The posterior

In our spinner example, Prior contains the prior probabilities (1/2, 1/2) and Likelihood contains the likelihoods (1/2, 1/6) since the result of the spin was blue (3).

To compute the product and posterior probabilities, you can use the bayesian_crank() function, which takes as input a data frame containing Model, Prior and Likelihood.

This exercise is part of the course

Beginning Bayes in R

Exercise instructions

The vector of models, Model, is available in your workspace.

Create the two vectors Prior and Likelihood using the values provided above.
Construct a data frame called bayes_df containing variables Model, Prior, and Likelihood, in that order.
Use the bayesian_crank() function to compute the posterior probabilities of Spinner A and Spinner B.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Create the vector of models: Model
Model <- c("Spinner A", "Spinner B")

# Define the vector of prior probabilities: Prior
Prior <- ___

# Define the vector of likelihoods: Likelihood
Likelihood <- ___

# Make a data frame with variables Model, Prior, Likelihood: bayes_df


# Compute the posterior probabilities

Edit and Run Code

This exercise is part of the course

Beginning Bayes in R

BeginnerSkill Level

0.0+

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This chapter introduces the idea of discrete probability models and Bayesian learning. You'll express your opinion about plausible models by defining a prior probability distribution, you'll observe new information, and then, you'll update your opinion about the models by applying Bayes' theorem.

Exercise 1: Discrete probability distributions Exercise 2: Most likely spin?Exercise 3: Chance of spinning an even number?Exercise 4: Constructing a spinner Exercise 5: Simulating spinner data Exercise 6: Bayes' rule Exercise 7: The prior Exercise 8: The likelihoods Exercise 9: The posterior

Current Exercise

Exercise 10: Interpreting the posterior Exercise 11: Sequential Bayes Exercise 12: Bayes with another spin

This chapter describes learning about a population proportion using discrete and continuous models. You'll use a beta curve to represent prior opinion about the proportion, take a sample and observe the number of successes and failures, and construct a beta posterior curve that combines both the information in the prior and in the sample. You'll then use the beta posterior curve to draw inferences about the population proportion.

Exercise 1: Bayes with discrete models Exercise 2: Constructing a discrete prior Exercise 3: Updating by Bayes' rule Exercise 4: Continuous prior Exercise 5: Working with a beta curve Exercise 6: Constructing a beta prior Exercise 7: Updating the beta prior Exercise 8: Bayesian updating Exercise 9: Testing a claim Exercise 10: Bayesian inference Exercise 11: Interval estimates Exercise 12: Compare with classical methods Exercise 13: Bayesian probability interval Exercise 14: Posterior simulation Exercise 15: Simulating from a beta curve Exercise 16: Why simulate?

This chapter introduces Bayesian learning about a population mean. You'll sample from a normal population with an unknown mean and a known standard deviation, construct a normal prior to reflect your opinion about the location of the mean before sampling, and see that the posterior distribution also has a normal form with updated values of the mean and standard deviation. You'll also get more practice drawing inferences from the posterior distribution, only this time, about a population mean.

Exercise 1: Normal sampling model Exercise 2: Reaction times Exercise 3: Updating by Bayes' rule Exercise 4: Bayes with a continuous prior Exercise 5: A continuous prior Exercise 6: Comparing normal priors Exercise 7: Updating the normal prior Exercise 8: The normal posterior Exercise 9: Compare with classical interval Exercise 10: Is Jim slow?Exercise 11: Simulation Exercise 12: Posterior simulation Exercise 13: Predictive simulation Exercise 14: Prediction vs. inference

Suppose you're interested in comparing proportions from two populations. You take a random sample from each population and you want to learn about the difference in proportions. This chapter will illustrate the use of discrete and continuous priors to do this kind of inference. You'll use a Bayesian regression approach to learn about a mean or the difference in means when the sampling standard deviation is unknown.

Exercise 1: Comparing two proportions Exercise 2: A discrete prior Exercise 3: Discrete posterior Exercise 4: Proportions with continuous priors Exercise 5: Independent beta priors Exercise 6: Posterior of proportions Exercise 7: Comparison of proportions Exercise 8: Normal model inference Exercise 9: Uniform prior Exercise 10: Learning about a percentile Exercise 11: Bayesian regression Exercise 12: Two group model Exercise 13: Standardized effect inference Exercise 14: Wrap-up and review