Updating by Bayes' rule

Suppose Madison constructs a prior for proportion of female college students who believe they are overweight, where the possible values are contained in P and the respective probabilities in Prior:

P <- c(0.5, 0.6, 0.7, 0.8, 0.9)
Prior <- c(0.3, 0.3, 0.2, 0.1, 0.1)

Imagine that a sample of n = 20 female students is selected and y = 16 of these students consider themselves to be overweight. The likelihood of 16 so-called "successes" in a sample of size 20 is given by the binomial density function:

dbinom(16, size = 20, prob = P)

where P is the binomial probability of success.

Now you can compute Madison's posterior probabilities for the unknown proportion P!

The vector of proportions P and the vector of probabilities Prior are both available in your workspace.

Remember: you can use the bayesian_crank() function to implement Bayes' rule!

This exercise is part of the course

Beginning Bayes in R

Exercise instructions

Use the dbinom() function to compute the vector of likelihoods. Store the result in Likelihood.
Create a Bayesian data frame called bayes_df with variables P, Prior, and Likelihood.
Use the bayesian_crank() function to compute the posterior probabilities. Save the result in bayes_df and print it to the console.
Pass bayes_df to the prior_post_plot() function to graph the prior and posterior probabilities contained in bayes_df.

Hands-on interactive exercise

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

# Define the values of the proportion: P
P <- c(0.5, 0.6, 0.7, 0.8, 0.9)

# Define Madison's prior: Prior
Prior <- c(0.3, 0.3, 0.2, 0.1, 0.1)

# Compute the likelihoods: Likelihood


# Create Bayes data frame: bayes_df


# Compute and print the posterior probabilities: bayes_df


# Graphically compare the prior and posterior

Edit and Run Code

This exercise is part of the course

Beginning Bayes in R

BeginnerSkill Level

0.0+

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

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Exercise 1: Bayes with discrete models Exercise 2: Constructing a discrete prior Exercise 3: Updating by Bayes' rule

Current Exercise

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?

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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

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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