Many points of contact between statistics and the philosophy of science are reviewed. Some of the topics mentioned are kinds of probability, weight of evidence (corroboration), tail probabilities ($p$-values), Bayes/non-Bayes compromises, "explicativity," induction and probabilistic causality.

Piecewise polynomials or splines extend the advantages of polynomials to include greater flexibility, local effects of parameter changes and the possibility of imposing useful constraints on estimated functions. Among these constraints is monotonicity, which can be an important property in many curve estimation problems. This paper shows the virtues of monotone splines through a number of statistical applications, including response variable transformation in nonlinear regression, transformation of variables in multiple regression, principal components and canonical correlation, and the use of monotone splines to model a dose-response function and to perform item analysis. Computational and inferential issues are discussed and illustrated.

This article outlines existing knowledge on optimal designs for comparing test treatments with controls under 0-, 1- and 2-way elimination of heterogeneity models. The results are motivated through numerical examples.