Simula la posteriore beta

Nei prossimi esercizi userai la funzione simulate_beta_posterior() che hai visto definita nell'ultimo video. In questo esercizio, prenderai confidenza con ciò che fa la funzione eseguendo tu stesso i calcoli che effettua.

Ti viene fornito un elenco di dieci lanci di moneta, chiamato tosses, in cui 1 indica testa, 0 croce, e definiamo testa come "successo". Per simulare la probabilità a posteriori di ottenere testa, userai una prior beta. Ricorda che se la prior è \(Beta(a, b)\), allora la posteriore è \(Beta(x, y)\), con:

\(x = \text{NumberOfHeads} + a\)

\(y = \text{NumberOfTosses} - \text{NumberOfHeads} + b\)

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Analisi dei dati bayesiana in Python

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# Set prior parameters and calculate number of successes
beta_prior_a = ____
beta_prior_b = ____
num_successes = np.sum(____)

# Generate 10000 posterior draws
posterior_draws = np.random.beta(
  ____ + ____, 
  ____ - ____ + ____, 
  10000)  

# Plot density of posterior_draws
sns.kdeplot(posterior_draws, shade=True)
plt.show()

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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: Test A/B Exercise 2: Simula la posteriore beta

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Exercise 3: Tassi di click posteriori Exercise 4: A o B, e quanto ne siamo sicuri?Exercise 5: Quanto può andar male?Exercise 6: Analisi decisionale Exercise 7: Analisi decisionale: costo Exercise 8: Analisi decisionale: profitto Exercise 9: Regressione e forecasting Exercise 10: Definire un modello di regressione bayesiana Exercise 11: Analisi dei parametri della regressione Exercise 12: Distribuzione predittiva

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