Posterior Analysis for Normalized Random Measures with Independent Increments

Abstract.  One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. In this paper, we provide a comprehensive Bayesian non-parametric analysis of random probabilities which are obtained by normalizing random measures with independent increments (NRMI). Special cases of these priors have already shown to be useful for statistical applications such as mixture models and species sampling problems. However, in order to fully exploit these priors, the derivation of the posterior distribution of NRMIs is crucial: here we achieve this goal and, indeed, provide explicit and tractable expressions suitable for practical implementation. The posterior distribution of an NRMI turns out to be a mixture with respect to the distribution of a specific latent variable. The analysis is completed by the derivation of the corresponding predictive distributions and by a thorough investigation of the marginal structure. These results allow to derive a generalized Blackwell–MacQueen sampling scheme, which is then adapted to cover also mixture models driven by general NRMIs.     

Supervised Classification for a Family of Gaussian Functional Models

Abstract. In the framework of supervised classification (discrimination) for functional data, it is shown that the optimal classification rule can be explicitly obtained for a class of Gaussian processes with ‘triangular’ covariance functions. This explicit knowledge has two practical consequences. First, the consistency of the well‐known nearest neighbours classifier (which is not guaranteed in the problems with functional data) is established for the indicated class of processes. Second, and more important, parametric and non‐parametric plug‐in classifiers can be obtained by estimating the unknown elements in the optimal rule. The performance of these new plug‐in classifiers is checked, with positive results, through a simulation study and a real data example.     

Joint Estimation of Intersecting Context Tree Models

We study a problem of model selection for data produced by two different context tree sources. Motivated by linguistic questions, we consider the case where the probabilistic context trees corresponding to the two sources are finite and share many of their contexts. In order to understand the differences between the two sources, it is important to identify which contexts and which transition probabilities are specific to each source. We consider a class of probabilistic context tree models with three types of contexts: those which appear in one, the other, or both sources. We use a BIC penalized maximum likelihood procedure that jointly estimates the two sources. We propose a new algorithm which efficiently computes the estimated context trees. We prove that the procedure is strongly consistent. We also present a simulation study showing the practical advantage of our procedure over a procedure that works separately on each data set.     

罗马法中的贸易--以介于传统与变革中的要物消费借贷契约为例

从教义学的角度可以看出,多处罗马法原始文献表明消费借贷是一种要物契约,即伴随着订立契约之合意、当事人通过让渡一定量的替代物而成立该种契约。然而仔细观察我们还会发现,这些原始文献还呈现了愈发重视合意要素的价值之趋势,如在所谓的交付的“去实物化”（“短手让渡”）中,在合意确定返还的地点和时间问题上,在与交付同时做出的返还替代物的庄严承诺（“要式口约”）中,以及在承诺提供消费借贷的要式口约中,均可看出此点。所以,罗马法体系中的消费借贷,既有法学家们从抽象意义上界定的要物契约,也有实践所催生的合意契约。这一历史考察,加上对古老欧洲大陆的近代民法典和各种软法草案的评价,有助于我们透彻理解欧洲民法学界关于要物消费借贷和合意消费借贷的二元争论。这些争论忽视了两种模式和谐并存之可能;而实际上,这种解决方案在罗马法中已经显现。     

Conjugacy as a Distinctive Feature of the Dirichlet Process

Abstract.  Recently the class of normalized random measures with independent increments, which contains the Dirichlet process as a particular case, has been introduced. Here a new technique for deriving moments of these random probability measures is proposed. It is shown that, a priori , most of the appealing properties featured by the Dirichlet process are preserved. When passing to posterior computations, we obtain a characterization of the Dirichlet process as the only conjugate member of the whole class of normalized random measures with independent increments.     

Paradoxes of Modernization: The new agrarian question and the peasant movement in Mexico

The clauses of this [social] contract are so determined by the nature of the act that the slightest modification would make them vain and ineffective; so that, although they have perhaps never been formally set forth, they are everywhere the same and everywhere tacitly admitted and recognized, until, on the violation of the social compact, each regains his original rights and resumes his natural liberty, while losing the conventional liberty in favour of which he renounced it.