Can HMC resolve small parameters along side large ones in the same group?

fitting-issues

#1

Hi I have a general HMC question. I am repeating the results of a paper, which was able to resolve some very small parameter values along side much larger ones. One example is a group of parameters that ranges from 0.015 to 0.607. By all indications, the same prior was given to the whole group. In none of my experiments can I ever get such a wide range in my parameter values. The very fact I had to choose a large variance in the prior to cover the larger values, it forces all the smaller values to a comparable range also.

Does any one have any insight into how such relative precision can be achieved?


#2

If you have a reasonable amount of data this should work fine so probably a bug in your model


#3

Please back up a bit. I tried this on a brain dead simple logistic regression model. there is not much that can go wrong. When I add more data, the result was going the wrong direction. Could you provide some simple example where this is true : more data gets you accurate result on both tiny and big parameter values using the same prior? Even better, if at all possible, one using logistic regression.


#4

I’d rather not. I guess in some data sparse settings with the wrong priors you might get inflated estimates of small effects in small groups, so that’s a possibility.


#5

Thank, I have been trying to solve this for months and have concluded along with other people that this is indeed the case, in contrast to your opinion. If you or anyone can show otherwise easily, would highly appreciate sharing the wisdom.

As for prior, I made my point that you must use higher variance to accommodate the large values in the group, which directly causes the smaller values to get inflated. You seem to be in disagreement with that? So it’s fair to say that you would be able to resolve small values regardless of the large variance in the prior? If I misread you, please comment.

As for data sparsity, I used N= 40, 1000, 100000. All cases have this problem.


#6

That’s interesting. At larger group sizes you’ll be hard pressed to find a prior that gives you the result you are suggesting with weakly informative priors.


#7

You can also try increasing the warmup time. This will give the mass matrix more time to adapt to different scales of parameters.

Also, if you can provide more details about what you are working on or even share the model code, it would help the people volunteering their time for the community to better assist you. As @sakrejda says with 100,000 data points, the data will dominate all but the most informative priors.


#8

Hi guys. On the strength on your recommendation, I did an experiment, this time using data from a working sample code, and I verified that indeed, I am able to resolve small and large parameter values together. This means the problems I was observing came from else where.

This is really big for me. Thanks very very much for your sound advice.