Hoe meer je gooit, hoe meer je leert

Stel, je bent een frequentist (voor één dag) en je krijgt de taak om de kans op kop te schatten met een (mogelijk oneerlijke) munt, maar zonder ook maar één worp te observeren. Wat zou je zeggen? Onmogelijk, er zijn geen gegevens! Dan mag je de munt één keer werpen. Je krijgt munt. Wat zeg je nu? Nou, als dat al je data is, zou je zeggen dat de kans op kop 0% is.

Waarschijnlijk voel je aan dat dit niet de beste antwoorden zijn. Maar wat is beter? Wat zou een Bayesian zeggen? Laten we dat uitzoeken! numpy en seaborn zijn al voor je geïmporteerd als respectievelijk np en sns.

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Bayesian Data Analysis in Python

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# Estimate and plot heads probability based on no data
heads_prob_nodata = ____
____(____, shade=True, label="no data")
plt.show()

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Bayesian Data Analysis in Python

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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.

Exercise 1: Wie is Bayes? Wat is Bayes?Exercise 2: Bayesianen vs. frequentisten Exercise 3: Kansverdelingen Exercise 4: Kansrekening en de stelling van Bayes Exercise 5: Laten we kaarten Exercise 6: Bayesiaans spamfilter Exercise 7: Wat zegt de test?Exercise 8: Proeven van Bayes Exercise 9: Een munt opgooien Exercise 10: Hoe meer je gooit, hoe meer je leert

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Exercise 11: Hé, is deze munt eerlijk?

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.

Exercise 1: Under the Bayesian hood Exercise 2: Towards grid approximation Exercise 3: Grid approximation without prior knowledge Exercise 4: Updating posterior belief Exercise 5: Prior belief Exercise 6: The truth of the prior Exercise 7: Picking the right prior Exercise 8: Simulating posterior draws Exercise 9: Reporting Bayesian results Exercise 10: Point estimates Exercise 11: Highest Posterior Density credible intervals Exercise 12: The meaning of credibility

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.

Exercise 1: A/B testing Exercise 2: Simulate beta posterior Exercise 3: Posterior click rates Exercise 4: A or B, and how sure are we?Exercise 5: How bad can it be?Exercise 6: Decision analysis Exercise 7: Decision analysis: cost Exercise 8: Decision analysis: profit Exercise 9: Regression and forecasting Exercise 10: Defining a Bayesian regression model Exercise 11: Analyzing regression parameters Exercise 12: Predictive distribution

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!

Exercise 1: Markov Chain Monte Carlo and model fitting Exercise 2: Markov Chain Monte Carlo Exercise 3: Sampling posterior draws Exercise 4: Interpreting results and comparing models Exercise 5: Inspecting posterior draws Exercise 6: Comparing models with WAIC Exercise 7: Making predictions Exercise 8: Sample from predictive density Exercise 9: Estimating test error Exercise 10: How much is an avocado?Exercise 11: Fitting the model Exercise 12: Inspecting the model Exercise 13: Optimizing the price Exercise 14: Final remarks