Packing and Hausdorff measures of stable trees

In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of L\'evy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991) which corresponds to the Brownian case. We provide results for the whole stable trees and for their level sets that are the sets of points situated at a given distance from the root. We first show that there is no exact packing measure for levels sets. We also prove that non-Brownian stable trees and their level sets have no exact Hausdorff measure with regularly varying gauge function, which continues previous results from a joint work with J-F Le Gall (2006).Comment: 40 page

A frequentist framework of inductive reasoning

Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly from limiting relative frequencies rather than computed according to the Bayes update rule. The proposal is developed as follows using the confidence measure of a scalar parameter of interest. (With the restriction to one-dimensional parameter space, a confidence measure is essentially a fiducial probability distribution free of complications involving ancillary statistics.) A betting game establishes a sense in which confidence measures are the only reliable inferential probability distributions. The equality between the probabilities encoded in a confidence measure and the coverage rates of the corresponding confidence intervals ensures that the measure's rule for assigning confidence levels to hypotheses is uniquely minimax in the game. Although a confidence measure can be computed without any prior distribution, previous knowledge can be incorporated into confidence-based reasoning. To adjust a p-value or confidence interval for prior information, the confidence measure from the observed data can be combined with one or more independent confidence measures representing previous agent opinion. (The former confidence measure may correspond to a posterior distribution with frequentist matching of coverage probabilities.) The representation of subjective knowledge in terms of confidence measures rather than prior probability distributions preserves approximate frequentist validity.Comment: major revisio

Identification of tumour-associated and germ line p53 mutations in canine mammary cancer

Mutations of the tumour suppressor p53 gene are found in a number of spontaneous canine cancers and may contribute to increased cytogenetic alterations and tumour formation. Using reverse transcription and DNA amplification, we isolated p53 cDNA from normal and tumour tissue of ten canine mammary cancer patients. DNA sequencing identified p53 mutations in three of the ten patients. These included tumour-associated p53 gene mutations within exons 2 and 5 and a germ line deletion of exons 3 to 7. These results support a role for p53 inactivation in canine mammary tumour formation and breed predisposition to cancer. Such information could prove invaluable in the successful outbreeding of inherited predisposition to cancer in the dog. A putative polymorphism was also identified at codon 69 in exon 4 and we discuss the possibility that similar polymorphisms may be associated with human breast cancer. © 1999 Cancer Research Campaig

Adaptive monte carlo maximum likelihood

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We examine asymptotics of adaptive importance sampling and a new algorithm, which uses resampling and MCMC. This algorithm is designed to reduce problems with degeneracy of importance weights. Our analysis is based on martingale limit theorems. We also describe how adaptive maximization algorithms of Newton-Raphson type can be combined with the resampling techniques. The paper includes results of a small scale simulation study in which we compare the performance of adaptive and non-adaptive Monte Carlo maximum likelihood algorithms

Partial quantile regression

Bilinear factor model, Longley data, Partial least squares, Quantile regression, Spectrometer data, Variance heterogeneity,