Bayesian Model Calibration

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@pymc-bot
How can I conduct a lift test experiments and create the experiment table using CausalPy or Pymc for model calibration?

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To conduct lift test experiments and create an experiment table using PyMC for model calibration, you can follow these steps:

  1. Define the Experiment Design: Clearly outline the control and treatment groups for your lift test. This involves deciding on the metrics you want to measure and the expected outcome of the treatment.

  2. Data Collection: Gather data from both the control and treatment groups. Ensure that the data is clean and pre-processed for analysis.

  3. Model Specification in PyMC:

    • Use PyMC to specify a Bayesian model that captures the causal effect of the treatment. This typically involves defining prior distributions for the parameters of interest and a likelihood function that relates the data to these parameters.
    • For example, you might model the lift as a difference in means between the treatment and control groups, using a normal distribution for the observed data.

  4. Implementing the Model in PyMC:

    import pymc as pm
import pytensor as pt

# Example data
control_data = ...
treatment_data = ...

with pm.Model() as model:
    # Priors for unknown model parameters
    mu_control = pm.Normal('mu_control', mu=0, sigma=10)
    mu_treatment = pm.Normal('mu_treatment', mu=0, sigma=10)
    sigma = pm.HalfNormal('sigma', sigma=10)

    # Likelihood (sampling distribution) of observations
    control_obs = pm.Normal('control_obs', mu=mu_control, sigma=sigma, observed=control_data)
    treatment_obs = pm.Normal('treatment_obs', mu=mu_treatment, sigma=sigma, observed=treatment_data)

    # Define the lift as the difference in means
    lift = pm.Deterministic('lift', mu_treatment - mu_control)

    # Inference
    trace = pm.sample()

# The trace object contains the posterior samples

  5. Analysis and Interpretation:

    • Use the trace object to analyze the posterior distribution of the lift. This will give you an estimate of the causal effect of the treatment.
    • You can use ArviZ, which is integrated with PyMC, to summarize and visualize the results.

  6. Creating the Experiment Table:

    • Summarize the results in a table format, showing the estimated lift, credible intervals, and any other relevant statistics.

This approach allows you to incorporate uncertainty in your estimates and make probabilistic statements about the effect of the treatment. If you need more specific guidance on any of these steps, please provide additional details about your experiment or data.

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