Sequential Bayesian inference for implicit hidden Markov models and current limitations

Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to estimate the hidden Markov process given the observations and a fixed parameter value. We review some of the recent developments allowing the inclusion of parameter uncertainty as well as model uncertainty. The shortcomings of the currently available methodology are emphasised from an algorithmic complexity perspective. The statistical objects of interest for time series analysis are illustrated on a toy "Lotka-Volterra" model used in population ecology. Some open challenges are discussed regarding the scalability of the reviewed methodology to longer time series, higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages, 10 figure

Variance asymptotics and scaling limits for Gaussian Polytopes

Let $K_n$ be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on $\R^d$. We establish variance asymptotics as $n \to \infty$ for the re-scaled intrinsic volumes and $k$-face functionals of $K_n$, $k \in \{0,1,...,d-1\}$, resolving an open problem. Variance asymptotics are given in terms of functionals of germ-grain models having parabolic grains with apices at a Poisson point process on $\R^{d-1} \times \R$ with intensity $e^h dh dv$. The scaling limit of the boundary of $K_n$ as $n \to \infty$ converges to a festoon of parabolic surfaces, coinciding with that featuring in the geometric construction of the zero viscosity solution to Burgers' equation with random input

Variance Asymptotics and Scaling Limits for Random Polytopes

Let K be a convex set in R d and let K $\lambda$ be the convex hull of a homogeneous Poisson point process P $\lambda$ of intensity $\lambda$ on K. When K is a simple polytope, we establish scaling limits as $\lambda$ $\rightarrow$ $\infty$ for the boundary of K $\lambda$ in a vicinity of a vertex of K and we give variance asymptotics for the volume and k-face functional of K $\lambda$, k $\in$ {0, 1, ..., d -- 1}, resolving an open question posed in [18]. The scaling limit of the boundary of K $\lambda$ and the variance asymptotics are described in terms of a germ-grain model consisting of cone-like grains pinned to the extreme points of a Poisson point process on R d--1 $\times$ R having intensity \sqrt de dh dhdv

Point: From animal models to prevention of colon cancer. Systematic review of chemoprevention in min mice and choice of the model system.

The Apc(Min/+) mouse model and the azoxymethane (AOM) rat model are the main animal models used to study the effect of dietary agents on colorectal cancer. We reviewed recently the potency of chemopreventive agents in the AOM rat model (D. E. Corpet and S. Tache, Nutr. Cancer, 43: 1-21, 2002). Here we add the results of a systematic review of the effect of dietary and chemopreventive agents on the tumor yield in Min mice. The review is based on the results of 179 studies from 71 articles and is displayed also on the internet http://corpet.net/min.(2) We compared the efficacy of agents in the Min mouse model and the AOM rat model, and found that they were correlated (r = 0.66; P < 0.001), although some agents that afford strong protection in the AOM rat and the Min mouse small bowel increase the tumor yield in the large bowel of mutant mice. The agents included piroxicam, sulindac, celecoxib, difluoromethylornithine, and polyethylene glycol. The reason for this discrepancy is not known. We also compare the results of rodent studies with those of clinical intervention studies of polyp recurrence. We found that the effect of most of the agents tested was consistent across the animal and clinical models. Our point is thus: rodent models can provide guidance in the selection of prevention approaches to human colon cancer, in particular they suggest that polyethylene glycol, hesperidin, protease inhibitor, sphingomyelin, physical exercise, epidermal growth factor receptor kinase inhibitor, (+)-catechin, resveratrol, fish oil, curcumin, caffeate, and thiosulfonate are likely important preventive agents

Custom transistor layout design techniques for random telegraph signal noise reduction in CMOS image sensors

Interface and near oxide traps in small gate area MOS transistors (gate area ,1 mm2) lead to RTS noise which implies the emergence of noisy pixels in CMOS image sensors. To reduce this noise, two simple and efficient layout techniques of custom transistors have been imagined. These techniques have been successfully implemented in an image sensor test chip fabricated in a 0.35 mm CMOS image sensor process. Experimental results demonstrate a significant reduction of the noisy pixels for the two different techniques