Generalized Species Sampling Priors With Latent Beta Reinforcements

Airoldi, Edoardo M.; Costa, Thiago V.; Bassetti, Federico; Leisen, Fabrizio; Guindani, Michele

doi:10.1080/01621459.2014.950735

Cited by 32 publications

(43 citation statements)

References 61 publications

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“…The HMM model is fit over a grid of values of K , and the model fit for each value of K is then assessed through a goodness-of-fit criterion, such as the deviance information criterion [64]. The second approach uses Bayesian non-parametrics [65, 66], which has the advantage of automatically learning the value of K but the disadvantage of the need to explore transdimensional parameter spaces, thus adding to the computational demands of the algorithm.…”

Section: Discussionmentioning

confidence: 99%

Time-dependence of graph theory metrics in functional connectivity analysis

et al. 2016

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Brain graphs provide a useful way to computationally model the network structure of the connectome, and this has led to increasing interest in the use of graph theory to quantitate and investigate the topological characteristics of the healthy brain and brain disorders on the network level. The majority of graph theory investigations of functional connectivity have relied on the assumption of temporal stationarity. However, recent evidence increasingly suggests that functional connectivity fluctuates over the length of the scan. In this study, we investigate the stationarity of brain network topology using a Bayesian hidden Markov model (HMM) approach that estimates the dynamic structure of graph theoretical measures of whole-brain functional connectivity. In addition to extracting the stationary distribution and transition probabilities of commonly employed graph theory measures, we propose two estimators of temporal stationarity: the S-index and N-index. These indexes can be used to quantify different aspects of the temporal stationarity of graph theory measures. We apply the method and proposed estimators to resting-state functional MRI data from healthy controls and patients with temporal lobe epilepsy. Our analysis shows that several graph theory measures, including small-world index, global integration measures, and betweenness centrality, may exhibit greater stationarity over time and therefore be more robust. Additionally, we demonstrate that accounting for subject-level differences in the level of temporal stationarity of network topology may increase discriminatory power in discriminating between disease states. Our results confirm and extend findings from other studies regarding the dynamic nature of functional connectivity, and suggest that using statistical models which explicitly account for the dynamic nature of functional connectivity in graph theory analyses may improve the sensitivity of investigations and consistency across investigations.

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Section: Discussionmentioning

confidence: 99%

Time-dependence of graph theory metrics in functional connectivity analysis

et al. 2016

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“…In their simulation study of several of these approaches, they found no dominant method and suggested choosing among them based on the inferential goals. More recently, Airoldi et al (2014) provided a general family of nonexchangeable species sampling sequences dependent on the realizations of a set of latent variables.…”

Section: Introductionmentioning

confidence: 99%

Random Partition Distribution Indexed by Pairwise Information

Dahl

Day

Tsai

2017

Journal of the American Statistical Association

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We propose a random partition distribution indexed by pairwise similarity information such that partitions compatible with the similarities are given more probability. The use of pairwise similarities, in the form of distances, is common in some clustering algorithms (e.g., hierarchical clustering), but we show how to use this type of information to define a prior partition distribution for flexible Bayesian modeling. A defining feature of the distribution is that it allocates probability among partitions within a given number of subsets, but it does not shift probability among sets of partitions with different numbers of subsets. Our distribution places more probability on partitions that group similar items yet keeps the total probability of partitions with a given number of subsets constant. The distribution of the number of subsets (and its moments) is available in closed-form and is not a function of the similarities. Our formulation has an explicit probability mass function (with a tractable normalizing constant) so the full suite of MCMC methods may be used for posterior inference. We compare our distribution with several existing partition distributions, showing that our formulation has attractive properties. We provide three demonstrations to highlight the features and relative performance of our distribution.

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“…In this paper we consider the Bayesian nonparametric approach introduced in Lijoi et al [24] and further investigated in Favaro et al [13] and Favaro et al [14]. Other recent contributions to species sampling problems in the Bayesian framework are, e.g., Navarrete et al [28], Zhang and Stern [33], Barger and Bunge [6], Bacallado et al [3], Lee et al [23], Airoldi et al [1] and Guindani et al [19].…”

Section: Introductionmentioning

confidence: 99%

“…Recall that, due to the de Finetti representation theorem, X n is part of the exchangeable sequence (X i ) i≥1 with directing measure Π. Under the nonparametric framework (1), and with Π belonging to the class of Gibbs-type priors by Gnedin and Pitman [17], results in Lijoi et al [24] and Favaro et al [14] provide explicit posterior distributions for several features of an additional unobserved sample (X n+1 , . .…”

Section: Introductionmentioning

confidence: 99%

A note on nonparametric inference for species variety with Gibbs-type priors

Favaro¹,

James²

2015

Electron. J. Statist.

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A Bayesian nonparametric methodology has been recently introduced for estimating, given an initial observed sample, the species variety featured by an additional unobserved sample of size m. Although this methodology led to explicit posterior distributions under the general framework of Gibbs-type priors, there are situations of practical interest where m is required to be very large and the computational burden for evaluating these posterior distributions makes impossible their concrete implementation. In this paper we present a solution to this problem for a large class of Gibbs-type priors which encompasses the two parameter Poisson-Dirichlet prior and, among others, the normalized generalized Gamma prior. Our solution relies on the study of the large m asymptotic behaviour of the posterior distribution of the number of new species in the additional sample. In particular we introduce a simple characterization of the limiting posterior distribution in terms of a scale mixture with respect to a suitable latent random variable; this characterization, combined with the adaptive rejection sampling, leads to derive a large m approximation of any feature of interest from the exact posterior distribution. We show how to implement our results through a simulation study and the analysis of a dataset in linguistics.MSC 2010 subject classifications: Primary 62F15, 60G57.

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Generalized Species Sampling Priors With Latent Beta Reinforcements

Cited by 32 publications

References 61 publications

Time-dependence of graph theory metrics in functional connectivity analysis

Time-dependence of graph theory metrics in functional connectivity analysis

Random Partition Distribution Indexed by Pairwise Information

A note on nonparametric inference for species variety with Gibbs-type priors

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