Problem #

I'm learning Bayesian statistics via Probabilistic Programming and Bayesian Methods for Hackers, but the book's examples use the deprecated PyMC library. I'm migrating to PyMC3 and got stuck on replacing the @pm.deterministic decorator. Here's the original PyMC code:

import numpy as np
import pymc as pm
count_data = np.loadtxt("txtdata.csv")
n_count_data = len(count_data)
alpha = 1.0 / count_data.mean()
lambda_1 = pm.Exponential("lambda_1", alpha)
lambda_2 = pm.Exponential("lambda_2", alpha)
tau = pm.DiscreteUniform("tau", lower=0, upper=n_count_data)
@pm.deterministic
def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):
    out = np.zeros(n_count_data)
    out[:tau] = lambda_1 # lambda before tau is lambda1
    out[tau:] = lambda_2 # lambda after (and including) tau is lambda2
    return out
observation = pm.Poisson("obs", lambda_, value=count_data, observed=True)
model = pm.Model([observation, lambda_1, lambda_2, tau])
mcmc = pm.MCMC(model)
mcmc.sample(40000, 10000, 1)
lambda_1_samples = mcmc.trace('lambda_1')[:]
lambda_2_samples = mcmc.trace('lambda_2')[:]
tau_samples = mcmc.trace('tau')[:]

I've started rewriting for PyMC3 but hit a wall with the deterministic function:

import numpy as np
import pymc3 as pm
from matplotlib import pyplot as plt
count_data = np.loadtxt("txtdata.csv")
n_count_data = len(count_data)
alpha = 1.0 / count_data.mean()
basic_model = pm.Model()
with basic_model:
    lambda_1 = pm.Exponential("lambda_1", alpha)
    lambda_2 = pm.Exponential("lambda_2", alpha)
    tau = pm.DiscreteUniform("tau", lower=0, upper=n_count_data)
    @pm.deterministics
    def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):
        out = np.zeros(n_count_data)
        out[:tau] = lambda_1 # lambda before tau is lambda1
        out[tau:] = lambda_2 # lambda after (and including) tau is lambda2
        return out
    observation = pm.Poisson("obs", lambda_, value=count_data, observed=True)

How can I fix this PyMC3 code to run correctly?

Solution #

PyMC3 removed the @pm.deterministic decorator entirely, and uses tensor operations (via Theano/TensorFlow) instead of raw NumPy array manipulation for model variables. Here's how to adapt your code:

Key Changes:

1. Replace the deterministic function with tensor-based conditional logic (using pm.math.where or pm.math.switch)
2. Remove the invalid @pm.deterministics decorator (you also had a typo: extra "s")
3. Update the observation variable to use PyMC3's observed parameter syntax (no value= needed)
4. Use PyMC3's modern sampling API (pm.sample() instead of pm.MCMC)

Full Working PyMC3 Code:

import numpy as np
import pymc3 as pm
import arviz as az  # For trace analysis/visualization (recommended for PyMC3)

# Load data
count_data = np.loadtxt("txtdata.csv")
n_count_data = len(count_data)
alpha = 1.0 / count_data.mean()

# Define the model
basic_model = pm.Model()
with basic_model:
    # Priors for the two lambda values
    lambda_1 = pm.Exponential("lambda_1", alpha)
    lambda_2 = pm.Exponential("lambda_2", alpha)
    
    # Prior for the change point tau
    tau = pm.DiscreteUniform("tau", lower=0, upper=n_count_data)
    
    # Define the piecewise lambda using tensor operations (replaces @pm.deterministic)
    # Create an index array for each time point
    idx = pm.math.arange(n_count_data)
    # Use where to select lambda_1 before tau, lambda_2 after
    lambda_ = pm.math.where(idx < tau, lambda_1, lambda_2)
    
    # Observed data (PyMC3 uses observed directly, no value= parameter)
    observation = pm.Poisson("obs", lambda_, observed=count_data)
    
    # Run MCMC sampling: tune = burn-in iterations, cores = parallel processing
    trace = pm.sample(40000, tune=10000, cores=2, return_inferencedata=True)

# Extract samples from the trace (using ArviZ's InferenceData object)
lambda_1_samples = trace.posterior["lambda_1"].values.flatten()
lambda_2_samples = trace.posterior["lambda_2"].values.flatten()
tau_samples = trace.posterior["tau"].values.flatten()

# Optional: Visualize the trace with ArviZ
az.plot_trace(trace)

Explanation:

• Tensor Conditional Logic: PyMC3 variables are tensors, not NumPy arrays, so we can't slice and assign values directly. pm.math.where() acts like a vectorized if-else, selecting lambda_1 for indices before tau and lambda_2 for indices after.
• Sampling API: pm.sample() handles MCMC setup automatically, including burn-in (via tune). The return_inferencedata=True flag returns an ArviZ object, which is the standard way to analyze and visualize PyMC3 results.
• Deterministic Variable Optional: If you want to save lambda_ to the trace (for later analysis), wrap it in pm.Deterministic:

  lambda_ = pm.Deterministic("lambda_", pm.math.where(idx < tau, lambda_1, lambda_2))
  

内容的提问来源于stack exchange，提问作者Alpha Delta