CODEWITHSUNDEEP
pymcmcmc
tetradeca7tope
tetradeca7tope

Reputation: 501

Metropolis Hastings with Custom Log likelihood in Pymc

I want to use pymc to use a MH chain to sample from a custom log likelihood. But I can't seem to get it to work and can't find a decent example online.

def getPymcVariable(data):

  def logp(value):
    ...
    return ljps # returns a float

  def random():
    return np.random.rand(numDims);

  dtype = type(random());
  initPt = [0.45, 0.24, 0.68];

  ret = pymc.Stochastic(logp = logp,
                        doc = 'SNLS RV',
                        name = 'SNLS',
                        parents = {},
                        random = random,
                        trace = True,
                        value = initPt,
                        dtype = dtype,
                        observed = False,
                        cache_depth = 2,
                        plot = True,
                        verbose = 0 );
  return ret


if __name__ == '__main__':

    data = np.loadtxt('../davisdata.txt');
    numExperiments = 30;
    numSamples = 10000;

    SNLS = getPymcVariable(data)
    model = pymc.Model([SNLS]);
    mcmcModel = pymc.MCMC(model);
    mcmcModel.use_step_method(pymc.Metropolis, SNLS, proposal_sd=1);
    mcmcModel.sample(numSamples, burn=0, thin=1);
    x = mcmcModel.trace('SNLS')[:]
    np.savetxt(fileName, x);

Its a 3 dimensional variable, has a uniform prior and a log likelihood computed in logp(). I want to run an MH chain with an adaptive proposal distribution. But each time I run the sampler it just returns a uniform distribution (in fact, it just returns samples from the random function above - when I modified it to 0.5*np.random.rand(numDims) it returned a Unif( (0,1)^3) distribution. )

However, I know that the logp function is being called.

There are a few more questions I have: - What is the purpose of the random function above ? I initially thought it was a prior but doesn't look like it.

Upvotes: 0

Views: 852

Answers (1)

Abraham D Flaxman
Abraham D Flaxman

Reputation: 2979

In PyMC2, I find it considerably simpler to use built-in distributions and the @potential decorator for this sort of task. Here is a minimal example:

X = pm.Uniform('X', 0, 1, value=[0.45, 0.24, 0.68])

@pm.potential
def SNLS(X=X):
    logp = -X[0]**2 / X[1]
    logp += -X[1]**2 / X[2]  # or whatever...
    return logp

You can select an adaptive metropolis step method as follows:

m = pm.MCMC([X, SNLS])
m.use_step_method(pm.AdaptiveMetropolis, X)

Here is a notebook that puts this together and plots the results.

Upvotes: 1

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