Fast and efficient Bayesian semi-parametric curve-fitting and clustering in massive data

Mukhopadhyay, Sabyasachi; Roy, Sisir; Bhattacharya, Sourabh

doi:10.1007/s13571-012-0044-1

Cited by 8 publications

(9 citation statements)

References 28 publications

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“…As is easily seen and is argued in Mukhopadhyay et al (2012), setting M = n and z i = i for i = 1, . .…”

Section: Componentsmentioning

confidence: 67%

“…We now extend our perfect sampling methodology to mixtures with unknown number of components, which is a variable-dimensional problem. In this context, the non-parametric approach of Escobar & West (1995) and the reversible jump MCMC (RJMCMC) approach of Richardson & Green (1997) (2011) (see also Mukhopadhyay, Roy & Bhattacharya (2012)) to include Escobar & West (1995) as a special case, and is much more efficient and computationally cheap compared to the latter.…”

Section: Obtaining Infimum and Supremum Ofmentioning

confidence: 99%

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Perfect Simulation for Mixtures with Known and Unknown Number of Components

Mukhopadhyay¹,

Bhattacharya²

2012

Bayesian Anal.

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We propose and develop a novel and effective perfect sampling methodology for simulating from posteriors corresponding to mixtures with either known (fixed) or unknown number of components. For the latter we consider the Dirichlet process-based mixture model developed by these authors, and show that our ideas are applicable to conjugate, and importantly, to nonconjugate cases. As to be expected, and as we show, perfect sampling for mixtures with known number of components can be achieved with much less effort with a simplified version of our general methodology, whether or not conjugate or non-conjugate priors are used. While no special assumption is necessary in the conjugate set-up for our theory to work, we require the assumption of compact parameter space in the non-conjugate set-up. However, we argue, with appropriate analytical, simulation, and real data studies as support, that such compactness assumption is not unrealistic and is not an impediment in practice. Not only do we validate our ideas theoretically and with simulation studies, but we also consider application of our proposal to three real data sets used by several authors in the past in connection with mixture models.The results we achieved in each of our experiments with either simulation study or real data application, are quite encouraging. However, the computation can be extremely burdensome in the case of large number of mixture components and in massive data sets. We discuss the role of parallel processing in mitigating the extreme computational burden.

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“…As is easily seen and is argued in Mukhopadhyay et al (2012), setting M = n and z i = i for i = 1, . .…”

Section: Componentsmentioning

confidence: 67%

Section: Obtaining Infimum and Supremum Ofmentioning

confidence: 99%

Perfect Simulation for Mixtures with Known and Unknown Number of Components

Mukhopadhyay¹,

Bhattacharya²

2012

Bayesian Anal.

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“…Note that our model consists of one more level of hierarchy of Dirichlet processes than considered in the applications of Teh et al (2006), who introduce hierarchical Dirichlet processes (HDP). Moreover, our likelihood based on Dirichlet processes ensuring at most M mixture components, is significantly different from those considered in the applications of Teh et al (2006), which are based on the traditional DP mixture; see Mukhopadhyay, Bhattacharya & Dihidar (2011), Mukhopadhyay, Roy & Bhattacharya (2012), Mukhopadhyay & Bhattacharya (2013) for details on the conceptual, computational and asymptotic advantages of our modeling style over the traditional DP mixture.…”

Section: Mixture Models Based On Dirichlet Processesmentioning

confidence: 98%

A Non-Gaussian, Nonparametric Structure for Gene-Gene and Gene-Environment Interactions in Case-Control Studies Based on Hierarchies of Dirichlet Processes

Bhattacharya¹,

Bhattacharya²

2017

Preprint

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It is becoming increasingly clear that complex interactions among genes and environmental factors play crucial roles in triggering complex diseases. Thus, understanding such interactions is vital, which is possible only through statistical models that adequately account for such intricate, albeit unknown, dependence structures.Bhattacharya & Bhattacharya (2016b) attempt such modeling, relating finite mixtures composed of Dirichlet processes that represent unknown number of genetic sub-populations through a hierarchical matrix-normal structure that incorporates gene-gene interactions, and possible mutations, induced by environmental variables. However, the product dependence structure implied by their matrix-normal model seems to be too simple to be appropriate for general complex, realistic situations.In this article, we propose and develop a novel nonparametric Bayesian model for case-control genotype data using hierarchies of Dirichlet processes that offers a more realistic and nonparametric dependence structure between the genes, induced by the environmental variables. In this regard, we propose a novel and highly parallelisable MCMC algorithm that is rendered quite efficient by the combination of modern parallel computing technology, effective Gibbs sampling steps, retrospective sampling and Transformation based Markov Chain Monte Carlo (TMCMC). We use appropriate Bayesian hypothesis testing procedures to detect the roles of genes and environment in case-control studies.We apply our ideas to 5 biologically realistic case-control genotype datasets simulated under distinct set-ups, and obtain encouraging results in each case. We finally apply our ideas to a real, myocardial infarction dataset, and obtain interesting results on gene-gene and gene-environment interaction, while broadly agreeing with the results reported in the literature.

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“…, p M jk with positive probability, so that, with positive probability, the actual number of mixture components in (2.1) falls below M , the maximum number of components, the mixing probabilities taking the form M * /M , where 1 ≤ M * ≤ M . See Majumdar et al (2013), Mukhopadhyay, Bhattacharya & Dihidar (2011), Mukhopadhyay, Roy & Bhattacharya (2012), Bhattacharya (2008), for the details.…”

Section: )mentioning

confidence: 99%

A Bayesian semiparametric approach to learning about gene–gene interactions in case-control studies

Bhattacharya

2018

Journal of Applied Statistics

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Gene-gene interactions are often regarded as playing significant roles in influencing variabilities of complex traits. Although much research has been devoted to this area, to date a comprehensive statistical model that addresses the various sources of uncertainties, seem to be lacking. In this paper, we propose and develop a novel Bayesian semiparametric approach composed of finite mixtures based on Dirichlet processes and a hierarchical matrix-normal distribution that can comprehensively account for the unknown number of sub-populations and gene-gene interactions.Then, by formulating novel and suitable Bayesian tests of hypotheses we attempt to single out the roles of the genes, individually, and in interaction with other genes, in case-control studies. We also attempt to identify the significant loci associated with the disease. Our model facilitates a highly efficient parallel computing methodology, combining Gibbs sampling and Transformation based MCMC (TMCMC). Application of our ideas to biologically realistic data sets revealed quite encouraging performance. We also applied our ideas to a real, myocardial infarction dataset, and obtained interesting results that partly agree with, and also complement, the existing works in this area, to reveal the importance of sophisticated and realistic modeling of gene-gene interactions.

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Fast and efficient Bayesian semi-parametric curve-fitting and clustering in massive data

Cited by 8 publications

References 28 publications

Perfect Simulation for Mixtures with Known and Unknown Number of Components

Perfect Simulation for Mixtures with Known and Unknown Number of Components

A Non-Gaussian, Nonparametric Structure for Gene-Gene and Gene-Environment Interactions in Case-Control Studies Based on Hierarchies of Dirichlet Processes

A Bayesian semiparametric approach to learning about gene–gene interactions in case-control studies

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