77 research outputs found
Asymptotic results for a generalized PĂČlya urn with delay and an applications to clinical trials
In this paper a new PĂČlya urn model is introduced and studied; in particular, a strong law of large numbers and two central limit theorems are proven. This urn generalizes a model studied in Berti et al. (2004), May et al. (2005) and in Crimaldi (2007) and it has natural applications in clinical trials. Indeed, the model include both delayed and missing (or null) responses. Moreover, a connection with the conditional identity in distribution of Berti et al. (2004) is given.
Free completely random measures
Free probability is a noncommutative probability theory introduced by Voiculescu where the concept of independence of classical probability is replaced by the concept of freeness. An important connection between free and classical infinite divisibility was established by Bercovici and Pata (1999) in form of a bijection, mapping the class of classical infinitely divisible laws into the class of free infinitely divisible laws. A particular class of infinitely divisible laws are the completely random measures introduced by Kingman (1967). In this paper, a free analogous of completely random measures is introduced and, a free Poisson process characterization is provided as well as a representation through a free cumulant transform. Furthermore, some examples are displayed.Bayesian non parametrics, Bercovici-Pata bijection, Free completely random measures, Free infinite divisibility, Free probability
An extension of Peskun ordering to continuous time Markov chains
Peskun ordering is a partial ordering defined on the space of transition matrices of discrete time Markov chains. If the Markov chains are reversible with respect to a common stationary distribution "greek Pi", Peskun ordering implies an ordering on the asymptotic variances of the resulting Markov chain Monte Carlo estimators of integrals with respect to "greek Pi". Peskun ordering is also relevant in the framework of time-invariance estimating equations in that it provides a necessary condition for ordering the asymptotic variances of the resulting estimators. In this paper Peskun ordering is extended from discrete time to continuous time Markov chains. Key words and phrases: Peskun ordering, Covariance ordering, Effciency ordering, MCMC, time-invariance estimating equations, asymptotic variance, continuous time Markov chains.
Coalescence time and second largest eigenvalue modulus in the monotone reversible case
If T is the coalescence time of the Propp and Wilson [15], perfect simulation algorithm, the aim of this paper is to show that T depends on the second largest eigenvalue modulus of the transition matrix of the underlying Markov chain. This gives a relationship between the ordering based on the speed of convergence to stationarity in total variation distance and the ordering dened in terms of speed of coalescence in perfect simulation. Key words and phrases: Peskun ordering, Covariance ordering, Effciency ordering, MCMC, time-invariance estimating equations, asymptotic variance, continuous time Markov chains.
Beta-Product Poisson-Dirichlet Processes
Time series data may exhibit clustering over time and, in a multiple time
series context, the clustering behavior may differ across the series. This
paper is motivated by the Bayesian non--parametric modeling of the dependence
between the clustering structures and the distributions of different time
series. We follow a Dirichlet process mixture approach and introduce a new
class of multivariate dependent Dirichlet processes (DDP). The proposed DDP are
represented in terms of vector of stick-breaking processes with dependent
weights. The weights are beta random vectors that determine different and
dependent clustering effects along the dimension of the DDP vector. We discuss
some theoretical properties and provide an efficient Monte Carlo Markov Chain
algorithm for posterior computation. The effectiveness of the method is
illustrated with a simulation study and an application to the United States and
the European Union industrial production indexes
Limiting behavior of the search cost distribution for the move-to-front rule in the stable case
Move-to-front rule is a heuristic updating a list of n items according to requests. Items are required with unknown probabilities (or ppopularities). The induced Markov chain is known to be ergodic [4]. 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 [3, 8] that both extend results proved by Kingman [7] 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
Limiting behavior of the search cost distribution for the move-to-front rule in the stable case
Move-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
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