I am an absolute new to probabilistic programming and to the pyro framework. I am trying to model a temporal sequence as a poisson process. My goal is to generate the sequence given fixed model parameters (generative algorithm) and then given the generated sequence I want to infer/fit the model parameters to cross check the inference process.
I generate a temporal sequence which via a non-homogeneous poisson processes(NHPP). The code for the thinning algorithm to generate the NHPP is given below along with a block on how to run it.
def thinning_algo(intensity_function, T, max_intensity = 2): times = torch.linspace(1e-5, T, 2000) max_intensity = intensity_function(times).max() thining_prob = lambda t: intensity_function(t)/max_intensity t = 0; N = 0; arrival_times = torch.tensor() while True: u1, u2 = pyro.sample("unif", dist.Uniform(0, 1), torch.tensor()) t = t - (u1.log()/max_intensity) if t < T: if u2 < thining_prob(t): arrival_times = torch.cat((arrival_times, torch.tensor([t]))) N += 1 else: return arrival_times
import numpy T = 50 #model Parameters to be inferred. high_rate = 100.0; low_rate = 0.0; phase_length = 25.0 #model parameters which will be inffered. rate_function = lambda x: low_rate + (high_rate-low_rate)*0.5*(1+numpy.sin(2*numpy.pi*x/phase_length)) arrival_times = thinning_algo(rate_function, T)
The log likelihood of the intensity is given by .
I want MAP estimate of the model parameters given the arrival times and any help would be greatly appreciated. Eventually, I want to have multiple NHPP with different parameters which come from some global prior.