PyMC: a few time-series observations (adaptation of a sample text message from Bayesian methods for hackers)

Question

I am trying to adapt a sample text message from Cameron Davidson-Pilon Bayesian methods for hackers, chapter 1, “Introducing our first hammer: PyMC” to handle several observations. The solution below seems to work, but I'm new to pymc, and I'm not sure if this is a good way to handle multiple time series observations in pymc. Any advice would be greatly appreciated!

To re-close the sample text message from Bayesian methods for hackers, the observations consist of 74 days of counting text messages, as shown in the figure below.

switchpoint (tau) (lambda1 lambda2), , Poisson, tau . pymc : tau = 45, lambda1 = 18 lambda2 = 23, , :

import numpy as np
import pymc

observation = np.loadtxt( './txtdata.csv' ) #data available at the book GitHub site
n_days      = observation.size    #number of days
alpha       = 1./20  #assume a mean of 20 messages per day
lambda1     = pymc.Exponential("lambda1", alpha)
lambda2     = pymc.Exponential("lambda2", alpha)
tau         = pymc.DiscreteUniform("tau", lower=0, upper=n_days)

@pymc.deterministic
def lambda_(tau=tau, lambda1=lambda1, lambda2=lambda2):
    a       = np.zeros(n_days)
    a[:tau] = lambda1
    a[tau:] = lambda2
    return a
observation_model  = pymc.Poisson("observation", lambda_, value=observation, observed=True)

model   = pymc.Model([observation_model, tau, lambda1, lambda2])
mcmc    = pymc.MCMC(model)
mcmc.sample(40000, 10000)

print()
print( mcmc.trace('tau')[:].mean() )
print( mcmc.trace('lambda1')[:].mean() )
print( mcmc.trace('lambda2')[:].mean() )

: ?

, , , , pymc.

tau = 45, lambda1 = 18 lambda2 = 23 :

n_observations = 5
n_days  = 74
alpha   = 1./20
lambda1 = pymc.Exponential("lambda1", alpha)
lambda2 = pymc.Exponential("lambda2", alpha)
tau     = pymc.DiscreteUniform("tau", lower=0, upper=n_days)

@pymc.deterministic
def lambda_single(tau=tau, lambda1=lambda1, lambda2=lambda2):
    a       = np.zeros(n_days)
    a[:tau] = lambda1
    a[tau:] = lambda2
    return a

observation_generator  = pymc.Poisson("observation_generator", lambda_single)
tau.set_value(45)
lambda1.set_value(18)
lambda2.set_value(23)
n_observations = 5
observations = np.array(  [observation_generator.random() for i in range(n_observations)]  )

5 x 74), , , 74 , .

- , : pymc? :

@pymc.deterministic
def lambda_multiple(tau=tau, lambda1=lambda1, lambda2=lambda2):
    a = np.zeros( (n_observations, n_days) )
    a[:, :tau] = lambda1
    a[:, tau:] = lambda2
    return a

observation_model  = pymc.Poisson("observations", lambda_multiple, value=observations, observed=True)

, -, tau, lambda1 lambda2, , ?