Scegliere la prior giusta

Continui a lavorare al compito di stimare l'efficacia del nuovo farmaco, ma con il piccolo campione di dati a disposizione sai che c'è molta incertezza nella tua stima. Per fortuna, un paio di paesi vicini sono riusciti a condurre esperimenti più estesi e hanno appena pubblicato i loro risultati. Puoi usarli come prior nella tua analisi!

Dopo aver passato in rassegna tutte le pubblicazioni, concludi che i tassi di efficacia riportati sono per lo più tra il 70% e il 90%. Sono stati registrati anche un paio di risultati sotto il 50%, ma non molti.

Quale delle seguenti distribuzioni rappresenta meglio queste informazioni a priori?

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Analisi dei dati bayesiana in Python

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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: Sotto il cofano bayesiano Exercise 2: Verso l’approssimazione a griglia Exercise 3: Approssimazione a griglia senza conoscenze pregresse Exercise 4: Aggiornare la credenza a posteriori Exercise 5: Convinzione a priori Exercise 6: La verità del prior Exercise 7: Scegliere la prior giusta

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Exercise 8: Simulare campioni a posteriori Exercise 9: Presentare i risultati bayesiani Exercise 10: Stime puntuali Exercise 11: Intervalli credibili di massima densità a posteriori Exercise 12: Il significato di credibilità

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