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Posterior Contraction Rates of the Phylogenetic Indian Buffet Processes.

ABSTRACT: By expressing prior distributions as general stochastic processes, nonparametric Bayesian methods provide a flexible way to incorporate prior knowledge and constrain the latent structure in statistical inference. The Indian buffet process (IBP) is such an example that can be used to define a prior distribution on infinite binary features, where the exchangeability among subjects is assumed. The phylogenetic Indian buffet process (pIBP), a derivative of IBP, enables the modeling of non-exchangeability among subjects through a stochastic process on a rooted tree, which is similar to that used in phylogenetics, to describe relationships among the subjects. In this paper, we study the theoretical properties of IBP and pIBP under a binary factor model. We establish the posterior contraction rates for both IBP and pIBP and substantiate the theoretical results through simulation studies. This is the first work addressing the frequentist property of the posterior behaviors of IBP and pIBP. We also demonstrated its practical usefulness by applying pIBP prior to a real data example arising in the field of cancer genomics where the exchangeability among subjects is violated.

SUBMITTER: Chen M

PROVIDER: S-EPMC4830498 | biostudies-literature | 2016 Jun

REPOSITORIES: biostudies-literature

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Posterior Contraction Rates of the Phylogenetic Indian Buffet Processes.

Chen Mengjie M Gao Chao C Zhao Hongyu H

Bayesian analysis 20150605 2

By expressing prior distributions as general stochastic processes, nonparametric Bayesian methods provide a flexible way to incorporate prior knowledge and constrain the latent structure in statistical inference. The Indian buffet process (IBP) is such an example that can be used to define a prior distribution on infinite binary features, where the exchangeability among subjects is assumed. The phylogenetic Indian buffet process (pIBP), a derivative of IBP, enables the modeling of non-exchangeab ...[more]

PMID: 27087886

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Project description:The role of left ventricular (LV) longitudinal contraction in ischemic mitral regurgitation (MR) remains unclear. We hypothesized that reduced longitudinal contraction disrupts normal mitral valve plane displacement during systole and leads to mitral valve tethering, thereby inducing ischemic MR. Twenty-three Yorkshire pigs underwent induction of different-sized posterior myocardial infarction (MI) using a percutaneous approach. The incidence of MR and its association with LV longitudinal strain were examined using speckle-tracking echocardiography at 1 mo post-MI to determine their relationship. A total of 17 pigs survived MI and completed the study. Pigs developed no more than mild MR after proximal left circumflex artery (LCx) occlusion (LCx group; n = 7). Addition of a first diagonal branch (D1) occlusion to LCx-MI (LCx + D1 group; n = 7) resulted in moderate to severe MR development 1 mo post-MI. LCx + D1 animals had lower longitudinal strain compared with the LCx group, whereas circumferential strain and LV rotation did not differ significantly. Posterolateral annular displacement toward the apex was significantly reduced in LCx + D1 animals, whereas the septal annular displacement was similar, suggesting an asymmetric mitral annular plane excursion in the LCx + D1 group. To exclude the contribution of papillary muscle infarction in MR development in our model, three pigs underwent obtuse marginal branch + D1 occlusion. None of these pigs developed significant MR after 1 mo. In conclusion, reduced longitudinal contraction contributes to the development of ischemic MR in a large posterior MI. NEW & NOTEWORTHY In this study, using our unique swine models of different-sized myocardial infarction, we showed, for the first time, that reduced longitudinal contraction contributes to the development of ischemic mitral regurgitation in a large posterior myocardial infarction. Our study adds new insights into the mechanisms of ischemic mitral regurgitation pathophysiology.

Dataset Information

Posterior Contraction Rates of the Phylogenetic Indian Buffet Processes.

Publications

Posterior Contraction Rates of the Phylogenetic Indian Buffet Processes.

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