This is a Proposed course

Question

The following is a proposed class exercise for a course introducing automated data-driven decision-making to new engineers, given their interest in the topic.

I'm interested in feedback. Does the exercise achieve its goal?

"Goal: To demonstrate how fundamental human decision-making can be modeled using Bayesian inference through a single data stream. This involves two key steps: 1) Calculating the prior probability, which represents the likelihood of a current truth based on initial data, and 2) Updating this prior probability with new evidence to determine the posterior probability, representing the likelihood of a future truth (hypothesis)."

This exercise would lead to the development of an improved fault prediction algorithm that uses the this bayesian inference to determine the probability of failure as the hypothesis.

from typing import Dict

def calculate_prior(data_stream: Dict[str, float]) -> float:
    """
    Calculate the prior probability based on the initial data stream instance.
    For simplicity, let's assume the data stream provides a measure of reliability between 0 and 1.
    
    :param data_stream: Dictionary containing data stream instance
    :return: Prior probability
    """
    # Example: Prior probability based on initial data reliability
    prior_probability = data_stream.get('initial_reliability', 0.5)
    if not 0 <= prior_probability <= 1:
        raise ValueError("Initial reliability must be between 0 and 1.")
    return prior_probability

def bayesian_update(prior: float, likelihood: float, evidence: float) -> float:
    """
    Perform Bayesian update to calculate the posterior probability.
    
    :param prior: Prior probability (P(H))
    :param likelihood: Likelihood of the evidence given the hypothesis (P(E|H))
    :param evidence: Probability of the evidence (P(E))
    :return: Posterior probability (P(H|E))
    """
    if not 0 <= prior <= 1:
        raise ValueError("Prior probability must be between 0 and 1.")
    if not 0 <= likelihood <= 1:
        raise ValueError("Likelihood must be between 0 and 1.")
    if not 0 <= evidence <= 1:
        raise ValueError("Evidence probability must be between 0 and 1.")
    if evidence == 0:
        raise ValueError("Evidence probability cannot be zero.")
    
    posterior = (likelihood * prior) / evidence
    return posterior

def process_data_stream(data_stream: Dict[str, float], hypothesis_likelihood: float, evidence_probability: float) -> float:
    """
    Process the data stream to calculate the prior and update it to get the posterior probability.
    
    :param data_stream: Dictionary containing data stream instance
    :param hypothesis_likelihood: Likelihood of the evidence given the hypothesis (P(E|H))
    :param evidence_probability: Probability of the evidence (P(E))
    :return: Posterior probability (P(H|E))
    """
    # Step 1: Calculate the prior
    prior = calculate_prior(data_stream)
    
    # Step 2: Perform Bayesian update to calculate the posterior
    posterior = bayesian_update(prior, hypothesis_likelihood, evidence_probability)
    
    return posterior

# Example data stream instance
data_stream_example = {
    'initial_reliability': 0.7,  # Initial reliability measure of the data
    'new_evidence': 0.8  # Likelihood of new evidence
}

# Example application
hypothesis_likelihood = 0.8  # P(E|H): Likelihood of the evidence given the hypothesis
evidence_probability = 0.9  # P(E): Probability of the evidence

# Process the data stream to get the posterior probability
posterior_probability = process_data_stream(data_stream_example, hypothesis_likelihood, evidence_probability)

print(f"Posterior Probability: {posterior_probability:.4f}")