Exercise

# Posterior point estimates

Recall the likelihood of the Bayesian regression model of weight \(Y\) by height \(X\): \(Y \sim N(m, s^2)\) where \(m = a + b X\). A 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:

```
> head(weight_chains, 2)
a b s iter
1 -113.9029 1.072505 8.772007 1
2 -115.0644 1.077914 8.986393 2
```

The posterior *means* of the intercept & slope parameters, \(a\) & \(b\), reflect the posterior mean *trend* in the relationship between weight & height. In contrast, the *full* posteriors of \(a\) & \(b\) reflect the *range* of plausible parameters, thus posterior uncertainty in the trend. You will examine the trend and uncertainty in this trend below. The `bdims`

data are in your workspace.

Instructions

**100 XP**

- Obtain
`summary()`

statistics of the`weight_sim_big`

chains. - The posterior mean of \(b\) is reported in Table 1 of the
`summary()`

. Use the raw`weight_chains`

to verify this calculation. - Construct a scatterplot of the
`wgt`

vs`hgt`

data in`bdims`

. Use`geom_abline()`

to superimpose the*posterior mean trend*. - Construct another scatterplot of
`wgt`

vs`hgt`

. Superimpose the 20 regression lines defined by the first 20 sets of \(a\) & \(b\) parameter values in`weight_chains`

.