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PyMC3 selects data in a model for switching point analysis

I create a time series that has a sharp change in the middle.

import numpy as np

size = 120 
x1 = np.random.randn(size)
x2 = np.random.randn(size) * 4
x = np.hstack([x1, x2])

This series is xas follows:

enter image description here

The goal is now to use PyMC3 to estimate the rear distribution of time when the change occurred (switching point). This should happen around index 120. I used the following code;

from pymc3 import Model, Normal, HalfNormal, DiscreteUniform
basic_model = Model()

with basic_model:
    mu1 = Normal('mu1', mu=0, sd=10)
    mu2 = Normal('mu2', mu=0, sd=10)
    sigma1 = HalfNormal('sigma1', sd=2)
    sigma2 = HalfNormal('sigma2', sd=2)
    tau = DiscreteUniform('tau', 0, 240)

    # get likelihoods
    y1 = Normal('y1', mu=mu1, sd=sigma1, observed=x[:tau])
    y2 = Normal('y2', mu=mu2, sd=sigma2, observed=x[tau:])

Doing this gives an error that I cannot use tauto slice an array. What will be the approach to solving this issue in PyMC? It looks like I will need a slicing that needs to be done with stochastics in PyMC.

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1 answer

, PyMC3 . t - .

import pymc3 as pm
basic_model = pm.Model()

with basic_model:
    mu1 = pm.Normal('mu1', mu=0, sd=10)
    mu2 = pm.Normal('mu2', mu=0, sd=10)
    sigma1 = pm.HalfNormal('sigma1', sd=2)
    sigma2 = pm.HalfNormal('sigma2', sd=2)
    switchpoint = pm.DiscreteUniform('switchpoint', t.min(), t.max())

    tau_mu = pm.switch(t >= switchpoint, mu1, mu2)
    tau_sigma = pm.switch(t >= switchpoint, sigma1, sigma2)

    y = pm.Normal('y1', mu=tau_mu, sd=tau_sigma, observed=x)
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