Mensimulasikan pengambilan sampel posterior

Anda baru saja memutuskan untuk menggunakan prior Beta(5, 2) untuk laju efektivitas. Anda juga menggunakan distribusi binomial untuk memodelkan data (menyembuhkan pasien sakit adalah "sukses", ingat?). Karena distribusi beta merupakan prior konjugat untuk likelihood binomial, Anda dapat langsung mensimulasikan posterior!

Anda tahu bahwa jika prior adalah \(Beta(a, b)\), maka posterior adalah \(Beta(x, y)\), dengan:

\(x = NumberOfSuccesses + a\),

\(y = NumberOfObservations - NumberOfSuccesses + b\).

Dapatkah Anda mensimulasikan distribusi posterior? Ingat bahwa secara keseluruhan Anda memiliki data 22 pasien, 19 di antaranya telah sembuh. numpy dan seaborn telah diimpor untuk Anda sebagai np dan sns masing-masing.

Latihan ini adalah bagian dari kursus

Analisis Data Bayesian dengan Python

Petunjuk latihan

Tetapkan jumlah pasien yang diobati dan yang sembuh ke num_patients_treated dan num_patients_cured.
Gunakan fungsi numpy yang sesuai untuk mengambil sampel dari distribusi posterior dan tetapkan hasilnya ke posterior_draws.
Plot distribusi posterior menggunakan fungsi seaborn yang sesuai.

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

# Define the number of patients treated and cured
num_patients_treated = ____
num_patients_cured = ____

# Simulate 10000 draws from the posterior distribuition
posterior_draws = ____(____ + ____, ____ - ____ + ____, 10000)

# Plot the posterior distribution
____(____, shade=True)
plt.show()

Edit dan Jalankan Kode

Latihan ini adalah bagian dari kursus

Analisis Data Bayesian dengan Python

SkillTag.level.intermediateSkillTag.label

4.8+

Mulai Kursus Gratis

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: Membongkar dapur Bayesian Exercise 2: Menuju pendekatan grid Exercise 3: Pendekatan grid tanpa pengetahuan awal Exercise 4: Memperbarui keyakinan posterior Exercise 5: Kepercayaan awal Exercise 6: Kebenaran tentang prior Exercise 7: Memilih prior yang tepat Exercise 8: Mensimulasikan pengambilan sampel posterior

Latihan Saat Ini

Exercise 9: Melaporkan hasil Bayesian Exercise 10: Estimasi titik Exercise 11: Interval kredibel Highest Posterior Density Exercise 12: Makna kredibilitas

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