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In [181]:

    
import numpy as np
import matplotlib.pyplot as plt
from scipy import linalg
%matplotlib inline



In [182]:

    
import sys
sys.path.append("../")



In [183]:

    
import PoissonProcessClasses as PP
import imp
imp.reload(PP)









    Out[183]:





<module 'PoissonProcessClasses' from '../PoissonProcessClasses.py'>



In [184]:

    
N = 100# number of observations 
d = 2 # number of covariates

The intensity is $\theta * X$ where $X$ is a row vector.



In [185]:

    
theta = np.array([2,-1])

We consider different shapes for the intensity: random, constant,sinusoidal:



In [186]:

    
#X = 0.1*np.random.normal(size = (d,N))
#X = np.reshape(np.ones(N,),(1,N))
#X = np.reshape(np.sin(np.arange(N)),(1,N))
X = np.vstack((np.reshape(np.ones(N,),(1,N)),np.reshape(np.sin(np.arange(N)),(1,N))))
X.shape









    Out[186]:





(2, 100)



In [187]:

    
dt = 0.01 # discretization step



In [188]:

    
l = np.exp(np.dot(X.T,theta))



In [189]:

    
u = np.random.uniform(size = len(l))
y = 1*(l*dt>u)
print(y)









    



[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]



In [190]:

    
model = PP.PPModel(X,dt = dt)



In [191]:

    
res = model.fit(y)









    



/Users/val/anaconda/lib/python3.4/site-packages/scipy/optimize/_minimize.py:362: RuntimeWarning: Method L-BFGS-B does not use Hessian information (hess).
  RuntimeWarning)



In [192]:

    
print('The estimated parameter is '+ str(res.x)+ '. The true parameter is '+str(theta)+'.')









    



The estimated parameter is [ 2.12872751 -0.85915756]. The true parameter is [ 2 -1].



In [196]:

    
plt.plot(l)
plt.hold(True)
plt.plot(np.exp(np.dot(X.T,res.x)),'r')









    Out[196]:





[<matplotlib.lines.Line2D at 0x109ec2cc0>]



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