200 research outputs found
Rate of convergence of predictive distributions for dependent data
This paper deals with empirical processes of the type
where
is a sequence of random variables and the
empirical measure. Conditions for to converge stably (in
particular, in distribution) are given, where ranges over a suitable class
of measurable sets. These conditions apply when is exchangeable or,
more generally, conditionally identically distributed (in the sense of Berti et
al. [Ann. Probab. 32 (2004) 2029--2052]). By such conditions, in some relevant
situations, one obtains that or even that
converges a.s. Results of this type are useful in
Bayesian statistics.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ191 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Rate of Convergence of Predictive Distributions for Dependent Data
This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B | X1, . . . ,Xn)} , where (Xn) is a sequence of random variables and µn = (1/n)SUM(i=1,..,n) d(Xi) the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution) are given, where B ranges over a suitable class of measurable sets. These conditions apply when (Xn) is exchangeable, or, more generally, conditionally identically distributed (in the sense of [6]). By such conditions, in some relevant situations, one obtains that supB|Cn(B)|-P->0 or even that n^(1/2) supB|Cn(B)| converges a.s.. Results of this type are useful in Bayesian statistics.Bayesian predictive inference, Central limit theorem, Conditional identity in distribution, Empirical distribution, Exchangeability, Predictive distribution, Stable convergence.
Central Limit Theorems For Multicolor Urns With Dominated Colors
An urn contains balls of d >= 2 colors. At each time n >= 1, a ball is drawn and then replaced together with a random number of balls of the same color. Let An =diag (An,1, . . . ,An,d) be the n-th reinforce matrix. Assuming EAn,j = EAn,1 for all n and j, a few CLT’s are available for such urns. In real problems, however, it is more reasonable to assume EAn,j = EAn,1 whenever n >= 1 and 1 limsup EAn,j whenever j > d0, for some integer 1 = 1) is independent but need not be identically distributed. Some statistical applications are given as well.Central limit theorem, Clinical trials, Random probability measure, Stable convergence, Urn model.
Asymptotics for randomly reinforced urns with random barriers
An urn contains black and red balls. Let be the proportion of black
balls at time and random barriers. At each time , a
ball is drawn. If is black and , then is replaced
together with a random number of black balls. If is red and
, then is replaced together with a random number of red
balls. Otherwise, no additional balls are added, and alone is replaced.
In this paper, we assume . Then, under mild conditions, it is shown
that for some random variable , and
\begin{gather*}
D_n:=\sqrt{n}\,(Z_n-Z)\longrightarrow\mathcal{N}(0,\sigma^2)\quad\text{conditionally
a.s.} \end{gather*} where is a certain random variance. Almost sure
conditional convergence means that \begin{gather*}
P\bigl(D_n\in\cdot\mid\mathcal{G}_n\bigr)\overset{weakly}\longrightarrow\mathcal{N}(0,\,\sigma^2)\quad\text{a.s.}
\end{gather*} where is a regular
version of the conditional distribution of given the past
. Thus, in particular, one obtains
stably. It is also shown that
a.s. and has non-atomic distribution.Comment: 13 pages, submitte
Central limit theorems for multicolor urns with dominated colors
An urn contains balls of d≥2 colors. At each time n≥1, a ball is drawn and then replaced together with a random number of balls of the same color. Let A n = diag (An,1,…,An,d) be the n-th reinforce matrix. Assuming that EAn,j=EAn,1 for all n and j, a few central limit theorems (CLTs) are available for such urns. In real problems, however, it is more reasonable to assume that EA n,j = EA n,1 whenever n ≥ 1 and 1 ≤ j ≤ d0 , liminfn EAn,1 > limsupn EAn,j whenever j > d0 for some integer 1≤d0≤d. Under this condition, the usual weak limit theorems may fail, but it is still possible to prove the CLTs for some slightly different random quantities. These random quantities are obtained by neglecting dominated colors, i.e., colors from d0+1 to d, and they allow the same inference on the urn structure. The sequence (An : n ≥ 1) is independent but need not be identically distributed. Some statistical applications are given as well
Legius syndrome: Case report and review of literature
A 8-month-old child was referred to our Dermatologic Unit for suspected Neurofibromatosis type 1 (NF 1), because of the appearance, since few days after birth, of numerous caf\ue9-au-lait spots (seven larger than 5 mm); no other sign evocative of NF 1 was found. Her family history was remarkable for the presence of multiple caf\ue9-au-lait spots in the mother, the grandfather and two aunts. The family had been already examined for NF 1, but no sign evocative of the disease was found. We then suspected Legius syndrome, a dominant disease characterized by a mild neurofibromatosis 1 phenotype. The diagnosis was confirmed by the finding of a mutation in SPRED1 gene, a feedback regulator of RAS/MAPK signaling. Here, we discuss the differential diagnosis of caf\ue8-au-lait spots and we briefly review the existing literature about Legius syndrome
Quanto costa incidere una stele? Costi di produzione e meccanismi di pubblicazione delle iscrizioni pubbliche in Grecia
Il contributo affronta la questione del finanziamento e del costo dei decreti pubblici e si propone di ricostruire, sulla base dell’ analisi dei casi esemplari di Atene, Delo e Cos, i fattori economici che determinavano la formazione del prezzo di una stele pubblica. A questo scopo si analizzano i processi di pubblicazione e produzione, dallo stanziamento dei fondi e dal bando dei contratti, al reperimento di materiale e mano d’opera, all’organizzazione della bottega, fino al trasporto e alla collocazione del prodotto finito. This paper analyzes the production of a marble stele and its costs from the public decision to publish an inscription to the erection of the final product. On the basis of the case studies of Athens, Cos and Delos, the paper discusses the supply of materials, the work of the mason, the labor cost and the letting out of the contracts for the production
Lisbeth Bredholt Christensen et Jesper Tae Jensen (éds.), Religion and Material Culture: Studying Religion and Religious Elements on the Basis of Objects, Architecture and Space
Il volume raccoglie gli atti di una conferenza tenutasi nel 2011 al Centre for Bible and Cultural Memory di Copenhagen e al National Museum of Denmark. La novità della pubblicazione è nell’affrontare attraverso un approccio materiale non solo il tema del culto (su cui già esiste vastissima letteratura), ma più in generale della religione, intesa anche nei suoi aspetti teologici, astratti e discorsivi. Intenzionalmente, la raccolta non si limita ad analizzare un solo ambito culturale o cronolo..
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