We propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space, each distribution being known up to a normalizing constant. These probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential Monte Carlo methods. This methodology allows us to derive simple algorithms to make parallel Markov chain Monte Carlo algorithms interact to perform global optimization and sequential Bayesian estimation and to compute ratios of normalizing constants. We illustrate these algorithms for various integration tasks arising in the context of Bayesian inference. Copyright 2006 Royal Statistical Society.

Approximate Bayesian computation (ABC) is a popular approach to address inference problems where the likelihood function is intractable, or expensive to calculate. To improve over Markov chain Monte Carlo (MCMC) implementations of ABC, the use of sequential Monte Carlo (SMC) methods has recently been suggested. Effective SMC algorithms that are currently available for ABC have a computational complexity that is quadratic in the number of Monte Carlo samples [4,17,19,21] and require the careful choice of simulation parameters. In this article an adaptive SMC algorithm is proposed which admits a computational complexity that is linear in the number of samples and determines on-the-fly the simulation parameters. We demonstrate our algorithm on a toy example and a population genetics example.

Members of the Dickkopf (Dkk) family of secreted proteins are potent inhibitors of Wnt/beta-catenin signaling. In this study we show that Dkk1, -2, and -3 are expressed distally in the epithelium, while Kremen1, the needed co-receptor, is expressed throughout the epithelium of the developing lung. Using TOPGAL mice [DasGupta, R., Fuchs, E., 1999. Multiple roles for activated LEF/TCF transcription complexes during hair follicle development and differentiation. Development 126, 4557-4568] to monitor the Wnt pathway, we show that canonical Wnt signaling is dynamic in the developing lung and is active throughout the epithelium and in the proximal smooth muscle cells (SMC) until E12.5. However, from E13.5 onwards, TOPGAL activity is absent in the SMC and is markedly reduced in the distal epithelium coinciding with the onset of Dkk-1 expression in the distal epithelium. To determine the role of Wnt signaling in early lung development, E11.5 organ cultures were treated with recombinant DKK1. Treated lungs display impaired branching, characterized by failed cleft formation and enlarged terminal buds, and show decreased alpha-smooth muscle actin (alpha-SMA) expression as well as defects in the formation of the pulmonary vasculature. These defects coincide with a pattern of decreased fibronectin (FN) deposition. DKK1-induced morphogenetic defects can be mimicked by inhibition of FN and overcome by addition of exogenous FN, suggesting an involvement of FN in Wnt-regulated morphogenetic processes.

International audienceThis paper discusses a novel strategy for simulating rare events and an associated Monte Carlo estimation of tail probabilities. Our method uses a system of interacting particles and exploits a Feynman-Kac representation of that system to analyze their fluctuations. Our precise analysis of the variance of a standard multilevel splitting algorithm reveals an opportunity for improvement. This leads to a novel method that relies on adaptive levels and produces, in the limit of an idealized version of the algorithm, estimates with optimal variance. The motivation for this theoretical work comes from problems occurring in watermarking and fin- gerprinting of digital contents, which represents a new field of applications of rare event simulation techniques. Some numerical results show performance close to the idealized version of our technique for these practical applications

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The key role played by Fgf10 during early lung development is clearly illustrated in Fgf10 knockout mice, which exhibit lung agenesis. However, Fgf10 is continuously expressed throughout lung development suggesting extended as well as additional roles for FGF10 at later stages of lung organogenesis. We previously reported that the enhancer trap Mlcv1v-nLacZ-24 transgenic mouse strain functions as a reporter for Fgf10 expression and displays decreased endogenous Fgf10 expression. In this paper, we have generated an allelic series to determine the impact of Fgf10 dosage on lung development. We report that 80% of the newborn Fgf10 hypomorphic mice die within 24 h of birth due to respiratory failure. These mutant mouse lungs display severe hypoplasia, dilation of the distal airways and large hemorrhagic areas. Epithelial differentiation and proliferation studies indicate a specific decrease in TTF1 and SP-B expressing cells correlating with reduced epithelial cell proliferation and associated with a decrease in activation of the canonical Wnt signaling in the epithelium. Analysis of vascular development shows a reduction in PECAM expression at E14.5, which is associated with a simplification of the vascular tree at E18.5. We also show a decrease in alpha-SMA expression in the respiratory airway suggesting defective smooth muscle cell formation. At the molecular level, these defects are associated with decrease in Vegfa and Pdgfa expression likely resulting from the decrease of the epithelial/mesenchymal ratio in the Fgf10 hypomorphic lungs. Thus, our results indicate that FGF10 plays a pivotal role in maintaining epithelial progenitor cell proliferation as well as coordinating alveolar smooth muscle cell formation and vascular development.

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