Analysis of variance for bayesian inference

This paper develops a multi-way analysis of variance for non-Gaussian multivariate distributions and provides a practical simulation algorithm to estimate the corresponding components of variance. It specifically addresses variance in Bayesian predictive distributions, showing that it may be decomposed into the sum of extrinsic variance, arising from posterior uncertainty about parameters, and intrinsic variance, which would exist even if parameters were known. Depending on the application at hand, further decomposition of extrinsic or intrinsic variance (or both) may be useful. The paper shows how to produce simulation-consistent estimates of all of these components, and the method demands little additional effort or computing time beyond that already invested in the posterior simulator. It illustrates the methods using a dynamic stochastic general equilibrium model of the US economy, both before and during the global financial crisis. JEL Classification: C11, C53Analysis of variance, Bayesian inference, posterior simulation, predictive distributions

Caminhos para a inclusão na aprendizagem da matemática: Dois estudantes Surdos no 12.º ano de escolaridade do ensino regular

O aumento da multiculturalidade e abertura das escolas portuguesas do ensino regular a alunos categorizados como apresentando necessidades educativas especiais (NEE) trouxe novos desafios aos agentes educativos (César, 2009; César & Oliveira, 2005). Espera-se que os professores dinamizem o currículo de forma adequada às características, interesses e necessidades dos alunos (César, 2003; César & Santos, 2006). Apesar das alterações legislativas que acompanham e incentivam estas mudanças (ME, 1991, 2008; UNESCO, 1994), os alunos categorizados como apresentando NEE ainda vivenciam barreiras na Escola (Rodrigues, 2003). Adaptar o currículo às particularidades de cada aluno é mais urgente na disciplina de matemática onde os fenómenos de insucesso académico e rejeição são muito frequentes (Abrantes, 1994; César & Kumpulainen, 2009; Oliveira, 2006). A importância atribuída à comunicação matemática (Abrantes, Serrazina, & Oliveira, 1999; NCTM, 2007) ilumina a premência da procura de suportes comunicacionais comuns que permitam aprendizagens com atribuição de sentidos (Bakhtin, 1929/1981). Mais ainda se se incluem Surdos, cujas características comunicacionais são muito particulares (Borges, 2009; Freire, 2006; Melro, 2003). Assumindo uma abordagem interpretativa (Denzin, 2002), realizámos dois estudos de caso intrínsecos (Stake, 1995). Cada um deles centra-se num estudante Surdo oralista. Ambos frequentam o 12.º ano de escolaridade, na mesma turma do ensino regular. Focamos adaptações introduzidas pela docente da disciplina e colegas ouvintes que facilitaram a aprendizagem da matemática e inclusão dos jovens Surdos. Os participantes deste estudo são os estudantes Surdos, as professoras de matemática e educação especial e os colegas de turma. Os instrumentos de recolha de dados foram a observação participante, entrevistas, conversas informais, protocolos dos alunos e recolha documental. Realizámos uma análise de conteúdo de índole narrativa (Clandinin & Connelly, 1998) de onde emergiram categorias indutivas (César, 2009; Hamido & César, 2009). Os resultados iluminam a existência de cinco padrões interactivos que se destacaram durante as aulas assistidas. Um deles era específico para a inclusão dos dois alunos Surdos nos processos de ensino e aprendizagem da matemática. Os restantes foram utilizados tanto com os alunos ouvintes como com os Surdos mas com maior frequência com os últimos. As adaptações específicas realizadas foram benéficas também para os alunos ouvintes.La montée du multiculturalisme et de l'ouverture de l'école portugaise de l'enseignement régulier aux élèves catégorisés comme présentant des besoins éducatifs spéciaux (BES) a apporté de nouveaux défis aux agents éducatifs (César, 2009; César & Oliveira, 2005). On s’attend à que les enseignants mettent en pratique le curriculum d'une manière adaptée aux caractéristiques, intérêts et besoins des étudiants (César, 2003; César & Santos, 2006). Malgré les modifications législatives qui accompagnent et encouragent ces changements (ME, 1991, 2008; UNESCO, 1994), les étudiants catégorisés comme présentant BES vivent encore face aux obstacles à leur scolarisation (Rodrigues, 2003). Adapter le curriculum aux particularités de chaque élève est plus urgent dans la discipline des mathématiques, où les phénomènes d’échec scolaire et de rejet sont très fréquents (Abrantes, 1994; César & Kumpulainen, 2009; Oliveira, 2006). L'importance attachée à la communication mathématique (Abrantes, Serrazina, & Oliveira, 1999; NCTM, 2007) illumine l'urgence de la recherche de moyens de communication partagés, qui permettent l'apprentissage avec l'attribution de sens (Bakhtin, 1929/1981). Encore plus si l'on inclut les Sourdes, dont les caractéristiques de communication sont très particulières (Borges, 2009; Freire, 2006; Melro, 2003). En choisissant une approche interprétative (Denzin, 2002), nous avons réalisé deux études de cas intrinsèques (Stake, 1995). Chacun d’eux se concentre sur un étudiant Sourd qui oralise. Ils participent à une même classe de 12e année de l'enseignement régulier. Nous nous concentrons sur les changements apportés par l’enseignant de la discipline et leurs collègues qui ne sont pas Sourds pour faciliter l'apprentissage des mathématiques et de l'inclusion des jeunes Sourds. Les participants à cette étude sont ces étudiants Sourds, ses camarades et leurs enseignants de mathématiques et de l'éducation spéciale. Les instruments de collecte de données ont été l'observation participante, entretiens, conversations informelles, protocoles des élèves et documents. Nous avons effectué une analyse de contenu de caractère narratif (Clandinin & Connelly, 1998) faisant apparaître des catégories inductives (César, 2009; Hamido & César, 2009). Les résultats éclairent l'existence de cinq types interactifs qui se sont démarqués pendant les classes observées. L'un d'eux était spécifique de l'inclusion de deux élèves Sourds dans l'enseignement et l'apprentissage des mathématiques. Les autres ont été utilisés à la fois avec les étudiants Sourds et leurs camarades, mais plus souvent avec les Sourds. Les adaptations spécifiques réalisées ont aussi été bénéfiques pour les camarades de ces étudiants

Breaching the Walls of the Inviolable Citadel: The Supreme Court\u27s Treatment of the Lemon Test and its Progeny

The Supreme Court in Kennedy v. Bremerton finally laid the three-pronged Lemon test to rest. Instead of Lemon and its progeny, Establishment Clause cases are now to be decided based upon the historical practices and understandings of our Founding Fathers. Subsequently, the Eleventh Circuit instructed the Middle District of Florida to its analysis in Rojas v. City of Ocala. In Rojas, a prayer vigil occurred in the City\u27s public square and featured uniformed police chaplains singing and engaging in Christian prayers. After this Note was written and submitted for publication, the district court issued its decision in Rojas on remand granting plaintiff\u27s motion for summary judgment which is consistent with the analysis provided in this Note. Following a careful review of the history of the Lemon test and its progeny, this Note examines the roots of the new historical-reference test

C2 piecewise cubic quasi-interpolants on a 6-direction mesh

We study two kinds of quasi-interpolants (abbr. QI) in the space of C2 piecewise cubics in the plane, or in a rectangular domain, endowed with the highly symmetric triangulation generated by a uniform 6-direction mesh. It has been proved recently that this space is generated by the integer translates of two multi-box splines. One kind of QIs is of differential type and the other of discrete type. As those QIs are exact on the space of cubic polynomials, their approximation order is 4 for sufficiently smooth functions. In addition, they exhibit nice superconvergent properties at some specific points. Moreover, the infinite norms of the discrete QIs being small, they give excellent approximations of a smooth function and of its first order partial derivatives. The approximation properties of the QIs are illustrated by numerical examples

Eighteenth century female authors: women and science in the Coruña Corpus of English Scientific Writing

[Abstract] This paper explores the use of linguistic features characteristic of impersonal or personal style in scientific writing by female authors in the eighteenth century. Variables such as discipline, subject-matter and genre are used to assess the ways in which abstract thought and argumentation are expressed by women, given that, even when these works were accepted by the scientific establishment, such modes of expression were more typical of men and men's writing in the context of the Modern Age. Data from different genres and disciplines (History, Philosophy, Astronomy and Life Sciences) will be used in order to obtain more reliable findings

A new approach for the validation based on the probabilistic properties of the integer ambiguity estimation

2002-2003 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Originalism and the Inseparability of Decision Procedures from Interpretive Standards

In his article, Originalism: Standard and Procedure, Professor Stephen E. Sachs describes a never-ending debate between originalism\u27s advocates and critics. Originalists argue that certain historical facts determine the Constitution\u27s meaning. But determining these facts is difficult, if not impossible for judges, attorneys, and the public. Sachs seeks to rise above this debate, arguing that the legal community should not expect originalism to offer a procedure for interpreting the Constitution. Instead, the legal community should treat originalism as a standard to judge interpretations. This Article takes issue with this approach. Originalism is not like other instances in law where statutes or opinions refer to other opinions, statutes, or third-party publications. Instead, originalism requires rigorous and complex analysis of historical facts to determine the Constitution\u27s original public meaning-an undertaking that most judges, attorneys, the public, and even legal academics may find challenging. Treating originalism as a standard does not avoid this concern, and originalism therefore remains unappealing when compared with alternate approaches to interpretation that do offer procedures for their implementation. Regardless, the legal community should confront these issues, rather than evade them