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  • 1

    The Bayesian way

    Free

    Take your first steps in the Bayesian world. In this chapter, you’ll be introduced to the basic concepts of probability and statistical distributions, as well as to the famous Bayes' Theorem, the cornerstone of Bayesian methods. Finally, you’ll build your first Bayesian model to draw conclusions from randomized coin tosses.

  • 2

    Bayesian estimation

    It’s time to look under the Bayesian hood. You’ll learn how to apply Bayes' Theorem to drug-effectiveness data to estimate the parameters of probability distributions using the grid approximation technique, and update these estimates as new data become available. Next, you’ll learn how to incorporate prior knowledge into the model before finally practicing the important skill of reporting results to a non-technical audience.

  • 3

    Bayesian inference

    Apply your newly acquired Bayesian data analysis skills to solve real-world business challenges. You’ll work with online sales marketing data to conduct A/B tests, decision analysis, and forecasting with linear regression models.

  • 4

    Bayesian linear regression with pyMC3

    In this final chapter, you’ll take advantage of the powerful PyMC3 package to easily fit Bayesian regression models, conduct sanity checks on a model's convergence, select between competing models, and generate predictions for new data. To wrap up, you’ll apply what you’ve learned to find the optimal price for avocados in a Bayesian data analysis case study. Good luck!

Initializing

Exercise

Simulate beta posterior

In the upcoming few exercises, you will be using the simulate_beta_posterior() function you saw defined in the last video. In this exercise, you will get a feel for what the function is doing by carrying out the computations it performs.

You are given a list of ten coin tosses, called tosses, in which 1 stands for heads, 0 for tails, and we define heads as a "success". To simulate the posterior probability of tossing heads, you will use a beta prior. Recall that if the prior is \(Beta(a, b)\), then the posterior is \(Beta(x, y)\), with:

\(x = \text{NumberOfHeads} + a\)

\(y = \text{NumberOfTosses} - \text{NumberOfHeads} + b\)

Instructions 1/2

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  • 1
    • Set both prior parameters, beta_prior_a and beta_prior_b, to 1.
    • Calculate the number of heads and assign it to num_successes.
    • Generate posterior draws according to the formula above and assign the result to posterior_draws.
  • 2
    • Set the prior parameters, beta_prior_a and beta_prior_b, to 1 and 10, respectively.
    • Calculate the number of heads and assign it to num_successes.
    • Generate posterior draws according to the formula above and assign the result to posterior_draws.