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.

Evolution of a debris flow channel monitored using a 3D terrestrial laser scanner

Like numerous torrents in mountainous regions, the Illgraben creek (canton of Wallis, SW Switzerland) produces almost every year several debris flows. The total area of the active catchment is only 4.7 km², but large events ranging from 50'000 to 400'000 m³ are common (Zimmermann 2000). Consequently, the pathway of the main channel often changes suddenly. One single event can for instance fill the whole river bed and dig new several-meters-deep channels somewhere else (Bardou et al. 2003). The quantification of both, the rhythm and the magnitude of these changes, is very important to assess the variability of the bed's cross section and long profile. These parameters are indispensable for numerical modelling, as they should be considered as initial conditions. To monitor the channel evolution an Optech ILRIS 3D terrestrial laser scanner (LIDAR) was used. LIDAR permits to make a complete high precision 3D model of the channel and its surroundings by scanning it from different view points. The 3D data are treated and interpreted with the software Polyworks from Innovmetric Software Inc. Sequential 3D models allow for the determination of the variation in the bed's cross section and long profile. These data will afterwards be used to quantify the erosion and the deposition in the torrent reaches. To complete the chronological evolution of the landforms, precise digital terrain models, obtained by high resolution photogrammetry based on old aerial photographs, will be used. A 500 m long section of the Illgraben channel was scanned on 18th of August 2005 and on 7th of April 2006. These two data sets permit identifying the changes of the channel that occurred during the winter season. An upcoming scanning campaign in September 2006 will allow for the determination of the changes during this summer. Preliminary results show huge variations in the pathway of the Illgraben channel, as well as important vertical and lateral erosion of the river bed. Here we present the results of a river bank on the left (north-western) flank of the channel (Figure 1). For the August 2005 model the scans from 3 viewpoints were superposed, whereas the April 2006 3D image was obtained by combining 5 separate scans. The bank was eroded. The bank got eroded essentially on its left part (up to 6.3 m), where it is hit by the river and the debris flows (Figures 2 and 3). A debris cone has also formed (Figure 3), which suggests that a part of the bank erosion is due to shallow landslides. They probably occur when the river erosion creates an undercut slope. These geometrical data allow for the monitoring of the alluvial dynamics (i.e. aggradation and degradation) on different time scales and the influence of debris flows occurrence on these changes. Finally, the resistance against erosion of the bed's cross section and long profile will be analysed to assess the variability of these two key parameters. This information may then be used in debris flow simulation.

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.

On the cellular site of two-pore channel TPC1 action in the Poaceae.

The slow vacuolar (SV) channel has been characterized in different dicots by patch-clamp recordings. This channel represents the major cation conductance of the largest organelle in most plant cells. Studies with the tpc1-2 mutant of the model dicot plant Arabidopsis thaliana identified the SV channel as the product of the TPC1 gene. By contrast, research on rice and wheat TPC1 suggested that the monocot gene encodes a plasma membrane calcium-permeable channel. To explore the site of action of grass TPC1 channels, we expressed OsTPC1 from rice (Oryza sativa) and TaTPC1 from wheat (Triticum aestivum) in the background of the Arabidopsis tpc1-2 mutant. Cross-species tpc1 complementation and patch-clamping of vacuoles using Arabidopsis and rice tpc1 null mutants documented that both monocot TPC1 genes were capable of rescuing the SV channel deficit. Vacuoles from wild-type rice but not the tpc1 loss-of-function mutant harbor SV channels exhibiting the hallmark properties of dicot TPC1/SV channels. When expressed in human embryonic kidney (HEK293) cells OsTPC1 was targeted to Lysotracker-Red-positive organelles. The finding that the rice TPC1, just like those from the model plant Arabidopsis and even animal cells, is localized and active in lyso-vacuolar membranes associates this cation channel species with endomembrane function.

Gain-of-function haplotype in the epithelial calcium channel TRPV6 is a risk factor for renal calcium stone formation.

The rate-limiting step of dietary calcium absorption in the intestine requires the brush border calcium entry channel TRPV6. The TRPV6 gene was completely sequenced in 170 renal calcium stone patients. The frequency of an ancestral TRPV6 haplotype consisting of three non-synonymous polymorphisms (C157R, M378V, M681T) was significantly higher (P = 0.039) in calcium stone formers (8.4%; derived = 502, ancestral = 46) compared to non-stone-forming individuals (5.4%; derived = 645, ancestral = 37). Mineral metabolism was investigated on four different calcium regimens: (i) free-choice diet, (ii) low calcium diet, (iii) fasting and (iv) after a 1 g oral calcium load. When patients homozygous for the derived haplotype were compared with heterozygous patients, no differences were found with respect to the plasma concentrations of 1,25-vitamin D, PTH and calcium, and the urinary excretion of calcium. In one stone-forming patient, the ancestral haplotype was found to be homozygous. This patient had absorptive hypercalciuria. We therefore expressed the ancestral protein (157R+378V+681T) in Xenopus oocytes and found a significantly enhanced calcium permeability when tested by a (45)Ca(2+) uptake assay (7.11 +/- 1.93 versus 3.61 +/- 1.01 pmol/min/oocyte for ancestral versus derived haplotype, P < 0.01). These results suggest that the ancestral gain-of-function haplotype in TRPV6 plays a role in calcium stone formation in certain forms of absorptive hypercalciuria.

Functional expression of a pseudohypoaldosteronism type I mutated epithelial Na+ channel lacking the pore-forming region of its alpha subunit.

The autosomal recessive form of type I pseudohypoaldosteronism (PHA-I) is an inherited salt-losing syndrome resulting from diminution-of-function mutations in the 3 subunits of the epithelial Na+ channel (ENaC). A PHA-I stop mutation (alpha(R508stop)) of the ENaC alpha subunit is predicted to lack the second transmembrane domain and the intracellular COOH-terminus, regions of the protein involved in pore function. Nonetheless, we observed a measurable Na+ current in Xenopus laevis oocytes that coexpress the beta and gamma subunits with the truncated alpha subunit. The mutant alpha was coassembled with beta and gamma subunits and was present at the cell surface at a lower density, consistent with the lower Na+ current seen in oocytes with the truncated alpha subunit. The single-channel Na+ conductance for the mutant channel was only slightly decreased, and the appearance of the macroscopic currents was delayed by 48 hours with respect to wild-type. Our data suggest novel roles for the alpha subunit in the assembly and targeting of an active channel to the cell surface, and suggest that channel pores consisting of only the beta and gamma subunits can provide significant residual activity. This activity may be sufficient to explain the absence of a severe pulmonary phenotype in patients with PHA-I.

Estimation of electronic coupling in π -stacked donor-bridge-acceptor systems: correction of the two-state model

Comparison of donor-acceptor electronic couplings calculated within two-state and three-state models suggests that the two-state treatment can provide unreliable estimates of Vda because of neglecting the multistate effects. We show that in most cases accurate values of the electronic coupling in a π stack, where donor and acceptor are separated by a bridging unit, can be obtained as Ṽ da = (E2 - E1) μ12 Rda + (2 E3 - E1 - E2) 2 μ13 μ23 Rda2, where E1, E2, and E3 are adiabatic energies of the ground, charge-transfer, and bridge states, respectively, μij is the transition dipole moments between the states i and j, and Rda is the distance between the planes of donor and acceptor. In this expression based on the generalized Mulliken-Hush approach, the first term corresponds to the coupling derived within a two-state model, whereas the second term is the superexchange correction accounting for the bridge effect. The formula is extended to bridges consisting of several subunits. The influence of the donor-acceptor energy mismatch on the excess charge distribution, adiabatic dipole and transition moments, and electronic couplings is examined. A diagnostic is developed to determine whether the two-state approach can be applied. Based on numerical results, we showed that the superexchange correction considerably improves estimates of the donor-acceptor coupling derived within a two-state approach. In most cases when the two-state scheme fails, the formula gives reliable results which are in good agreement (within 5%) with the data of the three-state generalized Mulliken-Hush model

The channel-activating protease CAP1/Prss8 is required for placental labyrinth maturation.

The serine protease CAP1/Prss8 is crucial for skin barrier function, lung alveolar fluid clearance and has been unveiled as diagnostic marker for specific cancer types. Here, we show that a constitutive knockout of CAP1/Prss8 leads to embryonic lethality. These embryos presented no specific defects, but it is during this period, and in particular at E13.5, that wildtype placentas show an increased expression of CAP1/Prss8, thus suggesting a placental defect in the knockout situation. The placentas of knockout embryos exhibited significantly reduced vascular development and incomplete cellular maturation. In contrary, epiblast-specific deletion of CAP1/Prss8 allowed development until birth. These CAP1/Prss8-deficient newborns presented abnormal epidermis, and died soon after birth due to impaired skin function. We thus conclude that a late placental insufficiency might be the primary cause of embryonic lethality in CAP1/Prss8 knockouts. This study highlights a novel and crucial role for CAP1/Prss8 in placental development and function.

Direct visualization of the trimeric structure of the ASIC1a channel, using AFM imaging.

There has been confusion about the subunit stoichiometry of the degenerin family of ion channels. Recently, a crystal structure of acid-sensing ion channel (ASIC) 1a revealed that it assembles as a trimer. Here, we used atomic force microscopy (AFM) to image unprocessed ASIC1a bound to mica. We detected a mixture of subunit monomers, dimers and trimers. In some cases, triple-subunit clusters were clearly visible, confirming the trimeric structure of the channel, and indicating that the trimer sometimes disaggregated after adhesion to the mica surface. This AFM-based technique will now enable us to determine the subunit arrangement within heteromeric ASICs.

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).

S-system parameter estimation for noisy metabolic profiles using newton-flow analysis.

Biochemical systems are commonly modelled by systems of ordinary differential equations (ODEs). A particular class of such models called S-systems have recently gained popularity in biochemical system modelling. The parameters of an S-system are usually estimated from time-course profiles. However, finding these estimates is a difficult computational problem. Moreover, although several methods have been recently proposed to solve this problem for ideal profiles, relatively little progress has been reported for noisy profiles. We describe a special feature of a Newton-flow optimisation problem associated with S-system parameter estimation. This enables us to significantly reduce the search space, and also lends itself to parameter estimation for noisy data. We illustrate the applicability of our method by applying it to noisy time-course data synthetically produced from previously published 4- and 30-dimensional S-systems. In addition, we propose an extension of our method that allows the detection of network topologies for small S-systems. We introduce a new method for estimating S-system parameters from time-course profiles. We show that the performance of this method compares favorably with competing methods for ideal profiles, and that it also allows the determination of parameters for noisy profiles.

Selective regulation of acid-sensing ion channel 1 by serine proteases.

Acid-sensing ion channels (ASICs) are neuronal Na(+) channels that belong to the epithelial Na(+) channel/degenerin family. ASICs are transiently activated by a rapid drop in extracellular pH. Conditions of low extracellular pH, such as ischemia and inflammation in which ASICs are thought to be active, are accompanied by increased protease activity. We show here that serine proteases modulate the function of ASIC1a and ASIC1b but not of ASIC2a and ASIC3. We show that protease exposure shifts the pH dependence of ASIC1a activation and steady-state inactivation to more acidic pH. As a consequence, protease exposure leads to a decrease in current response if ASIC1a is activated by a pH drop from pH 7.4. If, however, acidification occurs from a basal pH of approximately 7, protease-exposed ASIC1a shows higher activity than untreated ASIC1a. We provide evidence that this bi-directional regulation of ASIC1a function also occurs in neurons. Thus, we have identified a mechanism that modulates ASIC function and may allow ASIC1a to adapt its gating to situations of persistent extracellular acidification.