Più lanci, più impari

Immagina di essere frequentista (solo per un giorno) e che ti sia stato chiesto di stimare la probabilità di ottenere testa con una moneta (eventualmente truccata), ma senza osservare alcun lancio. Cosa diresti? È impossibile, non ci sono dati! Poi, ti è permesso lanciare la moneta una volta. Esce croce. Cosa dici ora? Beh, se questi sono tutti i tuoi dati, diresti che la probabilità di testa è 0%.

Probabilmente senti, nel profondo, che queste risposte non sono le migliori. Ma cosa sarebbe meglio? Cosa direbbe un bayesiano? Scopriamolo! numpy e seaborn sono già stati importati come np e sns.

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Analisi dei dati bayesiana 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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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: Chi è Bayes? Che cos'è Bayes?Exercise 2: Bayesiani vs. Frequentisti Exercise 3: Distribuzioni di probabilità Exercise 4: Probabilità e teorema di Bayes Exercise 5: Giochiamo a carte Exercise 6: Filtro antispam bayesiano Exercise 7: Cosa dice il test?Exercise 8: Assaporando Bayes Exercise 9: Lanciare una moneta Exercise 10: Più lanci, più impari

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Exercise 11: Ehi, questa moneta è equa?

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