Comment: Bayesian Checking of the Second Levels of Hierarchical Models

Comment: Bayesian Checking of the Second Levels of Hierarchical Models [arXiv:0802.0743]Comment: Published in at http://dx.doi.org/10.1214/07-STS235D the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Evolution and complexity: the double-edged sword

We attempt to provide a comprehensive answer to the question of whether, and when, an arrow of complexity emerges in Darwinian evolution. We note that this expression can be interpreted in different ways, including a passive, incidental growth, or a pervasive bias towards complexification. We argue at length that an arrow of complexity does indeed occur in evolution, which can be most reasonably interpreted as the result of a passive trend rather than a driven one. What, then, is the role of evolution in the creation of this trend, and under which conditions will it emerge? In the later sections of this article we point out that when certain proper conditions (which we attempt to formulate in a concise form) are met, Darwinian evolution predictably creates a sustained trend of increase in maximum complexity (that is, an arrow of complexity) that would not be possible without it; but if they are not, evolution will not only fail to produce an arrow of complexity, but may actually prevent any increase in complexity altogether. We conclude that, with regard to the growth of complexity, evolution is very much a double-edged sword

Bayes Factors Based on Test Statistics

Traditionally, the use of Bayes factors has required the specification of proper prior distributions on model parameters implicit to both null and alternative hypotheses. In this paper, I describe an approach to defining Bayes factors based on modeling test statistics. Because the distributions of test statistics do not depend on unknown model parameters, this approach eliminates the subjectivity normally associated with the definition of Bayes factors. For standard test statistics, including the _2, F, t and z statistics, the values of Bayes factors that result from this approach can be simply expressed in closed form