Improper vs finitely additive distributions as limits of countably additive probabilities

In Bayesian statistics, improper distributions and finitely additive probabilities (FAPs) are the two main alternatives to proper distributions, i.e. countably additive probabilities. Both of them can be seen as limits of proper distribution sequences w.r.t. to some specific convergence modes. Therefore, some authors attempt to link these two notions by this means, partly using heuristic arguments. The aim of the paper is to compare these two kinds of limits. We show that improper distributions and FAPs represent two distinct characteristics of a sequence of proper distributions and therefore, surprisingly, cannot be connected by the mean of proper distribution sequences. More specifically, for a sequence of proper distribution which converge to both an improper distribution and a set of FAPs, we show that another sequence of proper distributions can be constructed having the same FAP limits and converging to any given improper distribution. This result can be mainly explained by the fact that improper distributions describe the behavior of the sequence inside the domain after rescaling, whereas FAP limits describe how the mass concentrates on the boundary of the domain. We illustrate our results with several examples and we show the difficulty to define properly a uniform FAP distribution on the natural numbers as an equivalent of the improper flat prior. MSC 2010 subject classifications: Primary 62F15; secondary 62E17,60B10

Improper vs finitely additive distributions as limits of countably additive probabilities

In Bayesian statistics, improper distributions and finitely additive probabilities (FAPs) are the two main alternatives to proper distributions, i.e. countably additive probabilities. Both of them can be seen as limits of proper distribution sequences w.r.t. to some specific convergence modes. Therefore, some authors attempt to link these two notions by this means, partly using heuristic arguments. The aim of the paper is to compare these two kinds of limits. We show that improper distributions and FAPs represent two distinct characteristics of a sequence of proper distributions and therefore, surprisingly, cannot be connected by the mean of proper distribution sequences. More specifically, for a sequence of proper distribution which converge to both an improper distribution and a set of FAPs, we show that another sequence of proper distributions can be constructed having the same FAP limits and converging to any given improper distribution. This result can be mainly explained by the fact that improper distributions describe the behavior of the sequence inside the domain after rescaling, whereas FAP limits describe how the mass concentrates on the boundary of the domain. We illustrate our results with several examples and we show the difficulty to define properly a uniform FAP distribution on the natural numbers as an equivalent of the improper flat prior. MSC 2010 subject classifications: Primary 62F15; secondary 62E17,60B10

The orientation of Henry Wilson(1812-1856).

Thesis (Ph.D.)--Boston UniversityHenry Wilson (Feb. 16, 1812 - Nov. 22, 1875). Sometime United States Senator and Vice-President. The first of eight children of Winthrop and Abigail (Witham) Colbath, he was born in Farmington, New Hampshire, and christened Jeremiah Jones Colbath. The family was so poor that at the age of ten and one half the boy was "bound out" to a nearby farmer, who agreed to provide room, board and one month of schooling per year in return for his labor. Upon receiving his freedom, in 1833, he had his name legally changed to Henry Wilson, hoping thus to escape the stigma of his father's alcoholism. Migrating to Natick, Massachusetts, he entered the shoemaker's trade. At the start of 1836, while visiting Washington during a trip to recover his health, he came in contact with slavery. The system disgusted him and its ultimate extinction by constitutional means became the main ambition of his life. Returning to Massachusetts, Wilson studied at various academies for a little more than a year, when the failure of a debtor left him penniless. Back in Natick, he taught school for one term and then became a factor in the "putting-out" system, delivering leather to shoemakers and selling the finished product. He continued intermittently in this business until 1847, when politics became his sole preoccupation. [TRUNCATED

Inference procedures for the piecewise exponential model when the data are arbitrarily censored

Lifetime data are often subject to complicated censoring mechanisms. In particular, point inspection schedules result in observations for which the exact failure times are known only to fall in an interval. Furthermore, overlapping intervals occur when more than one inspection schedule is employed. While well-known parametric and nonparametric inference procedures exist, the piecewise exponential (PEX) model provides a flexible alternative. The PEX model is characterized by a piecewise-constant hazard function with specified jump points. The jump points may be determined as a function of the data, giving the model a nonparametric interpretation, or according to physical considerations related to the process but independent of the data. Assumptions concerning the shape of the hazard function can be incorporated into the model;The EM algorithm provides a useful method of estimation, particularly as the number of hazard jump points increases. Its convergence is guaranteed even when the MLE lies on the boundary of the parameter space. A version of the EM algorithm is used to construct approximate confidence intervals based on inverting the likelihood ratio test statistic. Asymptotic properties of the PEX estimator are given for certain censoring mechanisms. A Monte Carlo study was done to investigate the effect of a constrained hazard function and of the choice of jump points on the resulting estimate of the survival function. The performance of the likelihood ratio based confidence intervals is also evaluated

Rewriting the Game: Queer Trans Strategies of Survival, Resistance, and Relationality in Twine Games

This thesis explores how a selection of video games, created by transgender people using the free software Twine, create space for the survival and flourishing of queer and trans subjects through visions of transformative relationships. It deploys the lenses of queer theories of failure (Halberstam, The Queer Art of Failure), disidentification (Muñoz, Disidentifications), and utopianism (Muñoz, Cruising Utopia) to perform close readings of the techniques of narrative and game mechanics used as strategies for survival, resistance, and relationality in anna anthropy’s Encyclopedia Fuckme and the Case of the Vanishing Entree and Queers in Love at the End of the World, Porpentine Charity Heartscape’s With Those We Love Alive, and ira prince’s Queer Trans Mentally Ill Power Fantasy. The analysis focuses on games produced in and around the moment of the “Twine revolution” (Harvey) that aimed in the early 2010s to radically re-envision video games as spaces for minoritized subjects to thrive. Even as the transformation of video games culture as a whole remains an unrealized ideal, this paper argues for the importance of revisiting the under-examined queer strategies these games depict and enact in order to imagine possibilities for “rewrit[ing] the game” (Halberstam in Halberstam and Juul), and through this for “rewrit[ing] the map of everyday life” (Muñoz, Cruising Utopia 25), possibilities which can allow for the flourishing of queer and trans modes of relationality within and against toxic and exclusive norms in game play and design

Développement et validation interne de scores de risque clinique afin de prédire le risque de tumeurs rénales et pulmonaires chez les gens atteints de la sclérose tubéreuse de Bourneville

Contexte : La sclérose tubéreuse de Bourneville (STB) affecte approximativement une naissance vivante sur 6000. Les principales sources de morbidité chez les enfants sont des manifestations cliniques affectant le cerveau et le cœur. Quant aux adolescents et aux adultes, ils sont à plus haut risque de développer des angiomyolipomes rénaux (AML) et la lymphangioléiomyomatose pulmonaire (LAM). Objectif : Ce projet de recherche a pour principal objectif de déterminer la capacité du fardeau de la maladie chez l’enfant à prédire le développement futur d’AML et de LAM chez l’adolescent et l’adulte. Méthodes : Les données sur 2420 participants de la TSC (Tuberous sclerosis complex) Alliance Natural History Database ont été utilisées pour développer des modèles de régression logistique afin de prédire les AML et la LAM. Ces modèles comptaient comme variables dix manifestations cliniques de la STB en plus du sexe biologique et de la mutation génétique. Les modèles développés ont été convertis en scores de risque clinique et une validation interne a ensuite été effectuée avec rééchantillonage par bootstrap afin d’évaluer leur performance prédictive à l’aide de mesures de discrimination et de calibration. Résultats : 1000 participants ont été diagnostiqués avec un AML, alors que la LAM a été détectée chez 107 participants. Les scores de risque clinique les moins élevés prédisaient des risques d’AML et de LAM de 0 % et de 5 %, tandis que les scores les plus élevés pouvaient prédire des risques allant jusqu’à 96 % et 54 %, respectivement. La performance prédictive des modèles allait de bonne à excellente (C-Index variant de 0,75 à 0,85). Conclusion : Les scores de risque clinique développés indiquent une bonne capacité des manifestations cliniques sélectionnées à prédire le risque futur des tumeurs, principalement pour les AML. Une validation externe devra cependant être menée afin de confirmer les résultats obtenus dans la présente étude.Background: Tuberous sclerosis complex (TSC) affects approximately 1/6000 live births. The primary sources of childhood morbidity and mortality are manifestations affecting the brain and heart. Adolescents and adults, on the other hand, are at the greatest risk of developing renal angiomyolipoma (AML) and pulmonary lymphangioleiomyomatosis (LAM). Objective: The main objective of this research project is to determine the ability of the burden of TSC in children to predict the risk of developing AML and LAM in adults. Methods: Data from 2420 participants in the TSC Natural History Database were used to develop logistic regression models to predict AMLs and LAM. Variables used for the models included 10 clinical manifestations of TSC, in addition to biological sex and genetic mutation. The models were converted into clinical risk scores and were internally validated using bootstrap resampling to evaluate their predictive performance with the help of discrimination and calibration measures. Results: 1000 participants were diagnosed with AML, while LAM was seen in 107 participants. The lowest clinical risk scores predicted a risk of AML and LAM of 5% and 0%, while the highest scores predicted a risk of 96% and 54%, respectively. The predictive performance of the models ranged from good to excellent (C-Indexes of 0.75 to 0.85). Conclusions: The clinical risk scores indicated a good ability for the selected clinical manifestations to predict the future risk of tumours, particularly of AML. External validation of the risk scores will be important to confirm the robustness of our findings

Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A

This thesis consists of two parts. In the first we prove that the Khovanov-Lauda-Rouquier algebras $R_\alpha$ of finite type are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in $R_\alpha$ are generated by idempotents. This in particular implies the (known) result that the global dimension of $R_\alpha$ is finite. In the second part we use the presentation of the Specht modules given by Kleshchev-Mathas-Ram to derive results about Specht modules. In particular, we determine all homomorphisms from an arbitrary Specht module to a fixed Specht module corresponding to any hook partition. Along the way, we give a complete description of the action of the standard KLR generators on the hook Specht module. This work generalizes a result of James. This dissertation includes previously published coauthored material