Potential probability with pymc

Question

(This question was originally published in statistics. A. I moved it here because it relates to pymc and the more general questions within it: in fact, the main goal is to better understand how pymc works pymc If any of the moderators think that it is not suitable for SO, I will clean it here.)

I read the pymc tutorial and many other questions both here and in SO.

I am trying to understand how to apply Bayes' theorem to calculate posterior probability using certain data. In particular, I have a set of independent parameters

From the data, I would like to conclude about the probability where is a specific event. Then the goal is to calculate

Additional comments :

• This is a kind of unsupervised learning, I know what happened and I want to know the parameters that maximize the likelihood . (*)
• I would also like to have a parallel procedure when I let pymc calculate the probability of receiving data, and then for each set of parameters . I want to get a back chance.

In the future, I will consider that and that probability is a multidimensional normal distribution with (due to independence).

Below is the code I'm using (for simplicity, suppose there are only two parameters). The code is still under development (I know that it cannot work!). But I find it useful to include it, and then clarify it after comments and answers in order to provide the skeleton for future reference.

 class ObsData(object): def __init__(self, params): self.theta1 = params[0] self.theta2 = params[1] class Model(object): def __init__(self, data): # Priors self.theta1 = pm.Uniform('theta1', 0, 100) self.theta2 = pm.Normal('theta2', 0, 0.0001) @pm.deterministic def model( theta1=self.theta1, theta2=self.theta2, ): return (theta1, theta2) # Is this the actual likelihood? self.likelihood = pm.MvNormal( 'likelihood', mu=model, tau=np.identity(2), value=data, # is it correct to put the data here? observed=True ) def mcmc(observed_data): data = ObsData(observed_data) pymc_obj = Model(data) model = pymc.MCMC(pymc_obj) model.sample(10000, verbose=0) # Does this line compute the likelihood and the normalisation factor? # How do I get the posterior distribution? 

The following questions arise:

• Does self.likelihood Bayesian probability?
• How to use the data? (I suspect value=data incorrect ..)
• Does .sample() really calculate the back probability?
• How do I get information from the back?
• (*) Should I include everything related to the fact that happened at some point?
• As a general question : is it possible to use pymc only to calculate the probability of receiving data and priorities?

Any comments, as well as a link to another question or tutorial are welcome!

Answer 1

For starters, I think you want to return (theta1 * theta2) from your model definition.

model.sample is a selection, not a calculation, of the rear distributions (assuming a sufficient burn, etc.) of your parameters, given your data, and the likelihood that specific values ​​for each tuple of parameters can be determined from the joint back after sampling.

I think you have a fundamental misunderstanding of MCMC at the moment. I can't think of a better way to answer your questions than point to the wonderful Bayesian methods for hackers.