What are your thoughts?

As for different results: You have to count how many times you evaluate the rng. It produces a reproducible sequence of random numbers, but if you use the rng a different number of times per loop iteration, then at the top of the next iteration you will of course get a different result.

delay_stage is inherently a non-negative. It should be unsigned int.

@bangerth This assert passes just fine, but with this setup (using a variable u), the mean value converges to 1 instead of 2. Simply removing the variable u and calling uniform_distribution() inside the conditional results in a mean of 2.

@bangerth Any thoughts on this? Why would the assignment of a variable affect the random values?

Need to run make indent.

Oh, you already beat me to it :-) So just squash things into fewer commits.

@bangerth Sorry, I'm having trouble squashing this branch. I thought I just needed to do:

git rebase master
git reset

But both of these commands just output "Current branch add-dram-producer is up to date."

For squashing, you need an "interactive" rebase. So do

  git rebase -i master

No reset should be necessary, but you'll find that

  git push origin

will fail. Read the error message and try to understand why you get it. Then ignore it by saying

  git push -f origin

@bangerth perfect, thank you!

remove separate function for log likelihood of rejected point update variable names combine loops, add documentation rename fix ifndef fix bugs add test for DRMH use a different iterator for inner loop add test output fix indentation use a better variable name for inner loop always do at least one stage use prefix increment add note about max_delays==0 move the n_samples to the last parameter update test to reflect changes to sample signature add another test fix indentation do not name ignored argument finish sentence use 0.5 for likelihood create another test multiply by acceptance ratio of previous sample more than one delayed rejection more than one delayed rejection finish implementing test fix likelihood and perturb make variables const create output file include likelihood check add assert for testing emulate regular MH update test case add shortcut back in add seed option fix style

dawsoneliasen commented Sep 2, 2020

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dawsoneliasen commented Sep 2, 2020

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dawsoneliasen marked this pull request as ready for review September 9, 2020 16:03

bangerth reviewed Sep 9, 2020

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bangerth reviewed Sep 23, 2020

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dawsoneliasen commented Oct 7, 2020

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Comment thread tests/delayed_rejection_mh_producer_02.cc

bangerth reviewed Oct 28, 2020

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Comment thread tests/delayed_rejection_mh_producer_03.cc Outdated

dawsoneliasen commented Oct 29, 2020

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bangerth reviewed Nov 4, 2020

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dawsoneliasen commented Nov 4, 2020

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dawsoneliasen force-pushed the add-dram-producer branch from ee56ab4 to 7937045 Compare November 18, 2020 22:29

dawsoneliasen force-pushed the add-dram-producer branch from 0240339 to 0461d32 Compare December 9, 2020 21:38

bangerth approved these changes Dec 10, 2020

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bangerth merged commit 745f7da into bangerth:master Dec 10, 2020

This was referenced Dec 10, 2020

Reference a delayed rejection publication. #150

Merged

Implement full delayed rejection algorithm #151

Open

Pass an argument by reference. #152

Merged

+                       * @param[in] log_likelihood A function object that, when called
+                       *   with a sample $x$, returns $\log(\pi(x))$, i.e., the natural
+                       *   logarithm of the likelihood function evaluated at the sample.
+                       * @param[in] perturb A function object that, when given a sample

+                // probabilities. We're moving the sample to the right, so that ratio
+                // is actually infinity, but we can lie about it for the purposes of
+                // this test.
+                return {x+1, 1.};

+                        // this is multiplied to the current acceptance_ratio
+                        double prev_acceptance_ratio = 1.0;
+                        // Delayed rejection loop
+                        for (int delay_stage = 0; delay_stage <= max_delays; ++delay_stage)

+                            double u = uniform_distribution(rng);
+                            assert(acceptance_ratio > 1 == acceptance_ratio >= u);
+                            if (acceptance_ratio > 1 || acceptance_ratio >= u)
+                              accepted_sample = true;



		// Always move to the right when trying to find a new trial sample.
		std::pair<SampleType,double> perturb (const SampleType &x, const std::vector<SampleType> y)

		if ((trial_log_likelihood - std::log(proposal_distribution_ratio) > current_log_likelihood) \|\|
		acceptance_ratio >= uniform_distribution(rng))

		@@ -0,0 +1 @@
		Mean value = 1.00056

Add delayed rejection metropolis hastings class by dawsoneliasen · Pull Request #136 · bangerth/SampleFlow · GitHub

Add delayed rejection metropolis hastings class - #136

Add delayed rejection metropolis hastings class#136bangerth merged 1 commit intobangerth:masterbangerth/SampleFlow:masterfrom dawsoneliasen:add-dram-producerdawsoneliasen/SampleFlow:add-dram-producerCopy head branch name to clipboard

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Add delayed rejection metropolis hastings class#136
bangerth merged 1 commit into
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dawsoneliasen commented Sep 1, 2020 •
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dawsoneliasen commented Sep 19, 2020 •
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