946 research outputs found
A Berry-Esseen theorem for Pitman's -diversity
This paper is concerned with the study of the random variable denoting
the number of distinct elements in a random sample of
exchangeable random variables driven by the two parameter Poisson-Dirichlet
distribution, . For , Theorem 3.8 in
\cite{Pit(06)} shows that
as . Here, is a
random variable distributed according to the so-called scaled Mittag-Leffler
distribution. Our main result states that \sup_{x \geq 0} \Big|
\ppsf\Big[\frac{K_n}{n^{\alpha}} \leq x \Big] - \ppsf[S_{\alpha,\theta} \leq x]
\Big| \leq \frac{C(\alpha, \theta)}{n^{\alpha}} holds with an explicit
constant . The key ingredients of the proof are a novel
probabilistic representation of as compound distribution and new, refined
versions of certain quantitative bounds for the Poisson approximation and the
compound Poisson distribution
Large deviation principles for the Ewens-Pitman sampling model
Let be the number of blocks with frequency in the exchangeable
random partition induced by a sample of size from the Ewens-Pitman sampling
model. We show that, as tends to infinity, satisfies a
large deviation principle and we characterize the corresponding rate function.
A conditional counterpart of this large deviation principle is also presented.
Specifically, given an initial sample of size from the Ewens-Pitman
sampling model, we consider an additional sample of size . For any fixed
and as tends to infinity, we establish a large deviation principle for the
conditional number of blocks with frequency in the enlarged sample, given
the initial sample. Interestingly, the conditional and unconditional large
deviation principles coincide, namely there is no long lasting impact of the
given initial sample. Potential applications of our results are discussed in
the context of Bayesian nonparametric inference for discovery probabilities.Comment: 30 pages, 2 figure
Approximating predictive probabilities of Gibbs-type priors
Gibbs-type random probability measures, or Gibbs-type priors, are arguably
the most "natural" generalization of the celebrated Dirichlet prior. Among them
the two parameter Poisson-Dirichlet prior certainly stands out for the
mathematical tractability and interpretability of its predictive probabilities,
which made it the natural candidate in several applications. Given a sample of
size , in this paper we show that the predictive probabilities of any
Gibbs-type prior admit a large approximation, with an error term vanishing
as , which maintains the same desirable features as the predictive
probabilities of the two parameter Poisson-Dirichlet prior.Comment: 22 pages, 6 figures. Added posterior simulation study, corrected
typo
Group versus individual discrimination among young workers: a distributional approach
We evaluate the gender wage gap and the unexplained gender wage differential for workers 15-29 year old during the period 1990-1997, using a particularly rich set of data from the Italian Social Security System covering all individuals in the labour markets of two Italian provinces. We estimate separate earnings functions for men and women correcting for endogeneity of education and we evaluate gender discrimination by studying the entire distribution of the unexplained wage gap as suggested by Jenkins (1994). We evaluate discrimination against females by means of bivariate density functions. This innovation makes it possible to condition the density distribution on the marginal distribution of any characteristic and to evaluate more precisely the existence of group and individual discrimination. Our analysis suggests that discrimination is not evenly distributed among women, in relation to their characteristics; in particular, there is evidence of lower discrimination against highly educated females. Moreover in 1997, compared to 1990, discrimination increased in a appreciable way, affecting human capital rich females more significantly. While our work is based in a very local context the richness of the data and the methodological innovation give the results a wider application.wage differentials, wage discrimination, gender
Asymptotics for a Bayesian nonparametric estimator of species variety
In Bayesian nonparametric inference, random discrete probability measures are
commonly used as priors within hierarchical mixture models for density
estimation and for inference on the clustering of the data. Recently, it has
been shown that they can also be exploited in species sampling problems: indeed
they are natural tools for modeling the random proportions of species within a
population thus allowing for inference on various quantities of statistical
interest. For applications that involve large samples, the exact evaluation of
the corresponding estimators becomes impracticable and, therefore, asymptotic
approximations are sought. In the present paper, we study the limiting
behaviour of the number of new species to be observed from further sampling,
conditional on observed data, assuming the observations are exchangeable and
directed by a normalized generalized gamma process prior. Such an asymptotic
study highlights a connection between the normalized generalized gamma process
and the two-parameter Poisson-Dirichlet process that was previously known only
in the unconditional case.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ371 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Bayesian nonparametric analysis of reversible Markov chains
We introduce a three-parameter random walk with reinforcement, called the
scheme, which generalizes the linearly edge reinforced
random walk to uncountable spaces. The parameter smoothly tunes the
scheme between this edge reinforced random walk and the
classical exchangeable two-parameter Hoppe urn scheme, while the parameters
and modulate how many states are typically visited. Resorting
to de Finetti's theorem for Markov chains, we use the
scheme to define a nonparametric prior for Bayesian analysis of reversible
Markov chains. The prior is applied in Bayesian nonparametric inference for
species sampling problems with data generated from a reversible Markov chain
with an unknown transition kernel. As a real example, we analyze data from
molecular dynamics simulations of protein folding.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1102 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
La teoria della complessità sociale e il postmoderno nel diritto. Un esempio paradigmatico: la teoria della rappresentanza di Salvatore Pugliatti
Il pensiero giuridico e la teoria generale della rappresentanza
elaborati da Salvatore Pugliatti costituiscono, ante
litteram, un rilevante e paradigmatico contributo per la
chiarificazione, anche in ambito giuridico, del concetto
contemporaneo di postmodernità, anticipando, e costituendo
già estrinsecazione, dell’ineliminabile rapporto
comunicativo e dialogante sussistente, per la teoria della
complessità sociale e del molteplice, tra la concretezza e la
pluralità delle istanze storiche e l’astrattezza e l’unitarietà
dei concetti che le cristallizzano in sistemi di pensiero
Brevi spunti di riflessione sull’attuale valenza del rapporto comunicativo tra diritto pubblico e diritto privato
Il rapporto tra la sfera pubblica e la sfera privata dell’esperienza giuridica italiana contemporanea, alla luce della normativa costituzionale e ordinaria, non è riduzione del diritto privato nel diritto pubblico, né, viceversa, riduzione del diritto pubblico a esplicitazione di interessi privati, ma deve concepirsi come insopprimibile e dialogica compresenza dinamica, e come comunicazione dialettica, dei due termini, pena la dissoluzione dell’unità dell’ordinamento
L'esperienza giuridica digitale tra teoria e prassi: spunti per una riflessione critica
Stefano Favaro "L'esperienza digitale tra teoria e prassi: spunti per una riflessione critica" in: Tigor: rivista di scienze della comunicazione. A.I (2009) n.1 (gennaio-giugno), pp. 71-87La rivoluzione giuridico-informatica del terzo millennio, sia sotto il profilo del diritto positivo dell’informatica che sotto il versante documentario e cognitivo, tratteggia l’esperienza giuridica digitale contemporanea come quella dimensione “computercentrica” le cui aporie, peraltro, sono superabili solo attraverso il recupero – paradossale ma imprescindibile – proprio della centralità, filosoficamente classica, dell’uomo
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