Density estimation and comparison with a penalized mixture approach

Schellhase, Christian; Kauermann, Göran

doi:10.1007/s00180-011-0289-6

Cited by 32 publications

(36 citation statements)

References 42 publications

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“…Adopting a global view, we can estimate the mixture in (1) as a whole using a non-parametric maximum likelihood approach in combination with the Vertex Exchange Method [9] or through the application of a penalised mixture approach [10]. However, in this paper, we will apply a local view and focus on the wild-type component only.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the wild‐type minimum inhibitory concentration value distribution

Jaspers

Aerts

Verbeke

et al. 2013

Statistics in Medicine

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Antimicrobial resistance has become one of the main public health burdens of the last decades, and monitoring the development and spread of non-wild-type isolates has therefore gained increased interest. Monitoring is performed based on the minimum inhibitory concentration (MIC) values, which are collected through the application of dilution experiments. In order to account for the unobserved population heterogeneity of wild-type and non-wild-type isolates, mixture models are extremely useful. Instead of estimating the entire mixture globally, it was our major aim to provide an estimate for the wild-type first component only. The characteristics of this first component are not expected to change over time, once the wild-type population has been confidently identified for a given antimicrobial. With this purpose, we developed a new method based on the multinomial distribution, and we carry out a simulation study to study the properties of the new estimator. Because the new approach fits within the likelihood framework, we can compare distinct distributional assumptions in order to determine the most suitable distribution for the wild-type population. We determine the optimal parameters based on the AIC criterion, and attention is also paid to the model-averaged approach using the Akaike weights. The latter is thought to be very suitable to derive specific characteristics of the wild-type distribution and to determine limits for the wild-type MIC range. In this way, the new method provides an elegant means to compare distinct distributional assumptions and to quantify the wild-type MIC distribution of specific antibiotic-bacterium combinations.

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Section: Introductionmentioning

confidence: 99%

Estimation of the wild‐type minimum inhibitory concentration value distribution

Jaspers

Aerts

Verbeke

et al. 2013

Statistics in Medicine

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“…Working with densities is often even more intuitive than using distribution functions and there exists a broad literature on mixture models dealing with density estimation (e.g. Schellhase and Kauermann 2012). However, as pointed out in the introduction, transferring the two sample problem to the density framework is not straightforwardly achieved by applying the existing techniques and may be computationally more demanding, so that much work has to be done here.…”

Section: Resultsmentioning

confidence: 99%

“…As shown by Hall et al (2005), the quantities in a reasonable mixture model with two nonparametric components are not identifiable for one-and two-dimensional problems even under certain independence assumptions. 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).…”

Section: Introductionmentioning

confidence: 99%

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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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“…The first stage determines the estimates of the first component using the MBM. Fixing the so-obtained estimates as being the true parameters of the wildtype component, that is, θ 1 , the density of the second component is determined using an extended version of the penalized mixture (PM) approach by Schellhase and Kauermann (2012). Nevertheless, a drawback of this two-stage procedure is that the parameters of the first component are not updated, but kept fixed at the initial estimates provided by the MBM.…”

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confidence: 99%

A Bayesian approach to the semiparametric estimation of a minimum inhibitory concentration distribution

Jaspers¹,

Lambert²,

Aerts³

2016

Ann. Appl. Stat.

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Bacteria that have developed a reduced susceptibility against antimicrobials pose a major threat to public health. Hence, monitoring their distribution in the general population is of major importance. This monitoring is performed based on minimum inhibitory concentration (MIC) values, which are collected through dilution experiments. We present a semiparametric mixture model to estimate the MIC density on the full continuous scale. The wild-type first component is assumed to be of a parametric form, while the nonwild-type second component is modelled nonparametrically using Bayesian P-splines combined with the composite link model. A Metropolis within Gibbs strategy was used to draw a sample from the joint posterior. The newly developed method was applied to a specific bacterium-antibiotic combination, that is, Escherichia coli tested against ampicillin. After obtaining an estimate for the entire density, model-based classification can be performed to check whether or not an isolate belongs to the wild-type subpopulation. The performance of the new method, compared to two existing competitors, is assessed through a small simulation study.

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Density estimation and comparison with a penalized mixture approach

Cited by 32 publications

References 42 publications

Estimation of the wild‐type minimum inhibitory concentration value distribution

Estimation of the wild‐type minimum inhibitory concentration value distribution

Correcting statistical models via empirical distribution functions

A Bayesian approach to the semiparametric estimation of a minimum inhibitory concentration distribution

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