Adaptively weighted maximum likelihood estimation of discrete distributions

SummaryDiscrete data arise in various research fields, typically when the observations are count data.I propose a robust and efficient parametric procedure for estimation of discrete distributions. The estimation is done in two phases. First, a very robust, but possibly inefficient, estimate of the model parameters is computed and used to indentify outliers. Then the outliers are either removed from the sample or given low weights, and a weighted maximum likelihood estimate (WML) is computed.The weights are determined via an adaptive process such that if the data follow the model, then asymptotically no observation is downweighted.I prove that the final estimator inherits the breakdown point of the initial one, and that its influence function at the model is the same as the influence function of the maximum likelihood estimator, which strongly suggests that it is asymptotically fully efficient.The initial estimator is a minimum disparity estimator (MDE). MDEs can be shown to have full asymptotic efficiency, and some MDEs have very high breakdown points and very low bias under contamination. Several initial estimators are considered, and the performances of the WMLs based on each of them are studied.It results that in a great variety of situations the WML substantially improves the initial estimator, both in terms of finite sample mean square error and in terms of bias under contamination. Besides, the performances of the WML are rather stable under a change of the MDE even if the MDEs have very different behaviors.Two examples of application of the WML to real data are considered. In both of them, the necessity for a robust estimator is clear: the maximum likelihood estimator is badly corrupted by the presence of a few outliers.This procedure is particularly natural in the discrete distribution setting, but could be extended to the continuous case, for which a possible procedure is sketched.RésuméLes données discrètes sont présentes dans différents domaines de recherche, en particulier lorsque les observations sont des comptages.Je propose une méthode paramétrique robuste et efficace pour l'estimation de distributions discrètes. L'estimation est faite en deux phases. Tout d'abord, un estimateur très robuste des paramètres du modèle est calculé, et utilisé pour la détection des données aberrantes (outliers). Cet estimateur n'est pas nécessairement efficace. Ensuite, soit les outliers sont retirés de l'échantillon, soit des faibles poids leur sont attribués, et un estimateur du maximum de vraisemblance pondéré (WML) est calculé.Les poids sont déterminés via un processus adaptif, tel qu'asymptotiquement, si les données suivent le modèle, aucune observation n'est dépondérée.Je prouve que le point de rupture de l'estimateur final est au moins aussi élevé que celui de l'estimateur initial, et que sa fonction d'influence au modèle est la même que celle du maximum de vraisemblance, ce qui suggère que cet estimateur est pleinement efficace asymptotiquement.L'estimateur initial est un estimateur de disparité minimale (MDE). Les MDE sont asymptotiquement pleinement efficaces, et certains d'entre eux ont un point de rupture très élevé et un très faible biais sous contamination. J'étudie les performances du WML basé sur différents MDEs.Le résultat est que dans une grande variété de situations le WML améliore largement les performances de l'estimateur initial, autant en terme du carré moyen de l'erreur que du biais sous contamination. De plus, les performances du WML restent assez stables lorsqu'on change l'estimateur initial, même si les différents MDEs ont des comportements très différents.Je considère deux exemples d'application du WML à des données réelles, où la nécessité d'un estimateur robuste est manifeste : l'estimateur du maximum de vraisemblance est fortement corrompu par la présence de quelques outliers.La méthode proposée est particulièrement naturelle dans le cadre des distributions discrètes, mais pourrait être étendue au cas continu.

Gac/Rsm signal transduction pathway of gamma-proteobacteria: from RNA recognition to regulation of social behaviour.

In many gamma-proteobacteria, the conserved GacS/GacA (BarA/UvrY) two-component system positively controls the expression of one to five genes specifying small RNAs (sRNAs) that are characterized by repeated unpaired GGA motifs but otherwise appear to belong to several independent families. The GGA motifs are essential for binding small, dimeric RNA-binding proteins of a single conserved family designated RsmA (CsrA). These proteins, which also occur in bacterial species outside the gamma-proteobacteria, act as translational repressors of certain mRNAs when these contain an RsmA/CsrA binding site at or near the Shine-Dalgarno sequence plus additional binding sites located in the 5' untranslated leader mRNA. Recent structural data have established that the RsmA-like protein RsmE of Pseudomonas fluorescens makes specific contacts with an RNA consensus sequence 5'-(A)/(U)CANGGANG(U)/(A)-3' (where N is any nucleotide). Interaction with an RsmA/CsrA protein promotes the formation of a short stem supporting an ANGGAN loop. This conformation hinders access of 30S ribosomal subunits and hence translation initiation. The output of the Gac/Rsm cascade varies widely in different bacterial species and typically involves management of carbon storage and expression of virulence or biocontrol factors. Unidentified signal molecules co-ordinate the activity of the Gac/Rsm cascade in a cell population density-dependent manner.

Pédiatrie 1. Formule Quadratique: une nouveauté pédiatrique et pratique pour estimer le taux de filtration glomérulaire [Quadratic formula: a new pediatric advance for glomerular filtration rate estimation].

A new formula for glomerular filtration rate estimation in pediatric population from 2 to 18 years has been developed by the University Unit of Pediatric Nephrology. This Quadratic formula, accessible online, allows pediatricians to adjust drug dosage and/or follow-up renal function more precisely and in an easy manner.

Tunable reporter signal production in feedback-uncoupled arsenic bioreporters.

Escherichia coli-based bioreporters for arsenic detection are typically based on the natural feedback loop that controls ars operon transcription. Feedback loops are known to show a wide range linear response to the detriment of the overall amplification of the incoming signal. While being a favourable feature in controlling arsenic detoxification for the cell, a feedback loop is not necessarily the most optimal for obtaining highest sensitivity and response in a designed cellular reporter for arsenic detection. Here we systematically explore the effects of uncoupling the topology of arsenic sensing circuitry on the developed reporter signal as a function of arsenite concentration input. A model was developed to describe relative ArsR and GFP levels in feedback and uncoupled circuitry, which was used to explore new ArsR-based synthetic circuits. The expression of arsR was then placed under the control of a series of constitutive promoters, which differed in promoter strength, and which could be further modulated by TetR repression. Expression of the reporter gene was maintained under the ArsR-controlled Pars promoter. ArsR expression in the systems was measured by using ArsR-mCherry fusion proteins. We find that stronger constitutive ArsR production decreases arsenite-dependent EGFP output from Pars and vice versa. This leads to a tunable series of arsenite-dependent EGFP outputs in a variety of systematically characterized circuitries. The higher expression levels and sensitivities of the response curves in the uncoupled circuits may be useful for improving field-test assays using arsenic bioreporters.

Non-invasive and non-occlusive blood pressure estimation via a chest sensor.

The clinical demand for a device to monitor Blood Pressure (BP) in ambulatory scenarios with minimal use of inflation cuffs is increasing. Based on the so-called Pulse Wave Velocity (PWV) principle, this paper introduces and evaluates a novel concept of BP monitor that can be fully integrated within a chest sensor. After a preliminary calibration, the sensor provides non-occlusive beat-by-beat estimations of Mean Arterial Pressure (MAP) by measuring the Pulse Transit Time (PTT) of arterial pressure pulses travelling from the ascending aorta towards the subcutaneous vasculature of the chest. In a cohort of 15 healthy male subjects, a total of 462 simultaneous readings consisting of reference MAP and chest PTT were acquired. Each subject was recorded at three different days: D, D+3 and D+14. Overall, the implemented protocol induced MAP values to range from 80 ± 6 mmHg in baseline, to 107 ± 9 mmHg during isometric handgrip maneuvers. Agreement between reference and chest-sensor MAP values was tested by using intraclass correlation coefficient (ICC = 0.78) and Bland-Altman analysis (mean error = 0.7 mmHg, standard deviation = 5.1 mmHg). The cumulative percentage of MAP values provided by the chest sensor falling within a range of ±5 mmHg compared to reference MAP readings was of 70%, within ±10 mmHg was of 91%, and within ±15mmHg was of 98%. These results point at the fact that the chest sensor complies with the British Hypertension Society (BHS) requirements of Grade A BP monitors, when applied to MAP readings. Grade A performance was maintained even two weeks after having performed the initial subject-dependent calibration. In conclusion, this paper introduces a sensor and a calibration strategy to perform MAP measurements at the chest. The encouraging performance of the presented technique paves the way towards an ambulatory-compliant, continuous and non-occlusive BP monitoring system.

Probabilistic evidential assessment of gunshot residue particle evidence (Part II) : Bayesian parameter estimation for experimental count data.

Part I of this series of articles focused on the construction of graphical probabilistic inference procedures, at various levels of detail, for assessing the evidential value of gunshot residue (GSR) particle evidence. The proposed models - in the form of Bayesian networks - address the issues of background presence of GSR particles, analytical performance (i.e., the efficiency of evidence searching and analysis procedures) and contamination. The use and practical implementation of Bayesian networks for case pre-assessment is also discussed. This paper, Part II, concentrates on Bayesian parameter estimation. This topic complements Part I in that it offers means for producing estimates useable for the numerical specification of the proposed probabilistic graphical models. Bayesian estimation procedures are given a primary focus of attention because they allow the scientist to combine (his/her) prior knowledge about the problem of interest with newly acquired experimental data. The present paper also considers further topics such as the sensitivity of the likelihood ratio due to uncertainty in parameters and the study of likelihood ratio values obtained for members of particular populations (e.g., individuals with or without exposure to GSR).

Plastinated Ethmoidal Region : II. The Preparation and Use of Radio-Opaque Artery Casts in Clinical Teaching.

In endoscopic sinus surgery, knowledge of the course of the internal ethmoida and orbital arteries is crucial.The maxillary and the internal carotid arteries of cadavers were injected with radio-opaque , red colorede silicone. The ethmoidal regions were perpared and plastinated using the standard S10 technique. On some specimens, the ophtalmic and ethmoidal arteries were dissected prior to plastination. The plastinated specimens of the ethmoidal blocks were successfullyintroduced into clinical teaching of sinus anatomy and surgery as an aid to study vaascularization an dits relationship to surgical procedures. Among the advantages of this method are the long-lasting preservation of dissected tissue, visualization of arteries during endoscopic and radiological examinations, and invaluable teachjing and training resources for endoscopic sinus surgery.

Estimation of inelastic seismic material properties of a surgical sea-bed from multi-component marine seismic data

To date, state-of-the-art seismic material parameter estimates from multi-component sea-bed seismic data are based on the assumption that the sea-bed consists of a fully elastic half-space. In reality, however, the shallow sea-bed generally consists of soft, unconsolidated sediments that are characterized by strong to very strong seismic attenuation. To explore the potential implications, we apply a state-of-the-art elastic decomposition algorithm to synthetic data for a range of canonical sea-bed models consisting of a viscoelastic half-space of varying attenuation. We find that in the presence of strong seismic attenuation, as quantified by Q-values of 10 or less, significant errors arise in the conventional elastic estimation of seismic properties. Tests on synthetic data indicate that these errors can be largely avoided by accounting for the inherent attenuation of the seafloor when estimating the seismic parameters. This can be achieved by replacing the real-valued expressions for the elastic moduli in the governing equations in the parameter estimation by their complex-valued viscoelastic equivalents. The practical application of our parameter procedure yields realistic estimates of the elastic seismic material properties of the shallow sea-bed, while the corresponding Q-estimates seem to be biased towards too low values, particularly for S-waves. Given that the estimation of inelastic material parameters is notoriously difficult, particularly in the immediate vicinity of the sea-bed, this is expected to be of interest and importance for civil and ocean engineering purposes.