Posterior-trekkingen simuleren

Je hebt net besloten een Beta(5, 2)-prior te gebruiken voor het werkingspercentage. Je gebruikt ook de binomiale verdeling om de data te modelleren (een zieke patiënt genezen is een "succes", weet je nog?). Omdat de bètaverdeling een geconjugeerde prior is voor de binomiale likelihood, kun je de posterior simpelweg simuleren!

Je weet dat als de prior \(Beta(a, b)\) is, de posterior \(Beta(x, y)\) is, met:

\(x = NumberOfSuccesses + a\),

\(y = NumberOfObservations - NumberOfSuccesses + b\).

Kun je de posteriorverdeling simuleren? Onthoud dat je in totaal data hebt over 22 patiënten, van wie er 19 zijn genezen. numpy en seaborn zijn al voor je geïmporteerd als respectievelijk np en sns.

Deze oefening maakt deel uit van de cursus

Bayesian Data Analysis in Python

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Oefeninstructies

Ken het aantal behandelde en genezen patiënten toe aan respectievelijk num_patients_treated en num_patients_cured.
Gebruik de juiste numpy-functie om te steken uit de posteriorverdeling en ken het resultaat toe aan posterior_draws.
Plot de posteriorverdeling met de juiste seaborn-functie.

Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# Define the number of patients treated and cured
num_patients_treated = ____
num_patients_cured = ____

# Simulate 10000 draws from the posterior distribuition
posterior_draws = ____(____ + ____, ____ - ____ + ____, 10000)

# Plot the posterior distribution
____(____, shade=True)
plt.show()

Code bewerken en uitvoeren

Deze oefening maakt deel uit van de cursus

Bayesian Data Analysis in Python

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Begin de cursus gratis

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: Who is Bayes? What is Bayes?Exercise 2: Bayesians vs. Frequentists Exercise 3: Probability distributions Exercise 4: Probability and Bayes' Theorem Exercise 5: Let's play cards Exercise 6: Bayesian spam filter Exercise 7: What does the test say?Exercise 8: Tasting the Bayes Exercise 9: Tossing a coin Exercise 10: The more you toss, the more you learn Exercise 11: Hey, is this coin fair?

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: Onder de Bayesiaanse motorkap Exercise 2: Op weg naar grid-approximatie Exercise 3: Rasterbenadering zonder voorkennis Exercise 4: Posterior bijwerken Exercise 5: A-prioriverwachting Exercise 6: De waarheid van de prior Exercise 7: De juiste prior kiezen Exercise 8: Posterior-trekkingen simuleren

Huidige oefening

Exercise 9: Bayesiaanse resultaten rapporteren Exercise 10: Puntschattingen Exercise 11: Highest Posterior Density-credible intervals Exercise 12: De betekenis van geloofwaardigheid

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