*4.2. KLDCP Estimates From Simulations*

For the tables showing the KLDCP simulation results, the columns are labeled as follows.


For the tables showing the KLD results, the columns are labeled as follows.


$$\frac{1}{M} \sum\_{m=1}^{M} -2\ell(\hat{\theta}^\*(m)|y).$$

We have that *M* = 200 for Sets 1–5 and *M* = 500 for Set 6.

(3) **ΔBDb** corresponds to the difference between the estimate of *E*(BD), with each BD corrected by *kb* and the estimate of *E*(KLD) described in (1). In other words, if we let *j* ∈ {1, 2 ... , 5000} be the number of simulated data sets, ;*BDj* be the BD estimate for each data set *j*, and *kjb* be the *kb* correction for data set *j*, then

$$\Delta \text{BDb} = \frac{1}{5000} \sum\_{j=1}^{5000} \left[ \overrightarrow{BD}\_j + k\_{jb} \right] - E(KLD).$$

(4) **ΔBDk** shows the same difference described in (3), but using *k* instead of *kb*, which results in

$$\Delta \text{BDk} = \frac{1}{5000} \sum\_{j=1}^{5000} \left[ \bar{B} \overline{D}\_j + k \right] - E(\text{KLD}).$$
