马尔可夫链蒙特卡洛（python，numpy）

Question

I am doing some research in physics, for which I need to analyze some data using a Markov Chain Monte Carlo (MCMC). I tried to just write one myself but I keep coming across bugs when python/numpy rounds a very very small number down to zero. Specifially when I need to do something like numpy.exp(-1000) . That expression itself is part of a larger math equation so I can't just take the log of it.

I know that there are MCMC modules available for python and I have taken a look at some of them but am having trouble understanding the documentation for them to apply them. Can anyone recommend one? What I have is a column of data that I plug into a probability distribution. This distribution also has two other variables which I will be conducting random walks on and recording each step in the markov chain. I will then need to make a histogram of each of those two variables based off the markov chain. I apologize if this question is too vague. Any ideas or suggestions are much appreciated, thanks!

Answer 1

Use higher-precision floats, if available on your system. For example, if you have float128 :

import numpy as np
print(np.exp(np.float128(-1000)))  # 5.07595889755e-435
print(np.exp(np.float128(-10000)))  #  1.13548386531e-4343

Also see longdouble . It really depends on your operating system to what is supported and how.

You can convert arrays that require this precision and work with them with Numpy functions:

# Example array with 3 dimensions
d = np.random.uniform(-10000, -100, 24)
d.shape = (2, 3, 4)

# Cast to a higher precision
D = d.astype(np.float128)
np.exp(D[:,2])  # array([[4.263772e-4326, 4.3465066e-1474, ...

Answer 2

Use PyMC - it's great. Work through the tutorials and you should soon understand how to build a model.

http://pymc-devs.github.io/pymc/tutorial.html