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Fundamentals of Bayesian Data Analysis in R

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更新日 2024/08

Learn what Bayesian data analysis is, how it works, and why it is a useful tool to have in your data science toolbox.

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RProbability & Statistics

4時間

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58 演習

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コース説明

Bayesian data analysis is an approach to statistical modeling and machine learning that is becoming more and more popular. It provides a uniform framework to build problem specific models that can be used for both statistical inference and for prediction. This course will introduce you to Bayesian data analysis: What it is, how it works, and why it is a useful tool to have in your data science toolbox.

前提条件

Introduction to R

1

What is Bayesian Data Analysis?

This chapter will introduce you to Bayesian data analysis and give you a feel for how it works.

A first taste of Bayes

Unknowns and ice creams

Let's try some Bayesian data analysis

Coin flips with prop_model

Zombie drugs with prop_model

Samples and posterior summaries

Looking at samples from prop_model

Summarizing the zombie drug experiment

You've done some Bayesian data analysis!

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2

How does Bayesian inference work?

In this chapter we will take a detailed look at the foundations of Bayesian inference.

The parts needed for Bayesian inference

Take a generative model for a spin

Take the binomial distribution for a spin

Using a generative model

How many visitors could your site get (1)?

Representing uncertainty with priors

Adding a prior to the model

Bayesian models and conditioning

Update a Bayesian model with data

How many visitors could your site get (3)?

What have we done?

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3

Why use Bayesian Data Analysis?

This chapter will show you four reasons why Bayesian data analysis is a useful tool to have in your data science tool belt.

Four good things with Bayes

Explore using the Beta distribution as a prior

Pick the prior that best captures the information

Change the model to use an informative prior

Contrasts and comparisons

Fit the model using another dataset

Calculating the posterior difference

Decision analysis

A small decision analysis 1

A small decision analysis 2

Change anything and everything

The Poisson distribution

Clicks per day instead of clicks per ad

Bayes is optimal, kind of...

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4

Bayesian inference with Bayes' theorem

Learn what Bayes theorem is all about and how to use it for statistical inference.

Probability rules

Cards and the sum rule

Cards and the product rule

Calculating likelihoods

From rbinom to dbinom

Calculating probabilities with dbinom

Bayesian calculation

Calculating a joint distribution

Conditioning on the data (again)

A conditional shortcut

Bayes' theorem

A Poisson model description

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5

More parameters, more data, and more Bayes

Learn about using the Normal distribution to analyze continuous data and try out a tool for practical Bayesian analysis in R.

The temperature in a Normal lake

rnorm, dnorm, and the weight of newborns

A Bayesian model of water temperature

A Bayesian model of Zombie IQ

Eyeballing the mean IQ of zombies?

Answering the question: Should I have a beach party?

Sampling from the zombie posterior

But how smart will the next zombie be?

A practical tool: BEST

The BEST models and zombies on a diet

BEST is robust

What have you learned? What did we miss?

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Fundamentals of Bayesian Data Analysis in R

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