Posterior credible intervals
Let's focus on slope parameter \(b\), the rate of change in weight over height. The posterior mean of \(b\) reflects the trend in the posterior model of the slope. In contrast, a posterior credible interval provides a range of posterior plausible slope values, thus reflects posterior uncertainty about \(b\). For example, the 95% credible interval for \(b\) ranges from the 2.5th to the 97.5th quantile of the \(b\) posterior. Thus there's a 95% (posterior) chance that \(b\) is in this range.
You will use RJAGS simulation output to approximate credible intervals for \(b\). The 100,000 iteration RJAGS simulation of the posterior, weight_sim_big, is in your workspace along with a data frame of the Markov chain output, weight_chains.
This is a part of the course
“Bayesian Modeling with RJAGS”
Exercise instructions
- Obtain
summary()statistics of theweight_sim_bigchains. - The
2.5%and97.5%posterior quantiles for \(b\) are reported in Table 2 of thesummary(). Applyquantile()to the rawweight_chainsto verify these calculations. Save this asci_95and print it. - Similarly, use the
weight_chainsdata to construct a 90% credible interval for \(b\). Save this asci_90and print it. - Construct a density plot of the \(b\) Markov chain values. Superimpose vertical lines representing the 90% credible interval for \(b\) using
geom_vline()withxintercept = ci_90.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Summarize the posterior Markov chains
# Calculate the 95% posterior credible interval for b
ci_95 <- quantile(___, probs = c(___, ___))
ci_95
# Calculate the 90% posterior credible interval for b
ci_90 <- ___
ci_90
# Mark the 90% credible interval
ggplot(___, aes(x = ___)) +
geom_density() +
geom_vline(xintercept = ___, color = "red")This exercise is part of the course
Bayesian Modeling with RJAGS
In this course, you'll learn how to implement more advanced Bayesian models using RJAGS.
In this chapter, you will extend the Normal-Normal model to a simple Bayesian regression model. Within this context, you will explore how to use rjags simulation output to conduct posterior inference. Specifically, you will construct posterior estimates of regression parameters using posterior means & credible intervals, you will test hypotheses using posterior probabilities, and you will construct posterior predictive distributions for new observations.
Exercise 1: A simple Bayesian regression modelExercise 2: Regression priorsExercise 3: Visualizing the regression priorsExercise 4: Weight & height dataExercise 5: Bayesian regression in RJAGSExercise 6: Define, compile, & simulate the regression modelExercise 7: Regression Markov chainsExercise 8: Posterior estimation & inferenceExercise 9: Posterior point estimatesExercise 10: Posterior credible intervalsExercise 11: Posterior probabilitiesExercise 12: Posterior predictionExercise 13: Inference for the posterior trendExercise 14: Calculating posterior predictionsExercise 15: Posterior predictive distributionWhat is DataCamp?
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