On a loss-based prior for the number of components in mixture models

Grazian, Clara; Villa, Cristiano; Liseo, Brunero

doi:10.1016/j.spl.2019.108656

Cited by 9 publications

(18 citation statements)

References 35 publications

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“…The results are reported in Table 6 . We notice that according to the computed index, we identify as best model the mixture with

components, which is in line with [ 16 ], and slightly more conservative than [ 15 , 16 ], where the number of components with non-zero weight is 5. Table 7 shows the posterior means for the parameters of the 4 components estimated.…”

Section: Mixture Modelssupporting

confidence: 70%

“…To support a particular theory about the formation of galaxies, the analysis aims to estimate the number of stellar populations. This is a benchmark data set, well investigated in the literature, for example in [ 14 , 15 , 16 ], among others. We consider the galaxies velocities as random variables distributed according to a mixture of k normal densities.…”

Section: Mixture Modelsmentioning

confidence: 99%

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An Objective Prior from a Scoring Rule

Walker

Villa

2021

Entropy

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In this paper, we introduce a novel objective prior distribution levering on the connections between information, divergence and scoring rules. In particular, we do so from the starting point of convex functions representing information in density functions. This provides a natural route to proper local scoring rules using Bregman divergence. Specifically, we determine the prior which solves setting the score function to be a constant. Although in itself this provides motivation for an objective prior, the prior also minimizes a corresponding information criterion.

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“…The results are reported in Table 6 . We notice that according to the computed index, we identify as best model the mixture with

Section: Mixture Modelssupporting

confidence: 70%

Section: Mixture Modelsmentioning

confidence: 99%

An Objective Prior from a Scoring Rule

Walker

Villa

2021

Entropy

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“…We propose the three-parameter beta-negative-binomial distribution as a prior on the number of components K which unifies priors proposed in Richardson and Green (1997); Nobile (2004); Cerquetti (2010); Miller and Harrison (2018); Grazian et al (2020). Building on Antoniak (1974); Nobile (2004); Gnedin and Pitman (2006), we derive the implicitly induced prior on the number of clusters K + for generalized MFMs.…”

Section: Introductionmentioning

confidence: 97%

Generalized Mixtures of Finite Mixtures and Telescoping Sampling

2021

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Within a Bayesian framework, a comprehensive investigation of mixtures of finite mixtures (MFMs), i.e., finite mixtures with a prior on the number of components, is performed. This model class has applications in model-based clustering as well as for semi-parametric density estimation and requires suitable prior specifications and inference methods to exploit its full potential. We contribute by considering a generalized class of MFMs where the hyperparameter γK of a symmetric Dirichlet prior on the weight distribution depends on the number of components. We show that this model class may be regarded as a Bayesian non-parametric mixture outside the class of Gibbs-type priors. We emphasize the distinction between the number of components K of a mixture and the number of clusters K+, i.e., the number of filled components given the data. In the MFM model, K+ is a random variable and its prior depends on the prior on K and on the hyperparameter γK . We employ a flexible prior distribution for the number of components K and derive the corresponding prior on the number of clusters K+ for generalized MFMs. For posterior inference we propose the novel telescoping sampler which allows Bayesian inference for mixtures with arbitrary component distributions without resorting to reversible jump Markov chain Monte Carlo (MCMC) methods. The telescoping sampler explicitly samples the number of components, but otherwise requires only the usual MCMC steps of a finite mixture model. The ease of its application using different component distributions is demonstrated on several data sets.

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“…As part of the analysis, it is necessary to define prior distributions for all the parameters in the model, describing the prior knowledge the experimenter has about them. We have decided to use the default prior proposed in Grazian et al (2018) for the number of components since it has been shown to have a good balance between conservativeness and accuracy and standard vague priors for the rest of the parameters as in Richardson and Green (1997), in order to reduce the influence of the prior on the posterior distribution. Bayesian estimation of mixture models is a non-standard problem, therefore Monte Carlo Markov chains (MCMC) methods are needed to approximate the posterior distribution (Robert and Casella, 2013…”

Section: The Proposed Modelsmentioning

confidence: 99%

Estimating MIC distributions and cutoffs through mixture models: an application to establish M. Tuberculosis resistance

Grazian¹

2019

Preprint

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Antimicrobial resistance is becoming a major threat to public health throughout the world. Researchers from around the world are attempting to contrast it by developing both new antibiotics and patientspecific treatments. It is, therefore, necessary to study these treatments, via phenotypic tests, and it is essential to have robust methods available to analyze the resistance patterns to medication, which could be applied to both new treatments and to new phenotypic tests. A general method is here proposed to study minimal inhibitory concentration (MIC) distributions and fixed breakpoints in order to separate sensible from resistant strains. The method has been applied to a new 96-well microtiter plate.

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On a loss-based prior for the number of components in mixture models

Cited by 9 publications

References 35 publications

An Objective Prior from a Scoring Rule

An Objective Prior from a Scoring Rule

Generalized Mixtures of Finite Mixtures and Telescoping Sampling

Estimating MIC distributions and cutoffs through mixture models: an application to establish M. Tuberculosis resistance

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