Posterior probabilities

You've used RJAGS output to explore and quantify the posterior trend & uncertainty \(b\). You can also use RJAGS output to assess specific hypotheses. For example: What's the posterior probability that, on average, weight increases by more than 1.1 kg for every 1 cm increase in height? That is, what's the posterior probability that \(b > 1.1\)?

You will approximate this probability by the proportion of \(b\) Markov chain values that exceed 1.1. The weight_chains data frame with the 100,000 iteration Markov chain output is in your workspace.

This exercise is part of the course

Bayesian Modeling with RJAGS

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Exercise instructions

Construct a density plot of the \(b\) Markov chain values and use geom_vline() to superimpose a vertical line at 1.1.
Use table() to summarize the number of \(b\) Markov chain values that exceed 1.1.
Use mean() to calculate the proportion of \(b\) Markov chain values that exceed 1.1.

Hands-on interactive exercise

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

# Mark 1.1 on a posterior density plot for b
ggplot(___, aes(x = ___)) + 
    geom_density() + 
    geom_vline(xintercept = ___, color = "red")

# Summarize the number of b chain values that exceed 1.1


# Calculate the proportion of b chain values that exceed 1.1

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