I have been successfully using Pymc 2.0 for inference in a few fast models. However, I'm trying to set up my first real case inference. I'm using a relatively "heavy" likelihood (it takes ~2 min per evaluation).

I noticed that the number of samples specified in the MCMC sampler do not match with the number of actual model evaluations. I do not know if this is a known behavior of pymc. Or I might be doing something very wrong.

I will try to explain it further:

I'm calling an external model with a deterministic decorator:

# Model deterministic part
def Model(W_bM = W_bM, n = n):
    #Load parameters
    Timelist = {'StartTime':186,'StopTime':217} 
    Parameterlist = {'n' : n,'W_b@Multiplier' : W_bM} 
    #Run Model instance  
    ModelInstance.model_run(Parameterlist, Timelist)

    #Read output section
    S031_Q_Mod = ReadOutput('IUWS.River_quantity.Dynamic.Simul.1.out.txt','.S031.Q').as_matrix()[:-1]
    S031_d_Mod = ReadOutput('IUWS.River_quantity.Dynamic.Simul.1.out.txt','.S031.d').as_matrix()[:-1]
    S008_d_Mod = ReadOutput('IUWS.River_quantity.Dynamic.Simul.1.out.txt','.S008.d').as_matrix()[:-1]
    Output = np.array([S031_Q_Mod, S031_d_Mod, S008_d_Mod])

    return Output

Then I set up the sampler:

m = pm.MCMC([n,W_bM, sigma_q031, sigma_d031, sigma_d008, Log_Gaussian_multivariate, Model], db='pickle', dbname='Model_DommelRiver_DepthandFlowCalibration.pickle')

In the external function called by the Model @Deterministic, I have a routine in which I run a model with a number of specified parameters and save a few output files (for later use). Thus I can see how many times this function was evaluated.

In a few runs I have performed, It saw that my function was called for 1500-1800 times instead of the 1000 specified. This is quite scary, since I can never be sure how long will the sampler take.

I'm using just a Metropolis-Hastings sampler, which to my understanding, evaluates the likelihood*prior, compares with the previous and then accepts-rejects the new proposal. This would produce 1000 samples for which there will be n repited elements (due to rejections).

But why is the sampler running more times than the specified? Is this perhaps a wrong connection of the external model? Or does pymc 2.0 behave like this?

Edited: Aditional Information

I wanted to check whether this would happen with a model which doesn't call my external function. I implemented a simple quadratic function as @deterministic and I placed a counter inside (so you can see how many times was this evaluated).

import pymc as pm
import numpy as np

# Regression with error Synthetic data
x = np.linspace(0,10,100)
y = 30 + 35*x - 2.4 * x**2 + np.random.normal(0, 6, len(x))

a = pm.Uniform('a', 0, 50)
b = pm.Uniform('b', 10, 60)
c = pm.Uniform('c', 0, 5)

# Parameters error model
sigma = pm.Uniform('sigma', 0, 20)

# Model
EvalNum = 0
def Model(a = a, b = b, c = c, x=x):
    global EvalNum
    EvalNum += 1
    return a + b*x - c * x**2

# Likelihood function
def Log_Gaussian_iid_univariate(value=y, model=Model, std_dev=sigma):
    return np.sum(-np.log(std_dev) - (value-model)**2 / (2*(std_dev**2)))

m = pm.MCMC([a,b,c, sigma, Log_Gaussian_iid_univariate, Model])
print '\n Number of Evaluations = {}'.format(EvalNum)

The counter shows that the model was evaluated 36980 times. When the m.sample argument was specifying 10000.

Is this mismatch representing rejected points? If rejection happens, I understand we should keep the previous parameter vector in the trace, which would count as a sample. I don't see why m.sample() should evaluate the function more than the specified trace length.

  • $\begingroup$ You can at least shave off the "-0.5*np.log(2)" term in the likelihood function $\endgroup$ – Vladislavs Dovgalecs Feb 20 '17 at 17:46
  • $\begingroup$ Yes, thanks. I can remove as well the np.log(np.pi) since is another constant. $\endgroup$ – Argantonio65 Feb 21 '17 at 9:37

This is as expected. Remember, in Metropolis-Hastings sampling, variables are proposed one-at-a-time, so the expected number of evaluations is always multiples of n. Your model is not particularly large, so I assume you have a large sample size?

You might look at PyMC3, which has gradient based samplers that propose values in k-space, and have much higher acceptance rates.

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