Browsing by Author "Quintana, FA"
Now showing 1 - 8 of 8
Results Per Page
Sort Options
- ItemA new class of skew-normal distributions(TAYLOR & FRANCIS INC, 2004) Arellano Valle, RB; Gomez, HW; Quintana, FAWe introduce a new family of asymmetric normal distributions that contains Azzalini's skew-normal (SN) distribution as a special case. We study the main properties of this new family, showing in particular that it may be generated via mixtures on the SN asymmetry parameter when the mixing distribution is normal. This property provides a Bayesian interpretation of the new family.
- ItemAssessing the order of dependence for partially exchangeable binary data(AMER STATISTICAL ASSOC, 1998) Quintana, FA; Newton, MAThe problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences, We obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts. These tests are facilitated with a new Monte Carlo scheme. Asymptotic tests are also discussed. In particular, we show that the likelihood ratio tests have an asymptotic chi-squared distribution, thus generalizing the results of Billingsley for the particular case of Markov chains. We apply these methods to several datasets, and perform a simulation to study their properties.
- ItemBayesian clustering and product partition models(BLACKWELL PUBL LTD, 2003) Quintana, FA; Iglesias, PLWe present a decision theoretic formulation of product partition models (PPMs) that allows a formal treatment of different decision problems such as estimation or hypothesis testing and clustering methods simultaneously. A key observation in our construction is the fact that PPMs can be formulated in the context of model selection. The underlying partition structure in these models is closely related to that arising in connection with Dirichlet processes. This allows a straightforward adaptation of some computational strategies-originally devised for nonparametric Bayesian problems-to our framework. The resulting algorithms are more flexible than other competing alternatives that are used for problems involving PPMs. We propose an algorithm that yields Bayes estimates of the quantities of interest and the groups of experimental units. We explore the application of our methods to the detection of outliers in normal and Student t regression models, with clustering structure equivalent to that induced by, a Dirichlet process prior. We also discuss the sensitivity of the results considering different prior distributions for the partitions.
- ItemComputational aspects of nonparametric Bayesian analysis with applications to the modeling of multiple binary sequences(AMER STATISTICAL ASSOC, 2000) Quintana, FA; Newton, MAWe consider Markov mixture models for multiple longitudinal binary sequences. Prior uncertainty in the mixing distribution is characterized by a Dirichlet process centered on a matrix beta measure. We use this setting to evaluate and compare the performance of three competing algorithms that arise more generally in Dirichlet process mixture calculations: sequential imputations, Gibbs sampling, and a predictive recursion, for which an extension of the sequential calculations is introduced. This facilitates the estimation of quantities related to clustering structure which is not available in the original formulation. A numerical comparison is carried out in three examples. Our findings suggest that the sequential imputations method is most useful for relatively small problems, and that the predictive recursion can be an efficient preliminary tool for more reliable, but computationally intensive, Gibbs sampling implementations.
- ItemMonte Carlo EM with importance reweighting and its applications in random effects models(ELSEVIER SCIENCE BV, 1999) Quintana, FA; Liu, JS; del Pino, GEIn this paper we propose a new Monte Carlo EM algorithm to compute maximum likelihood estimates in the context of random effects models. The algorithm involves the construction of efficient sampling distributions for the Monte Carlo implementation of the E-step, together with a reweighting procedure that allows repeatedly using a same sample of random effects. In addition, we explore the use of stochastic approximations to speed up convergence once stability has been reached. Our algorithm is compared with that of McCulloch (1997). Extensions to more general problems are discussed. (C) 1999 Elsevier Science B.V. All rights reserved.
- ItemNonparametric Bayesian assessment of the order of dependence for binary sequences(AMER STATISTICAL ASSOC, 2004) Quintana, FA; Muller, PThis article discusses inference on the order of dependence in binary sequences. The proposed approach is based on the notion of partial exchangeability of order k. A partially exchangeable binary sequence of order k can be represented as a mixture of Markov chains. The mixture is with respect to the unknown transition probability matrix theta. We use this defining property to construct a semiparametric model for binary sequences by assuming a nonparametric prior on the transition matrix theta. This enables us to consider inference on the order of dependence without constraint to a particular parametric model. Implementing posterior simulation in the proposed model is complicated by the fact that the dimension of theta changes with the order of dependence k. We discuss appropriate posterior simulation schemes based on a pseudo prior approach. We extend the model to include covariates by considering an alternative parameterization as an autologistic regression which allows for a straightforward introduction of covariates. The regression on covariates raises the additional inference problem of variable selection. We discuss appropriate posterior simulation schemes, focusing on inference about the order of dependence. We discuss and develop the model with covariates only to the extent needed for such inference.
- ItemOptimal sampling for repeated binary measurements(CANADIAN JOURNAL STATISTICS, 2004) Quintana, FA; Muller, PThe authors consider the optimal design of sampling schedules for binary sequence data. They propose an approach which allows a variety of goals to be reflected in the utility function by including deterministic sampling cost, a term related to prediction, and if relevant, a term related to learning about a treatment effect. To this end, they use a nonparametric probability model relying on a minimal number of assumptions. They show how their assumption of partial exchangeability for the binary sequence of data allows the sampling distribution to be written as a mixture of homogeneous Markov chains of order k. The implementation follows the approach of Quintana & Muller (2004), which uses a Dirichlet process prior for the mixture.
- ItemStatistical inference for a general class of asymmetric distributions(ELSEVIER SCIENCE BV, 2005) Arellano Valle, RB; Gomez, HW; Quintana, FAWe consider a general class of asymmetric univariate distributions depending on a real-valued parameter a, which includes the entire family of univariate symmetric distributions as a special case. We discuss the connections between our proposal and other families of skew distributions that have been studied in the statistical literature. A key element in the construction of such families of distributions is that they can be stochastically represented as the product of two independent random variables. From this representation we can readily derive theoretical properties, easy-to-implement simulation schemes as well as extensions to the multivariate case. We also study statistical inference for this class based on the method of moments and maximum likelihood. We give special attention to the skew-power exponential distribution, but other cases like the skew-t distribution are also considered. Finally, the statistical methods are illustrated with 3 examples based on real datasets. (C) 2004 Elsevier B.V. All rights reserved.