Clarifying Relative Plausibility: A Rejoinder

Geometry of relative plausibility and belief of singletons

The study of the interplay between belief and probability has recently been posed in a geometric framework, in which belief and plausibility functions are represented as points of simplices in a Cartesian space. All Bayesian approximations of a belief function b form two homogeneous groups, which we call “affine” and “epistemic” families. In this paper, in particular, we focus on relative plaus...

Rejoinder

We thank the editor Professor David Steinberg for organizing this stimulating discussion. We are also grateful to all the discussants for their constructive comments about the method proposed in our paper (denoted as QZW hereafter). Profile monitoring is a relatively new research area; but, it has a profound application background (cf., Wang and Tsung 2005, Woodall et al. 2004). Due to the fact...

Rejoinder

Rejoinder

Regarding Jennifer’s criticism of the “independence” assumption in expression (2) of the paper, we agree that this is surely not true though it may be roughly true. However, the “correlation” calculation in (2) is a bit more complicated than it initially appears in that the calculation is with respect to a uniform distribution over say, the locations in unit i. In fact, the randomness arises fr...

Rejoinder

We would like to thank all the discussants for their contributions. Our paper attempts only a first step towards a satisfactory linkage between complexity theory and coding-based inference and these discussions will help to blaze the paths for future exploration. We also take this opportunity to remind the reader that, in our opinion, MDL and MML agree on many, many points. While we certainly d...