(Auxiliary Functions and Moments). For a random variable X, the characteristic function E(eitX) always exists since eitX is a bounded random variable (with complex values).…
(A Box Calculus Verification). The purpose of this exercise is to generalize and unify the calculations we made for functions of Brownian motion with…
Apply Student t regression (Section 5.7) to the stack loss data in Example 4.4, with degrees of freedom ν an unknown. Lange et al.…
In Example 6.1 use a likelihood calculation and derive the posterior mean of the likelihood and deviance. Use the AIC and BIC criteria to…
In Example 7.5 (attitudes to working mothers) compare inferences from the residuals Wi − Xiβ with those based on Monte Carlo estimates of the conditional…
In Example 11.6 (Indonesian rice farm data) assess gain from introducing AR1 errors (in addition to unstructured errors) in both random and fixed effects…
In Example 13.2 compare a 5-point discrete mixture on the log-logistic shape parameter with the variable scale model to downweight aberrant cases, namely ui ∼…
Suppose a binary response has true prevalence Pr(Y = 1) = π but that observed responses are subject to misclassification with probabilities α0 = Pr(y…
Project: Section 1.3 focuses on using unlabeled, unrooted trees to model RNA secondary structure. However, rooted and/or labeled trees can also be used to…
Project: We also define here a biologically motivated statistic called the pseudoknot number pknot(M). A pseudoknot occurs in a strand of RNA when the…
