Univariate Bayesian nonparametric mixture modeling with unimodal kernels

Rodríguez, Carlos E.; Walker, Stephen G.

doi:10.1007/s11222-012-9351-7

Cited by 23 publications

(19 citation statements)

References 30 publications

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“…Consequently, the effects of misspecification need to be carefully considered if these posteriors are to be used as measures of heterogeneity. Steps toward addressing the issue of robustness have been taken by Woo and Sriram (2006, 2007) and Rodríguez and Walker (2014), however, this is an important problem demanding further study. Despite these issues, sample clusterings and estimates of the number of components or clusters can provide a useful tool for exploring complex datasets, particularly in the case of high-dimensional data that cannot easily be visualized. It should always be borne in mind, though, that the results can only be interpreted as being correct to the extent that the model assumptions are correct.…”

Section: A1 Examples Where Mfms May Be More Suitable Than Dpmsmentioning

confidence: 99%

Section: A1 Examples Where Mfms May Be More Suitable Than Dpmsmentioning

confidence: 99%

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Mixture Models With a Prior on the Number of Components

Miller

Harrison

2017

Journal of the American Statistical Association

202

301

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A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric Dirichlet weights, and put a prior on the number of components—that is, to use a mixture of finite mixtures (MFM). The most commonly-used method of inference for MFMs is reversible jump Markov chain Monte Carlo, but it can be nontrivial to design good reversible jump moves, especially in high-dimensional spaces. Meanwhile, there are samplers for Dirichlet process mixture (DPM) models that are relatively simple and are easily adapted to new applications. It turns out that, in fact, many of the essential properties of DPMs are also exhibited by MFMs—an exchangeable partition distribution, restaurant process, random measure representation, and stick-breaking representation—and crucially, the MFM analogues are simple enough that they can be used much like the corresponding DPM properties. Consequently, many of the powerful methods developed for inference in DPMs can be directly applied to MFMs as well; this simplifies the implementation of MFMs and can substantially improve mixing. We illustrate with real and simulated data, including high-dimensional gene expression data used to discriminate cancer subtypes.

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Section: A1 Examples Where Mfms May Be More Suitable Than Dpmsmentioning

confidence: 99%

Section: A1 Examples Where Mfms May Be More Suitable Than Dpmsmentioning

confidence: 99%

Mixture Models With a Prior on the Number of Components

Miller

Harrison

2017

Journal of the American Statistical Association

202

301

View full text Add to dashboard Cite

show abstract

“…These include Markov chain Monte Carlo methods, non-iterative Monte Carlo methods, and asymptotic methods. Other Bayesian methods based on mixtures include Ley and Steel [40], Liang et al [32], Schäfer et al [41], Rodrguez and Walker [42], and Abd and AlZaydi [43]. Some frequentist mixtures include Abd and Al-Zaydi [44], and AL-Hussaini and Hussein [45].…”

Section: Posterior Model Selection Uncertaintymentioning

confidence: 99%

Effects of Bayesian Model Selection on Frequentist Performances: An Alternative Approach

Nguefack‐Tsague¹,

Zucchini²

2016

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It is quite common in statistical modeling to select a model and make inference as if the model had been known in advance; i.e. ignoring model selection uncertainty. The resulted estimator is called post-model selection estimator (PMSE) whose properties are hard to derive. Conditioning on data at hand (as it is usually the case), Bayesian model selection is free of this phenomenon. This paper is concerned with the properties of Bayesian estimator obtained after model selection when the frequentist (long run) performances of the resulted Bayesian estimator are of interest. The proposed method, using Bayesian decision theory, is based on the well known Bayesian model averaging (BMA)'s machinery; and outperforms PMSE and BMA. It is shown that if the unconditional model selection probability is equal to model prior, then the proposed approach reduces BMA. The method is illustrated using Bernoulli trials.

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“…The Ministry of Social Development (SEDESOL, according to its initials in Spanish) in Mexico is one of many government dependencies. The aim of SEDESOL is to help and improve the social backwardness that prevails in a high percentage of the households in Typically the sub-populations are assumed to be normal but other alternatives, to deal for example with possible asymmetric structures of the subpopulation, have also been considered (Rodríguez and Walker, 2014;Canale and Scarpa, 2016). In the case of mixed-scale data, Everitt (1988) introduced the use of latent variables and thresholding approach to deal with binary and ordinal variables.…”

Section: Introductionmentioning

confidence: 99%

Model-based approach for household clustering with mixed scale variables

Carmona

Nieto‐Barajas

Canale

2018

Adv Data Anal Classif

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The Ministry of Social Development in Mexico is in charge of creating and assigning social programmes targeting specific needs in the population for the improvement of quality of life. To better target the social programmes, the Ministry is aimed to find clusters of households with the same needs based on demographic characteristics as well as poverty conditions of the household. Available data consists of continuous, ordinal, and nominal variables and the observations are not iid but come from a survey sample based on a complex design. We propose a Bayesian nonparametric mixture model that jointly models a set of latent variables, as in an underlying variable response approach, associated to the observed mixed scale data and accommodates for the different sampling probabilities. The performance of the model is assessed via simulated data. A full analysis of socio-economic conditions in households in the Mexican State of Mexico is presented. the country. To fulfil this objective, SEDESOL creates social programmes to target specific needs in the population.Currently, each existing social programme has its own rules of operation and its own way of selecting the potential households to be benefited by the programme, but in general they all use household income as the main selection criterion. In order to simplify the selection of potential candidates and to better target the programmes to the correct population, SEDESOL wants to create a clustering of households based on needs, socio-economical and demographical features as well as poverty conditions.In 2009, the Council for National Evaluation (CONEVAL, 2009) proposed a methodology for measuring the poverty conditions in households in terms of multiple indicators. These include the income dimension, social deprivations and social cohesion. As a result of this new methodology a multi-dimensional measurement was created based on seven indicators: income, and six deprivation indicators such as education, access to health services, access to social security, housing quality, access to basic public services and access to feeding. These will be the core set of variables used in the clustering later on.In January of 2004 a new general law for social development was passed in Mexico. It establishes that poverty measurements must be calculated every two years at a state level and every five years at a municipality level. For these purposes, the National Institute for Official Statistics (INEGI) implemented a survey based on a complex design of households.This national survey of income and expenses in households (ENIGH) through a module of socio-economic conditions (MCS) collects the required information to produce the multidimensional poverty indicators at a household level and in some cases at an individual level.These household poverty indicators are then expanded with the corresponding sampling design weights to produce poverty indicators at a state level.Model-based clustering approaches (McLachlan and Basford, 1988; Banfiedl and Raftery, 1993) rely on a probability ...

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Univariate Bayesian nonparametric mixture modeling with unimodal kernels

Cited by 23 publications

References 30 publications

Mixture Models With a Prior on the Number of Components

Mixture Models With a Prior on the Number of Components

Effects of Bayesian Model Selection on Frequentist Performances: An Alternative Approach

Model-based approach for household clustering with mixed scale variables

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