Response to McCue’s Reply to Lewis’s Comment on “The Statistical Foundations of the EI Method”
نویسنده
چکیده
In his reply to my comment, McCue repeats the same error he made in his original paper. To quickly restate the central issue, let β and β be distributed truncated normal on the unit square and let T = βX + β(1−X) for a some constant X ∈ (0, 1). The question is: what is the distribution of β given T? King (1997) claims that β|T is univariate truncated normal on the interval (max(0, (T +X − 1)/X),min(1, T/X)). McCue’s paper disputes this claim. My comment shows that King’s assertion is correct. McCue’s reply to my comment rebuts my proof and reasserts McCue’s original objection to King’s claim about β|T . My proof presented in a comment in the TAS directly derived the joint distribution of β and T and then derived the conditional distribution of β|T from that joint distribution. In what follows, I show why McCue’s objection to my proof is groundless. However, before working through the algebra, consider a few Monte Carlo simulations that demonstrate my contention. The point of departure for these Monte Carlo experiments is the joint distribution of T and β. Monte Carlo techniques for drawing conditional distributions directly from joint distributions are well-known and widely employed in the simulation literature. McCue does not contest my derivation of the joint distribution of β and T and, therefore, he should not object to sampling β|T directly from this joint distribution. Figure 1 shows histograms
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