AdityaSavara
commented
4 years ago So what we need to do is... a) Check for positive definite in posterior_cov_matrix, and if it fails then give user warning to use mcmc_modulate_accept_probability (they actually might need to go much higher than what the instructions provided say, I had to go as high as 1000 with eight parameters, so we need to revise our instructions). Also, to consider to increase/decrease the mcmc step size and increase the sample length, change the starting point. b) later, put code to force positive definite. I think that this may be happening due to covariances of zero. One thing we can do is to put in an arbitrarily small covariance that is something like 1/100 * mu_var that way it is effectively zero on the scale of the mumpce plot. c) even later, give user suggestions of how to change mcmc step size. In future, I want to make mcmc step size an array instead of a single value (separate step sizes for each variable). I think pymc does that automatically. So another option for c is to wait until the pymc engine is inluded as an option.
To run the example attached to this post in the following zip file, use runfile_Example8_optimization_mcmc.py. It should take under a minute to run. 200323_2.2a-MiniExample.zip
I received this error:
I think it is because a matrix (probably posterior cov) had negative or zero values due to numerical errors or insufficient sampling. https://stackoverflow.com/questions/21604498/numpy-cholesky-decomposition-linalgerror
I think that what we should do is give people a warning while also forcing the matrix to become positive definite.
For forcing: There is some r code, don't now if it's in python https://rdrr.io/cran/stsm/man/force-defpos.html here is a small python script: https://stackoverflow.com/questions/43238173/python-convert-matrix-to-positive-semi-definite
For warning: I found that for my case increasing hte mcmc step length and increasing the mcmc_modulate_accept_probability to 1000 solved my problem. More details of what I think should be put in the warning will be in the comments below.