Module 12: Uncertainty Quantification - Participation Exercises

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Module 12: Uncertainty Quantification - Participation Exercises#

Exercise 12.1: Reflection - Communicating Uncertainty#

Type: 🤔 Reflection (3 min)

Your model predicts a reactor yield of 75% with a 95% confidence interval of [65%, 85%].

Reflect:

  1. How would you explain this to a plant manager who asks “So what’s the yield going to be?”

  2. Why might the manager find uncertainty uncomfortable?

  3. Why is communicating uncertainty important for decision-making?

Your reflection:

Exercise 12.2: Mini-Exercise - Bootstrap Confidence Intervals#

Type: 🔧 Mini-Exercise (8 min)

Calculate a bootstrap confidence interval for a regression coefficient.

import numpy as np
from sklearn.linear_model import LinearRegression

# Simple linear data
np.random.seed(42)
n = 50
X = np.random.uniform(0, 10, n).reshape(-1, 1)
y = 2.5 * X.ravel() + 5 + np.random.randn(n) * 2  # True slope = 2.5

# Single model fit
model = LinearRegression().fit(X, y)
print(f"Point estimate for slope: {model.coef_[0]:.3f}")

# TASK: Implement bootstrap to get confidence interval
n_bootstrap = 1000
bootstrap_slopes = []

for i in range(n_bootstrap):
    # 1. Sample with replacement from the data
    # indices = ???
    
    # 2. Fit model on bootstrap sample
    # X_boot = ???
    # y_boot = ???
    # model_boot = ???
    
    # 3. Store the coefficient
    # bootstrap_slopes.append(???)
    pass

# 4. Calculate 95% CI
# ci_lower = np.percentile(bootstrap_slopes, ???)
# ci_upper = np.percentile(bootstrap_slopes, ???)
# print(f"95% CI for slope: [{ci_lower:.3f}, {ci_upper:.3f}]")

Point estimate for slope: 2.455

Exercise 12.3: Discussion - Sources of Uncertainty#

Type: đź’¬ Discussion (5 min)

A machine learning model has multiple sources of uncertainty.

Categorize these sources as “aleatory” (irreducible) or “epistemic” (reducible):

  1. Measurement noise in sensors

  2. Model doesn’t include an important variable

  3. Inherent randomness in a chemical process

  4. Not enough training data

  5. Wrong model architecture

Which can we reduce by collecting more data?

Classification:

Source

Aleatory or Epistemic?

Can more data help?

1. Measurement noise

2. Missing variable

3. Process randomness

4. Limited training data

5. Wrong architecture

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