Modellen vergelijken met WAIC

Nu je het eerste, basismodel succesvol hebt gebouwd, kijk je nog eens naar de beschikbare data. Je ziet een variabele wind_speed. Dat zou weleens een sterke voorspeller kunnen zijn voor het aantal verhuurde fietsen! Tegen de wind in fietsen is niet zo leuk, toch?

Je past een nieuw model met deze extra voorspeller:

formula = "num_bikes ~ temp + work_day + wind_speed"

with pm.Model() as model_2:
    pm.GLM.from_formula(formula, data=bikes)
    trace_2 = pm.sample(draws=1000, tune=500)

Is je nieuwe model_2 beter dan model_1, het model zonder windsnelheid? Vergelijk de twee modellen met de Widely Applicable Information Criterion, of WAIC, om erachter te komen!

Zowel trace_1 als trace_2 zijn beschikbaar in je werkruimte, en pycm3 is geïmporteerd als pm.

Deze oefening maakt deel uit van de cursus

Bayesian Data Analysis in Python

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Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# Gather trace_1 and trace_2 into a dictionary
traces_dict = ____

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Deze oefening maakt deel uit van de cursus

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: 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: 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: Markovketen-Monte Carlo en het fitten van modellen Exercise 2: Markov Chain Monte Carlo Exercise 3: Steekproeven trekken uit de posterior Exercise 4: Resultaten interpreteren en modellen vergelijken Exercise 5: Posterior-trekkingen inspecteren Exercise 6: Modellen vergelijken met WAIC

Huidige oefening

Exercise 7: Voorspellingen maken Exercise 8: Steekproeven uit predictieve dichtheid Exercise 9: Testfout inschatten Exercise 10: Wat kost een avocado?Exercise 11: Het model fitten Exercise 12: Het model inspecteren Exercise 13: De prijs optimaliseren Exercise 14: Tot slot