On Bayesian nonparametric modelling of two correlated distributions

Kolossiatis, Michalis; Griffin, Jim E.; Steel, Mark F. J.

doi:10.1007/s11222-011-9283-7

Cited by 21 publications

(16 citation statements)

References 17 publications

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“…Figure 7.7 shows posterior predictive inference for a patient from a future third study j D 3. Kolossiatis et al (2013) discuss an interesting variation of the model (7.5) and (7.6). They propose a specific choice of prior for that together with the DP priors for F j ensures an implied DP prior for the linear combination G j .…”

Section: Example 21 (Two Related Studies -Calgb 8881 and 9160)mentioning

confidence: 99%

Hierarchical Models

Müller¹,

Quintana²,

Jara³

et al. 2015

Springer Series in Statistics

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One of the great success stories of Bayesian methods in biostatistics is inference in hierarchical models. The model-based Bayesian approach allows for coherent propagation of uncertainties and borrowing of strength across submodels and more. In this chapter we discuss nonparametric Bayesian approaches in hierarchical models, including nonparametric priors on random effects distributions and extensions of such models across multiple related studies. Honest accounting for uncertainties becomes particularly important for applications to classification, when we use posterior predictive inference for a future experimental unit to estimate unknown membership in one of several subpopulations.

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Section: Example 21 (Two Related Studies -Calgb 8881 and 9160)mentioning

confidence: 99%

Hierarchical Models

Müller¹,

Quintana²,

Jara³

et al. 2015

Springer Series in Statistics

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“…The problem of multimodality of the posterior distribution in these models and a computational solution, a split-merge move, are described in Kolossiatis et al (2012). In our model, it is useful to link the underlying measures to their corresponding columns in the D-matrix.…”

Section: Step 1: Split-merge Movementioning

confidence: 99%

Comparing Distributions by using Dependent Normalized Random-Measure Mixtures

Griffin

Kolossiatis

Steel

2013

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary.A methodology for the simultaneous Bayesian non-parametric modelling of several distributions is developed. Our approach uses normalized random measures with independent increments and builds dependence through the superposition of shared processes. The properties of the prior are described and the modelling possibilities of this framework are explored in detail. Efficient slice sampling methods are developed for inference.Various posterior summaries are introduced which allow better understanding of the differences between distributions. The methods are illustrated on simulated data and examples from survival analysis and stochastic frontier analysis.

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“…The methods often rely on adjusted versions of the EM algorithm (Pilla and Lindsay 2001) or a Newton method (Wang 2010;Schellhase and Kauermann 2012) and in addition can make use of appropriate data transformations (Hettmansperger and Thomas 2000). There also exist several nonparametric approaches to problems involving multiple samples and finite mixture models, as for example proposed by Kolossiatis et al (2013). However, to the authors' knowledge, there is no literature addressing the two sample problem outlined above in the context of mixture models.…”

Section: Introductionmentioning

confidence: 99%

Correcting statistical models via empirical distribution functions

Munteanu

Wornowizki

2015

Comput Stat

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We consider the two-sample homogeneity problem where the information contained in two samples is used to test the equality of the underlying distributions. In cases where one sample is simulated by a procedure modelling the data generating process of another observed sample, a mere rejection of the null hypothesis is unsatisfactory. Instead, the data analyst would like to know how the simulation can be improved. Based on the popular Kolmogorov-Smirnov test and a general mixture model, we propose an algorithm that determines an appropriate correction distribution function. Complementing the simulation sample by a given proportion of observations sampled from this distribution reduces the Kolmogorov-Smirnov distance between the modified and the observed sample. Therefore, the correction distribution indicates possible improvements to the current simulation process. We prove our algorithm to run in linear time when applied to sorted samples. We further illustrate its intuitive results on simulated as well as on real data sets from astrophysics and bioinformatics. Keywords Nonparametric mixture model · Kolmogorov-Smirnov test · Quantify discrepancy between data and model · Efficient algorithm B Max Wornowizki

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On Bayesian nonparametric modelling of two correlated distributions

Cited by 21 publications

References 17 publications

Hierarchical Models

Hierarchical Models

Comparing Distributions by using Dependent Normalized Random-Measure Mixtures

Correcting statistical models via empirical distribution functions

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