Sufficient burn-in for Gibbs samplers for a hierarchical random effects model

We consider Gibbs and block Gibbs samplers for a Bayesian hierarchical version of the one-way random effects model. Drift and minorization conditions are established for the underlying Markov chains. The drift and minorization are used in conjunction with results from J. S. Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558-566] and G. O. Roberts and R. L. Tweedie [Stochastic Process. Appl. 80 (1999) 211-229] to construct analytical upper bounds on the distance to stationarity. These lead to upper bounds on the amount of burn-in that is required to get the chain within a prespecified (total variation) distance of the stationary distribution. The results are illustrated with a numerical example

Counting lifts of Brauer characters

In this paper we examine the behavior of lifts of Brauer characters in p-solvable groups where p is an odd prime. In the main result, we show that if \phi \in IBrp(G) is a Brauer character of a solvable group such that \phi has an abelian vertex subgroup Q, then the number of lifts of \phi in Irr(G) is at most |Q|. In order to accomplish this, we develop several results about lifts of Brauer characters in p-solvable groups that were previously only known to be true in the case of groups of odd order.Comment: A different proof of Theorem 1 is in the paper "The number of lifts of Brauer characters with a normal vertex" by J.P. Cossey, M.L.Lewis, and G. Navarro. Hence, we do not expect to try to publish this note. We feel that the proof in this paper is of independent interes

Lifts and vertex pairs in solvable groups

Suppose $G$ is a $p$-solvable group, where $p$ is odd. We explore the connection between lifts of Brauer characters of $G$ and certain local objects in $G$, called vertex pairs. We show that if $\chi$ is a lift, then the vertex pairs of $\chi$ form a single conjugacy class. We use this to prove a sufficient condition for a given pair to be a vertex pair of a lift and to study the behavior of lifts with respect to normal subgroups

The interannual variability of polar cap recessions as a measure of Martian climate and weather: Using Earth-based data to augment the time line for the Mars observer mapping mission

The recessions of the polar ice caps are the most visible and most studied indication of seasonal change on Mars. Circumstantial evidence links these recessions to the seasonal cycles of CO2, water, and dust. The possible advent of a planet encircling storm during the Mars Observer (MO) mission will provide a detailed correlation with a cap recession for that one Martian year. That cap recession will then be compared with other storm and nonstorm years. MO data will also provide a stronger link between cap recessions and the water and CO2 cycles. Cap recession variability might also be used to determine the variability of these cycles. After nearly a century of valiant attempts at measuring polar cap recessions, including Mariner 9 and Viking data, MO will provide the first comprehensive dataset. In contrast to MO, the older data are much less detailed and precise and could be forgotten, except that it will still be the only information on interannual variability. By obtaining simultaneous Earth-based observations (including those from Hubble) during the MO mission, direct comparisons can be made between the datasets

The great dust storm of 1986

It is reported that on the global scale, no major dust storm activity was seen during telescopic observations of Mars during the several months or so preceeding this conference. However, the corresponding season on Mars was early fall, which is at the beginning of the dust storm season. It was too early to tell, therefore, if a great dust storm was going to occur that year. Current observations and what they show about present atmospheric conditions and the recession of the South Polar Cap is discussed

(2360) Proposal to reject the name Chenopodium caudatum (Amaranthaceae / Chenopodiaceae)

nomenclature Chenopodium caudatu