Stochastic properties of generalized finite mixture models with dependent components

AbstractIn this paper we consider a new generalized finite mixture model formed by dependent and identically distributed (d.i.d.) components. We then establish results for the comparisons of lifetimes of two such generalized finite mixture models in two different cases: (i) when the two mixture models are formed from two random vectors $\textbf{X}$ and $\textbf{Y}$ but with the same weights, and (ii) when the two mixture models are formed with the same random vectors but with different weights. Because the lifetimes of k-out-of-n systems and coherent systems are special cases of the mixture model considered, we used the established results to compare the lifetimes of k-out-of-n systems and coherent systems with respect to the reversed hazard rate and hazard rate orderings.

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Summarizing Finite Mixture Model with Overlapping Quantification

Entropy ◽

10.3390/e23111503 ◽

2021 ◽

Vol 23 (11) ◽

pp. 1503

Author(s):

Shunki Kyoya ◽

Kenji Yamanishi

Keyword(s):

Mutual Information ◽

Mixture Models ◽

Mixture Model ◽

Finite Mixture Models ◽

Finite Mixture Model ◽

Finite Mixture ◽

Model Based Clustering ◽

Multiple Components ◽

Clustering Data ◽

Novel Concept

Finite mixture models are widely used for modeling and clustering data. When they are used for clustering, they are often interpreted by regarding each component as one cluster. However, this assumption may be invalid when the components overlap. It leads to the issue of analyzing such overlaps to correctly understand the models. The primary purpose of this paper is to establish a theoretical framework for interpreting the overlapping mixture models by estimating how they overlap, using measures of information such as entropy and mutual information. This is achieved by merging components to regard multiple components as one cluster and summarizing the merging results. First, we propose three conditions that any merging criterion should satisfy. Then, we investigate whether several existing merging criteria satisfy the conditions and modify them to fulfill more conditions. Second, we propose a novel concept named clustering summarization to evaluate the merging results. In it, we can quantify how overlapped and biased the clusters are, using mutual information-based criteria. Using artificial and real datasets, we empirically demonstrate that our methods of modifying criteria and summarizing results are effective for understanding the cluster structures. We therefore give a new view of interpretability/explainability for model-based clustering.

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Modeling the crashes count using finite mixture models

Muthanna Journal of Pure Science ◽

10.52113/2/07.01.2020/13-27 ◽

2019 ◽

Vol 7 (1) ◽

pp. 13-27

Author(s):

Safaa K. Kadhem ◽

Sadeq A. Kadhim

Keyword(s):

Bayesian Inference ◽

Mixture Models ◽

Gibbs Sampler ◽

Simulation Study ◽

Finite Mixture Models ◽

Synthetic Data ◽

Finite Mixture Model ◽

Finite Mixture ◽

Model Parameters ◽

Mcmc Method

"This paper aims at the modeling the crashes count in Al Muthanna governance using finite mixture model. We use one of the most common MCMC method which is called the Gibbs sampler to implement the Bayesian inference for estimating the model parameters. We perform a simulation study, based on synthetic data, to check the ability of the sampler to find the best estimates of the model. We use the two well-known criteria, which are the AIC and BIC, to determine the best model fitted to the data. Finally, we apply our sampler to model the crashes count in Al Muthanna governance.

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Latent class and finite mixture models for multilevel data sets

Statistical Methods in Medical Research ◽

10.1177/0962280207081238 ◽

2008 ◽

Vol 17 (1) ◽

pp. 33-51 ◽

Cited By ~ 117

Author(s):

Jeroen K Vermunt

Keyword(s):

Mixture Models ◽

Random Effects ◽

Latent Class ◽

Finite Mixture Models ◽

Expectation Maximization Algorithm ◽

Likelihood Estimation ◽

Finite Mixture ◽

Model Parameters ◽

Data Sets ◽

Special Cases

An extension of latent class (LC) and finite mixture models is described for the analysis of hierarchical data sets. As is typical in multilevel analysis, the dependence between lower-level units within higher-level units is dealt with by assuming that certain model parameters differ randomly across higher-level observations. One of the special cases is an LC model in which group-level differences in the logit of belonging to a particular LC are captured with continuous random effects. Other variants are obtained by including random effects in the model for the response variables rather than for the LCs. The variant that receives most attention in this article is an LC model with discrete random effects: higher-level units are clustered based on the likelihood of their members belonging to the various LCs. This yields a model with mixture distributions at two levels, namely at the group and the subject level. This model is illustrated with three rather different empirical examples. The appendix describes an adapted version of the expectation—maximization algorithm that can be used for maximum likelihood estimation, as well as providing setups for estimating the multilevel LC model with generally available software.

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ORDERINGS OF FINITE MIXTURE MODELS WITH LOCATION-SCALE DISTRIBUTED COMPONENTS

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964820000467 ◽

2020 ◽

pp. 1-21

Author(s):

Ghobad Barmalzan ◽

Sajad Kosari ◽

Narayanaswamy Balakrishnan

Keyword(s):

Mixture Models ◽

Hazard Rate ◽

Finite Mixture Models ◽

Stochastic Order ◽

Finite Mixture ◽

Model Parameters ◽

Hazard Rate Order ◽

Reversed Hazard Rate ◽

Usual Stochastic Order ◽

Distributed Components

In this paper, we consider finite mixture models with components having distributions from the location-scale family. We then discuss the usual stochastic order and the reversed hazard rate order of such finite mixture models under some majorization conditions on location, scale and mixing probabilities as model parameters.

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Accommodating Missing Data in Mixture Models for Classification by Opinion-Changing Behavior

Journal of Educational and Behavioral Statistics ◽

10.3102/10769986026002233 ◽

2001 ◽

Vol 26 (2) ◽

pp. 233-268 ◽

Cited By ~ 1

Author(s):

Jennifer L. Hill

Keyword(s):

Missing Data ◽

Mixture Models ◽

Finite Mixture Models ◽

Finite Mixture Model ◽

Finite Mixture ◽

Pollution Reduction ◽

Model Structure ◽

Response Data ◽

New Information ◽

Do So

Popular theories in political science regarding opinion-changing behavior postulate the existence of one or both of two broad categories of people: those with stable opinions over time; and those who appear to hold no solid opinion and, when asked to make a choice, do so seemingly at random. The model presented here explores evidence for a third category: durable changers. People in this group will change their opinions in a rational, informed manner, after being exposed to new information. Survey data collected at four time points over nearly two years track Swiss citizens' readiness to support pollution-reduction policies. We analyzed the data using finite mixture models that allow estimation of the percentage in the poluation falling in each category for each question as well as the frequency of certain types of relevant behaviors within each category. These models extend the finite mixture model structure used in Hill and Kriesi (2001a,b) to accommodate missing response data. This extension increases the sample size by nearly 60% and weakens the missing-data assumptions required. We describe augmented models and fitting algorithms corresponding to different assumptions about the missing-data mechanism as well as the differences in results obtained.

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A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures

Risks ◽

10.3390/risks9060115 ◽

2021 ◽

Vol 9 (6) ◽

pp. 115

Author(s):

Despoina Makariou ◽

Pauline Barrieu ◽

George Tzougas

Keyword(s):

Decision Making ◽

Mixture Models ◽

Finite Mixture Models ◽

Risk Measures ◽

Finite Mixture ◽

Parametric Family ◽

Collective Decision Making ◽

Multiple Sources ◽

Mixture Modelling ◽

Expert Opinions

The key purpose of this paper is to present an alternative viewpoint for combining expert opinions based on finite mixture models. Moreover, we consider that the components of the mixture are not necessarily assumed to be from the same parametric family. This approach can enable the agent to make informed decisions about the uncertain quantity of interest in a flexible manner that accounts for multiple sources of heterogeneity involved in the opinions expressed by the experts in terms of the parametric family, the parameters of each component density, and also the mixing weights. Finally, the proposed models are employed for numerically computing quantile-based risk measures in a collective decision-making context.

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