Group Importance Sampling for Particle Filtering and MCMC

Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implicitly in different works in the literature. The provided analysis yields several theoretical and practical consequences. For instance, we discuss the application of GIS into the Sequential Importance Resampling framework and show that Independent Multiple Try Metropolis schemes can be interpreted as a standard Metropolis-Hastings algorithm, following the GIS approach. We also introduce two novel Markov Chain Monte Carlo (MCMC) techniques based on GIS. The first one, named Group Metropolis Sampling method, produces a Markov chain of sets of weighted samples. All these sets are then employed for obtaining a unique global estimator. The second one is the Distributed Particle Metropolis-Hastings technique, where different parallel particle filters are jointly used to drive an MCMC algorithm. Different resampled trajectories are compared and then tested with a proper acceptance probability. The novel schemes are tested in different numerical experiments such as learning the hyperparameters of Gaussian Processes, two localization problems in a wireless sensor network (with synthetic and real data) and the tracking of vegetation parameters given satellite observations, where they are compared with several benchmark Monte Carlo techniques. Three illustrative Matlab demos are also provided.Comment: To appear in Digital Signal Processing. Related Matlab demos are provided at https://github.com/lukafree/GIS.gi

Rhinoplasty. The Difficult Nasal Tip: Total Resection of the Alar Cartilages

There are many ways to reconstruct and make nasal tips more attractive. Sometimes we cannot find the best way unless we at least remove all surplus from the tip. This may occur in primary or secondary rhinoplasty. In principle, anything is possible when relocating and reconstructing. However, sometimes we face reality when we uncover the tip: broken or bulging cartilages that are difficult to put right. For this reason, in 1987 we thought of totally resectioning the alar cartilages in a case of secondary rhinoplasty with an unsightly appearance. After a year the result was seen to be correct from an aesthetic and a functional perspective and is still so today. Aesthetically, it kept its shape and did not collapse with nasal respiratory failure. We covered the end of the crus medialis with a small, temporary, one- to two-layered fascia patch. Except in exceptional cases, we now use this procedure: Total sectioning of the alar cartilages including the domes, or maintenance of them by preserving the fibroadipose tip tissue with a suture in the middle of the end of the crus medialis and by covering this with temporary fascia, which usually has two layers depending on the thickness of the skin of the tip. This procedure is indicated mainly in secondary rhinoplasty when the cartilages of the tip are completely destroyed, and in primary rhinoplasty when the tip is excessively wide and bulbous. Our philosophy is, therefore, elegance and beauty of the nasal tip with a solid and equilateral base without prejudices

Derivation of the blackfold effective theory

We study fluctuations and deformations of black branes over length scales larger than the horizon radius. We prove that the Einstein equations for the perturbed p-brane yield, as constraints, the equations of the effective blackfold theory. We solve the Einstein equations for the perturbed geometry and show that it remains regular on and outside the black brane horizon. This study provides an ab initio derivation of the blackfold effective theory and gives explicit expressions for the metrics near the new black holes and black branes that result from it, to leading order in a derivative expansion.Comment: 20 pages. v4: Typo corrected in eq. (6.11) -- erratum in the published versio

Large and small-scale structures and the dust energy balance problem in spiral galaxies

The interstellar dust content in galaxies can be traced in extinction at optical wavelengths, or in emission in the far-infrared. Several studies have found that radiative transfer models that successfully explain the optical extinction in edge-on spiral galaxies generally underestimate the observed FIR/submm fluxes by a factor of about three. In order to investigate this so-called dust energy balance problem, we use two Milky Way-like galaxies produced by high-resolution hydrodynamical simulations. We create mock optical edge-on views of these simulated galaxies (using the radiative transfer code SKIRT), and we then fit the parameters of a basic spiral galaxy model to these images (using the fitting code FitSKIRT). The basic model includes smooth axisymmetric distributions along a S\'ersic bulge and exponential disc for the stars, and a second exponential disc for the dust. We find that the dust mass recovered by the fitted models is about three times smaller than the known dust mass of the hydrodynamical input models. This factor is in agreement with previous energy balance studies of real edge-on spiral galaxies. On the other hand, fitting the same basic model to less complex input models (e.g. a smooth exponential disc with a spiral perturbation or with random clumps), does recover the dust mass of the input model almost perfectly. Thus it seems that the complex asymmetries and the inhomogeneous structure of real and hydrodynamically simulated galaxies are a lot more efficient at hiding dust than the rather contrived geometries in typical quasi-analytical models. This effect may help explain the discrepancy between the dust emission predicted by radiative transfer models and the observed emission in energy balance studies for edge-on spiral galaxies.Comment: 9 pages, 5 figures, accepted for publication in A&

Summarizing the state of the terrestrial biosphere in few dimensions

In times of global change, we must closely monitor the state of the planet in order to understand gradual or abrupt changes early on. In fact, each of the Earth's subsystems – i.e. the biosphere, atmosphere, hydrosphere, and cryosphere – can be analyzed from a multitude of data streams. However, since it is very hard to jointly interpret multiple monitoring data streams in parallel, one often aims for some summarizing indicator. Climate indices, for example, summarize the state of atmospheric circulation in a region. Although such approaches are also used in other fields of science, they are rarely used to describe land surface dynamics. Here, we propose a robust method to create indicators for the terrestrial biosphere using principal component analysis based on a high-dimensional set of relevant global data streams. The concept was tested using 12 explanatory variables representing the biophysical states of ecosystems and land-atmosphere water, energy, and carbon fluxes. We find that two indicators account for 73 % of the variance of the state of the biosphere in space and time. While the first indicator summarizes productivity patterns, the second indicator summarizes variables representing water and energy availability. Anomalies in the indicators clearly identify extreme events, such as the Amazon droughts (2005 and 2010) and the Russian heatwave (2010), they also allow us to interpret the impacts of these events. The indicators also reveal changes in the seasonal cycle, e.g. increasing seasonal amplitudes of productivity in agricultural areas and in arctic regions. We assume that this generic approach has great potential for the analysis of land-surface dynamics from observational or model data

Henchir

Le mot henchir tient une place très importante dans la toponymie de la Berbérie orientale où l’on dénombre des centaines d’occurrences associées à des noms de personnes, de plantes, d’animaux, de formes de relief. Ce toponyme demeure mystérieux quant à son origine. Selon la plupart des linguistes la racine n’est pas arabe. Ch. Tissot dit que henchir est emprunté à la langue berbère mais ce mot est inconnu dans les régions berbérophones du Maghreb central et du Maroc et on ne voit pas de quell..