Confrontare i modelli con WAIC

Ora che hai costruito con successo il primo modello di base, dai un’altra occhiata ai dati a tua disposizione. Noti una variabile chiamata wind_speed. Potrebbe essere un ottimo predittore del numero di biciclette noleggiate! Pedalare controvento non è proprio divertente, vero?

Adatti un altro modello con questo predittore aggiuntivo:

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)

Il tuo nuovo model_2 è migliore di model_1, quello senza la velocità del vento? Confronta i due modelli usando il Widely Applicable Information Criterion, o WAIC, per scoprirlo!

Sia trace_1 che trace_2 sono disponibili nel tuo workspace e pycm3 è stato importato come pm.

Questo esercizio fa parte del corso

Analisi dei dati bayesiana in Python

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# Gather trace_1 and trace_2 into a dictionary
traces_dict = ____

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Questo esercizio fa parte del corso

Analisi dei dati bayesiana 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: Markov Chain Monte Carlo e stima del modello Exercise 2: Markov Chain Monte Carlo Exercise 3: Campionare dal posterior Exercise 4: Interpretare i risultati e confrontare i modelli Exercise 5: Ispezionare i campioni posteriori Exercise 6: Confrontare i modelli con WAIC

Esercizio in corso

Exercise 7: Fare previsioni Exercise 8: Campiona dalla densità predittiva Exercise 9: Stima dell'errore sul test Exercise 10: Quanto costa un avocado?Exercise 11: Adattare il modello Exercise 12: Ispezionare il modello Exercise 13: Ottimizzare il prezzo Exercise 14: Considerazioni finali