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from matplotlib.pyplot import plot
from ssa import SSA
from pystan import stan

%matplotlib inline


    

In [3]:

    

N = 100
alpha = 1
mu = 10

x, t = SSA(3,N,a=alpha,mu=mu)

x = x.astype(int) # path data supposed to be integers.

path_data = {
    'N' : N,
    't' : t,
    'x' : x
}


    

In [4]:

    

# Setup STAN :
model_description = """
data{
  int<lower=0> N; ## number of time steps
  vector[N] t; ## time value at each time step
  int<lower=0> x[N]; ## population value at each time step
}

transformed data{
  int<lower=0> x0; ## starting population value
  x0 <- x[1];
}

parameters{
  real<lower=0> alpha; ## birth rate parameter 
  real<lower=0> mu; ## death rate parameter
}

model {
      x ~ poisson(alpha/mu+(x0-alpha/mu)*exp(-mu*t)); 
}
"""


    

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fit = stan(model_code=model_description,
           data=path_data, chains=1,iter=1000)

print fit


    

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