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.

Hearing loss in Adult Women with Turner Syndrome

L'objectiu d'aquest estudi és definir els patrons d’hipoacúsia en dones amb Síndrome de Turner i els possibles factors que poden afavorir el desenvolupament d’hipoacúsia neurosensorial en dones adultes amb Síndrome de Turner. Es va trobar que més de la meitat de les dones amb Sindrome de Turner presenten hipoacúsia a l’audiometria, confirmat pels potencials evocats auditius de tronc; la hipoacúsia neurosensorial és el tipus de pèrdua d'audició més freqüent entre dones de mitjana edat amb síndrome de Turner i l'edat, el cariotip i la història prèvia d'otitis mitja recurrent són possibles factors de risc per l’aparició d’hipoacúsia en aquestes pacients.

Risk assessment of recurrence in sporadic retinoblastoma using a molecular-based algorithm.

PURPOSE: Most RB1 mutations are unique and distributed throughout the RB1 gene. Their detection can be time-consuming and the yield especially low in cases of conservatively-treated sporadic unilateral retinoblastoma (Rb) patients. In order to identify patients with true risk of developing Rb, and to reduce the number of unnecessary examinations under anesthesia in all other cases, we developed a universal sensitive, efficient and cost-effective strategy based on intragenic haplotype analysis. METHODS: This algorithm allows the calculation of the a posteriori risk of developing Rb and takes into account (a) RB1 loss of heterozygosity in tumors, (b) preferential paternal origin of new germline mutations, (c) a priori risk derived from empirical data by Vogel, and (d) disease penetrance of 90% in most cases. We report the occurrence of Rb in first degree relatives of patients with sporadic Rb who visited the Jules Gonin Eye Hospital, Lausanne, Switzerland, from January 1994 to December 2006 compared to expected new cases of Rb using our algorithm. RESULTS: A total of 134 families with sporadic Rb were enrolled; testing was performed in 570 individuals and 99 patients younger than 4 years old were identified. We observed one new case of Rb. Using our algorithm, the cumulated total a posteriori risk of recurrence was 1.77. CONCLUSIONS: This is the first time that linkage analysis has been validated to monitor the risk of recurrence in sporadic Rb. This should be a useful tool in genetic counseling, especially when direct RB1 screening for mutations leaves a negative result or is unavailable.

Peripapillary neovascular membrane: A rare cause of acute vision loss in pediatric idiopathic intracranial hypertension.

We report a 14-year-old boy who presented with vision loss secondary to peripapillary neovascular membrane (PPNVM) as the initial and only symptom of papilledema secondary to idiopathic intracranial hypertension. After one lumbar puncture, visual acuity progressively recovered during the course of 1 week and further improved with the administration of oral acetazolamide. One year after the onset of vision loss, the patient's visual acuity had recovered to baseline measurements. The previously active PPNVM had involuted into a residual peripapillary fibrotic scar. To our knowledge, this is the first report of PPNVM complicating idiopathic intracranial hypertension in a child.

Modification of the Perrine-Baum diagram to improve the calculation of high voltage electric lines

Through the history of Electrical Engineering education, vectorial and phasorial diagrams have been used as a fundamental learning tool. At present, computational power has replaced them by long data lists, the result of solving equation systems by means of numerical methods. In this sense, diagrams have been shifted to an academic background and although theoretically explained, they are not used in a practical way within specific examples. This fact may be against the understanding of the complex behavior of the electrical power systems by students. This article proposes a modification of the classical Perrine-Baum diagram construction to allowing both a more practical representation and a better understanding of the behavior of a high-voltage electric line under different levels of load. This modification allows, at the same time, the forecast of the obsolescence of this behavior and line’s loading capacity. Complementary, we evaluate the impact of this tool in the learning process showing comparative undergraduate results during three academic years

Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H2 O and N H3. The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2 H4+ X̃2B 3u←C2 H4X̃1 Ag band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B 3u←C2H4X̃1 Ag band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2 D4 results to be not as good as those for C2 H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested

A comparative analysis of two methods for the calculation of electric-field-induced perturbations to molecular vibration

Two common methods of accounting for electric-field-induced perturbations to molecular vibration are analyzed and compared. The first method is based on a perturbation-theoretic treatment and the second on a finite-field treatment. The relationship between the two, which is not immediately apparent, is made by developing an algebraic formalism for the latter. Some of the higher-order terms in this development are documented here for the first time. As well as considering vibrational dipole polarizabilities and hyperpolarizabilities, we also make mention of the vibrational Stark effec

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

An overview is given on a study which showed that not only in chemical reactions but also in the favorable case of nontotally symmetric vibrations where the chemical and external potentials keep approximately constant, the generalized maximum hardness principle (GMHP) and generalized minimum polarizability principle (GMPP) may not be obeyed. A method that allows an accurate determination of the nontotally symmetric molecular distortions with more marked GMPP or anti-GMPP character through diagonalization of the polarizability Hessian matrix is introduced

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

Low postseroconversion CD4 count and rapid decrease of CD4 density identify HIV+ fast progressors.

CD4 expression in HIV replication is paradoxical: HIV entry requires high cell-surface CD4 densities, but replication requires CD4 down-modulation. However, is CD4 density in HIV+ patients affected over time? Do changes in CD4 density correlate with disease progression? Here, we examined the role of CD4 density for HIV disease progression by longitudinally quantifying CD4 densities on CD4+ T cells and monocytes of ART-naive HIV+ patients with different disease progression rates. This was a retrospective study. We defined three groups of HIV+ patients by their rate of CD4+ T cell loss, calculated by the time between infection and reaching a CD4 level of 200 cells/microl: fast (<7.5 years), intermediate (7.5-12 years), and slow progressors (>12 years). Mathematical modeling permitted us to determine the maximum CD4+ T cell count after HIV seroconversion (defined as "postseroconversion CD4 count") and longitudinal profiles of CD4 count and density. CD4 densities were quantified on CD4+ T cells and monocytes from these patients and from healthy individuals by flow cytometry. Fast progressors had significantly lower postseroconversion CD4 counts than other progressors. CD4 density on T cells was lower in HIV+ patients than in healthy individuals and decreased more rapidly in fast than in slow progressors. Antiretroviral therapy (ART) did not normalize CD4 density. Thus, postseroconversion CD4 counts define individual HIV disease progression rates that may help to identify patients who might benefit most from early ART. Early discrimination of slow and fast progressors suggests that critical events during primary infection define long-term outcome. A more rapid CD4 density decrease in fast progressors might contribute to progressive functional impairments of the immune response in advanced HIV infection. The lack of an effect of ART on CD4 density implies a persistent dysfunctional immune response by uncontrolled HIV infection.

Simultaneous loss of beta- and gamma-catenin does not perturb hematopoiesis or lymphopoiesis.

Hematopietic stem cells (HSCs) maintain life-long hematopoiesis in the bone marrow via their ability to self-renew and to differentiate into all blood lineages. Although a central role for the canonical wnt signaling pathway has been suggested in HSC self-renewal as well as in the development of B and T cells, conditional deletion of beta-catenin (which is considered to be essential for Wnt signaling) has no effect on hematopoiesis or lymphopoiesis. Here, we address whether this discrepancy can be explained by a redundant and compensatory function of gamma-catenin, a close homolog of beta-catenin. Unexpectedly, we find that combined deficiency of beta- and gamma-catenin in hematopoietic progenitors does not impair their ability to self-renew and to reconstitute all myeloid, erythroid, and lymphoid lineages, even in competitive mixed chimeras and serial transplantations. These results exclude an essential role for canonical Wnt signaling (as mediated by beta- and/or gamma-catenin) during hematopoiesis and lymphopoiesis.

The early Miocene rotation of the Corso-Sardinian block. New paleomagnetic constraints for the end of the motion

The paleomagnetic investigations carried out in the 70's on Oligo-Miocene volcanics of Sardinia have demonstrated that the island was turned by 35-30 degrees clockwise from 33 Ma up to 3-1-20.5 Ma and rotated counterclockwise in a few million years [De Jong et al., 1969, 1973; Bobier et Coulon, 1970; Coulon et al., 1974; Manzoni, 1974, 1975; Bellon rr nl.. 1977: Edel et Lortscher, 1977; Edel, 1979, 1980]. Since then, the end of the rotation fixed at 19 Ma by Montigny er al. [1981] was the subject of discussions and several studies associating paleomagnetism and radiometric dating were undertaken [Assorgia er al., 1994: Vigliotti et Langenheim, 1995: Deino et al., 1997; Gattacceca rt Deino, 1999]. This is a contribution to this debate that is hampered by thr important secular variation recorded in the volcanics. The only way to get our of this problem is to sample series of successive flows as completely as possible, and to reduce the effect of secular variation by the calculation of means. Sampling was performed north of Bonorva in 5 pyroclastic flows that belong to the upper ignimbritic series SI2 according to Coulon rr nl. [1974] or LBLS according to Assorgia et al. [1997] (fig. I). Ar-40/Ar-39 dating of biotites from the debris flow (MDF) has yielded an age or 18.35 +/- 0.03 Ma [Dubois, 2000]. Five of the investigated sites are located beneath the debris flow ITV, TVB, TVD, SPM85, SPM86), one site was cured in the matrix of the debris flow (MDF) and one in 4 metric blocks included in the flow (DFC). Another site was sampled in the upper ash flow (PDM) that marks the end of the pyroclastic activity, just before the marine transgression. According to micropaleontological and radiometric dating this transgression has occurred between 18.35 and 17.6 Ma [Dubois, 2000]. After removal of a soft viscous component, the thermal demagnetization generally shows a univectorial behaviour of the remanent magnetization (fig. 2a). The maximum unblocking temperatures of 580-620 degrees (tab. I) and a rapid saturation below 100 mT (fig. 3) indicate that the carrier of the characteristic magnetization is magnetite. The exception comes: from the upper site PDM in which were found two characteristic components, one with a normal polarity and low unblocking temperatures up to 350 degreesC and one with a reversed polarity and maximum unblocking temperatures at 580-600 degreesC of magnetite. After calculation of a mean direction for each flow, the mean << Al >> direction 4 degrees /57 degrees (alpha (95) = 13 degrees) computed with the mean directions for the 5 flows may be considered as weakly affected by secular variation. But the results require a more careful examination. The declinations are N to NNW beneath the debris flow. NNW in the debris flow. and NNE (or SSW) above the debris flow, The elongated distribution of the directions obtained at sites TVB and TVD. scattered from the mean direction of TV to the mean direction of MDF is interpreted as due to partial overprinting during the debris How volcanic episode, The low temperature component PDMa is likely related to the alteration seen on thin sections and is also viewed as an overprint. As NNE/SSW directions occur as well below (mean direction << B >> : 5 degrees /58 degrees) as above the debris flow (PDMb : 200 degrees/-58 degrees). the NNW directions (<< C >> : 337 degrees /64 degrees) associated with the debris flow volcanism may be interpreted as resulting from a magnetic field excursion. According to the polarity scale of Cande and Kent [1992, 1995] and the radiometric age of MDF, the directions with normal polarity (TV, TVB, TVD, SPM85. SPM86a. MDF. DFC) may represent the period 5En. while the directions with reversed polarity PDMb and SPM86b were likely acquired during the period 5Dr. Using the mean << Al >> direction, the mean << B >>, or the PDM direction (tab. I). the deviation in declination with the direction of stable Europe 6.4 degrees /58.7 degrees (alpha (95) = 8 degrees) for a selection of 4 middle Tertiary poles by Besse et Courtillot [1991] or 7 degrees /56 degrees (alpha (95) = 3 degrees) for 19 poles listed by Edel [1980] can be considered as negligible. Using the results from the uppermost ignimbritic layer of Anglona also emplaced around 18.3 Ma [Odin rt al.. 1994]. the mean direction << E >> (3 degrees /51.5 degrees) leads to the same conclusion. On the contrary, when taking into account all dated results available for the period 5En (mean direction << D >> 353 degrees /56 degrees for 45 sites) (tab. II). the deviation 13 degrees is much more significant. As the rotation of Sardinia started around 21-20.5 Ma. the assumption of a constant velocity of rotation and the deviations of the Sardinia directions with respect to the stable Europe direction locate the end of the motion between 18.3 and 17.2 or 16.7 Ma (fig. 4). During the interval 18.35-17.5 Ma, the marine transgression took place. At the same period a NE-SW shortening interpreted as resulting from the collision of Sardinia with Apulia affected different parts of the island [Letouzey et al., 1982]. Consequently, the new paleomagnetic results and the tectono-sedimentary evolution are in favour of an end of the rotation at 17.5-18 Ma.