1,721,354 research outputs found
Means of nonparametric priors based on Increasing Additive Processes
No full textWe provide a survey on some distributional results concerning means of random probability measure constructed via suitable transformation of an increasing additive process (abbreviated as IAP), i.e. increasing, not necessarily hopmogeneous, and purely discontinuous Lévy process. In particular, we deal with normalized random measures having independent increments and with neutral to the right (NTR) random probability measures. The former are obtained by normalizing IAPs and the exact distribution of a mean is found by resorting to a well-known inversion formula for characteristic functions. Morevoer, expressions of the posterior distributions of those means, in the presence of exchangeable observations, are given. Also the latter may be characterized in terms of IAPs and we show the connection between a mean of a NTR prior and the so-called exponential functional. We study finiteness and absolute continuity of these functionals and provide some formulae for computing their moments, provided they exist. All the results contained in the first section can be found in Lijoi, Regazzini and Pruenster (2000) whereas those of Section 2 are based on Epifani, Lijoi and Pruenster (2002)
Bayesian nonparametric estimators derived from conditional Gibbs structures
Full text linkWe consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditi onal distributions and the corresponding Bayesian nonparametric estimators, which can be readily exploited for predicting various features of additional samples. The results provide useful tools for genomic applications where prediction of future outcomes is require
Limiting behavior of the search cost distribution for the move-to-frontrule in the stable case
No full textMove-to-front rule is a heuristic updating a list of n items according to requests. Items are required with unknown probabilities (or popularities). The induced Markov chain is known to be ergodic. A main problem is the study of the distribution of the search cost defined as the position of the required item. Here we first establish the link between two recent papers of Barrera and Paroissin and Lijoi and Pruenster that both extend the results proved by Kingman on the expected stationary search cost. By combining the results contained in these papers, we obtain the limiting behavior for any moments of the stationary search cost as n tends to infinity
Limiting behavior of the search cost distribution for the move-to-front rule in the stable case
Full text linkMove-to-front rule is a heuristic updating a list of n items according to requests. Items are required with unknown probabilities (or popularities). The induced Markov chain is known to be ergodic. One main problem is the study of the distribution of the search cost defined as the position of the required item. Here we first establish the link between two recent papers of Barrera and Paroissin and Lijoi and Pruenster that both extend results proved by Kingman on the expected stationary search cost. Combining results contained in these papers, we obtain the limiting behavior for any moments of the stationary seach cost as n tends to infinity.Normalized random measure, Random discrete distribution, Stable subordinator, Problem of heaps
Large sample properties of Gibbs-type priors
No full textIn this paper we concisely summarize some recent findings that can be found in De Blasi, Lijoi and Pruenster (2012) and concern large sample properties of Gibbs-type priors. We shall specifically focus on consistency according to the frequentist approach which postulates the existence of a “ true ” distribution P_0 that generates the data. We show that the asymptotic behaviour of the posterior is completely determined by the probability of obtaining a new distinct observation. Exploiting the predictive structure of Gibbs-type priors, we are able to establish that consistency holds essentially always for discrete P0 , whereas inconsistency may occur for diffuse P_0. Such findings are
further illustrated by means of three specific priors admitting closed form expressions and exhibiting a wide range of asymptotic behaviours
Limiting behavior of the search cost distribution for the move-to-front rule in the stable case
Full text linkMove-to-front rule is a heuristic updating a list of n items according to requests. Items are required with unknown probabilities (or popularities). The induced Markov chain is known to be ergodic. A main problem is the study of the distribution of the search cost defined as the position of the required item. Here we first establish the link between two recent papers of Barrera and Paroissin and Lijoi and Pruenster that both extend the results proved by Kingman on the expected stationary search cost. By combining the results contained in these papers, we obtain the limiting behavior for any moments of the stationary search cost as n tends to infinity
Filippo Ascolani, Antionio Lijoi and Igor Prunster’s contribution to the Discussion of “Martingale Posterior Distributions” by Fong, Holmes and Walker
No full textDiscussion of "Martingale Posterio Distributions" by E. Fong, C. Holmes and S. Walker in connection to principled predictio
Scienza giuridica, democrazia e diritto: interpretazioni costituzionali in Austria dall'Impero alla Repubblica
No full textFilippo Ascolani, Antonio Lijoi and Igor Prünster's contribution to the Discussion of 'Root and community inference on the latent growth process of a network' by Crane and Xu
No full textDiscussion of 'Root and community inference on the latent growth process of a network' by Crane and X
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