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  3. Monte Carlo Simulations in Python
  • 1

    Introduction to Monte Carlo Simulations

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    What are Monte Carlo simulations and when are they useful? After covering these foundational questions, you’ll learn how to perform simple simulations such as estimating the value of pi. You’ll also learn about resampling, a special type of Monte Carlo Simulation.

  • 2

    Foundations for Monte Carlo

    Now that you can run your own simple simulations, you’re ready to explore real-world application of Monte Carlo simulations across various industries. Then, you’ll dive into the heart of what makes a good simulation work: sampling from the correct probability distribution. You’ll learn about probability distributions for discrete, continuous, and multivariate random variables.

  • 3

    Principled Monte Carlo Simulation

    Once you’re comfortable with your choice of probability distribution, you’re ready to follow a principled Monte Carlo simulation workflow using a dataset of diabetes patient characteristics and outcomes. You will explore the data, perform a simulation, and generate summary statistics to communicate your simulation results.

  • 4

    Model Checking and Results Interpretation

    Discover how to evaluate your Monte Carlo models and communicate the results with easy-to-read visualizations in Seaborn. Finally, use sensitivity analysis to understand how changes to model inputs will impact your results, and practice this concept by simulating how business profits are impacted by changes to sales and inflation!

Initializing

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Permutation practice

Are NBA players heavier than US adult males? You are now interested in calculating the 95% confidence interval of the mean difference (in kilograms) between NBA players and US adult males. You'll use the two lists provided.

Permutation is great when testing for difference, so that's the resampling method you'll use here!

nba_weights = [96.7, 101.1, 97.9, 98.1, 98.1, 100.3, 101.0, 98.0, 97.4, 100.5, 100.3, 100.2, 100.6]
us_adult_weights = [75.1, 100.1, 95.2, 81.0, 72.0, 63.5, 80.0, 97.1, 94.3, 80.3, 93.5, 85.8, 95.1]

Note that each of the above lists has 13 weights listed.

The following have been imported for you: random, numpy as np, seaborn as sns, and matplotlib.pyplot as plt.

Anweisungen

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  • Define all_weights as a list which contains the values from both nba_weights and us_adult_weights.
  • Perform the permutation on all_weights using np.random.permutation().
  • Assign the first 13 permutated samples to perm_nba and the remaining 13 to perm_adult.