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.

MP2RAGE provides new clinically-compatible correlates of mild cognitive deficits in relapsing-remitting multiple sclerosis.

Despite that cognitive impairment is a known early feature present in multiple sclerosis (MS) patients, the biological substrate of cognitive deficits in MS remains elusive. In this study, we assessed whether T1 relaxometry, as obtained in clinically acceptable scan times by the recent Magnetization Prepared 2 Rapid Acquisition Gradient Echoes (MP2RAGE) sequence, may help identifying the structural correlate of cognitive deficits in relapsing-remitting MS patients (RRMS). Twenty-nine healthy controls (HC) and forty-nine RRMS patients underwent high-resolution 3T magnetic resonance imaging to obtain optimal cortical lesion (CL) and white matter lesion (WML) count/volume and T1 relaxation times. T1 z scores were then obtained between T1 relaxation times in lesion and the corresponding HC tissue. Patient cognitive performance was tested using the Brief Repeatable Battery of Neuro-psychological Tests. Multivariate analysis was applied to assess the contribution of MRI variables (T1 z scores, lesion count/volume) to cognition in patients and Bonferroni correction was applied for multiple comparison. T1 z scores were higher in WML (p < 0.001) and CL-I (p < 0.01) than in the corresponding normal-appearing tissue in patients, indicating relative microstructural loss. (1) T1 z scores in CL-I (p = 0.01) and the number of CL-II (p = 0.04) were predictors of long-term memory; (2) T1 z scores in CL-I (β = 0.3; p = 0.03) were independent determinants of long-term memory storage, and (3) lesion volume did not significantly influenced cognitive performances in patients. Our study supports evidence that T1 relaxometry from MP2RAGE provides information about microstructural properties in CL and WML and improves correlation with cognition in RRMS patients, compared to conventional measures of disease burden.

Viestintä- ja henkilöhakupalvelu liikkuville käyttäjille

Matkapuhelin on nopeasti muuttunut puhevälineestä monipuoliseksi kommunikointilaitteeksi, joka mahdollistaa eri tyyppisten yhteydenpitomenetelmien käytön suurelle osalle maailman väestöä. Nykyään palvelusovellusten toteuttaminen matkapuhelimiin on mahdollista myös muille osapuolille kuin matkapuhelimien valmistajille. Tässä diplomityössä esitellään matkapuhelinoperaattorin toteuttama viestintä- ja henkilöhakupalvelu liikkuville käyttäjille, joka yhdistää yhden mobiilipalvelun alle henkilöstöhakupalvelun sekä useita viestintämenetelmiä. Diplomityössä esiteltävä mobiilipalvelu on toteutettu WAP-teknologian avulla. Mobiilipalvelu on osa TeliaSoneralla palvelukonseptina toteutettua SME-viestintäjärjestelmää (Smart Messaging Exchange), jonka tavoitteena on pilotoida viestintä- ja läsnäolotietopalveluita. Tässä diplomityössä esitellään SME-viestintäjärjestelmä keskittyen sen WAP-palveluun ja WAP-palvelun toteuttamisessa käytettyihin tekniikoihin. Diplomityön työosuutena on SME-viestintäjärjestelmän WAP-palvelun toteuttaminen.

Forgiveness in Two Minds: Understanding Forgiveness Through Dual-Process Theory

In this thesis, I examined the relevance of dual-process theory to understanding forgiveness. Specifically, I argued that the internal conflict experienced by laypersons when forgiving (or finding themselves unable to forgive) and the discrepancies between existing definitions of forgiveness can currently be best understood through the lens of dual-process theory. Dual-process theory holds that individuals engage in two broad forms of mental processing corresponding to two systems, here referred to as System 1 and System 2. System 1 processing is automatic, unconscious, and operates through learned associations and heuristics. System 2 processing is effortful, conscious, and operates through rule-based and hypothetical thinking. Different definitions of forgiveness amongst both lay persons and scholars may reflect different processes within each system. Further, lay experiences with internal conflict concerning forgiveness may frequently result from processes within each system leading to different cognitive, affective, and behavioural responses. The study conducted for this thesis tested the hypotheses that processing within System 1 can directly affect one's likelihood to forgive, and that this effect is moderated by System 2 processing. I used subliminal conditioning to manipulate System 1 processing by creating positive or negative conditioned attitudes towards a hypothetical transgressor. I used working memory load (WML) to inhibit System 2 processing amongst half of the participants. The conditioning phase of the study failed and so no conclusions could be drawn regarding the roles of System 1 and System 2 in forgiveness. The implications of dual-process theory for forgiveness research and clinical practice, and directions for future research are discussed.