DETECTING LATENT TAXA: MONTE CARLO COMPARISON OF TAXOMETRIC, MIXTURE MODEL, AND CLUSTERING PROCEDURES

AbstractWe extend the uniform mixture model of Gao et al. (Ann Oper Res, 2019. 10.1007/s10479-019-03236-9) to the case of linear regression. Gao et al. (Ann Oper Res, 2019. 10.1007/s10479-019-03236-9) proposed that to characterize the probability distributions of multimodal and irregular data observed in engineering, a uniform mixture model can be used. This model is a weighted combination of multiple uniform distribution components. This case is of empirical interest since, in many instances, the distribution of the error term in a linear regression model cannot be assumed unimodal. Bayesian methods of inference organized around Markov chain Monte Carlo are proposed. In a Monte Carlo experiment, significant efficiency gains are found in comparison to least squares justifying the use of the uniform mixture model.

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A Novel Approach for Multimodal Biometric Score Fusion Using Gaussian Mixture Model and Monte Carlo Method

2009 International Conference on Advances in Recent Technologies in Communication and Computing ◽

10.1109/artcom.2009.8 ◽

2009 ◽

Author(s):

Raghavendra R. ◽

Ashok Rao ◽

Hemantha Kumar G.

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Gaussian Mixture Model ◽

Mixture Model ◽

Gaussian Mixture ◽

Novel Approach ◽

Score Fusion

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Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2008.0178 ◽

2008 ◽

Vol 363 (1512) ◽

pp. 3955-3964 ◽

Cited By ~ 52

Author(s):

Mark Pagel ◽

Andrew Meade

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Mixture Model ◽

Branch Length ◽

Monte Carlo Algorithm ◽

Morphological Data ◽

Reversible Jump ◽

Rate Variation ◽

Ancestral State

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon—known as heterotachy—can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our ‘pattern-heterogeneity’ mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of ‘significance’ such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.

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Nonlinear mixture model of mixed pixels in remote sensing satellite images based on Monte Carlo simulation

Advances in Space Research ◽

10.1016/j.asr.2007.04.096 ◽

2008 ◽

Vol 41 (11) ◽

pp. 1715-1723 ◽

Cited By ~ 22

Author(s):

Kohei Arai

Keyword(s):

Remote Sensing ◽

Monte Carlo Simulation ◽

Monte Carlo ◽

Mixture Model ◽

Satellite Images ◽

Mixed Pixels ◽

Remote Sensing Satellite

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Monte Carlo Based Non-Linear Mixture Model of Earth Observation Satellite Imagery Pixel Data

International Journal of Advanced Computer Science and Applications ◽

10.14569/ijacsa.2012.030804 ◽

2012 ◽

Vol 3 (8) ◽

Author(s):

Kohei Arai

Keyword(s):

Monte Carlo ◽

Mixture Model ◽

Satellite Imagery ◽

Earth Observation ◽

Non Linear ◽

Linear Mixture Model ◽

Earth Observation Satellite

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Hamiltonian Monte Carlo with Random Effect for Analyzing Cyclist Crash Severity

Signals ◽

10.3390/signals2030032 ◽

2021 ◽

Vol 2 (3) ◽

pp. 527-539

Author(s):

Mahdi Rezapour ◽

Khaled Ksaibati

Keyword(s):

Monte Carlo ◽

Mixture Model ◽

Random Effect ◽

Finite Mixture Model ◽

Finite Mixture ◽

Model Fit ◽

Crash Severity ◽

Optimum Amount ◽

Mixed Effect ◽

Hamiltonian Monte Carlo

Vulnerable traffic users, such as bikers and pedestrians, account for a significant number of fatalities on the roadways. Extensive research has been conducted in the literature review to identify factors to those crashes. Studying factors to those crashes is especially important in the Western state in the US, due to one of the highest fatality rates in the nation and its unique geographic conditions. The first step in identifying factors to the severity of cyclist crashes is to find the underlying factors to that type of crash, while accounting for the heterogeneity in the dataset. Various techniques such as mixed parameter or mixed effect models have been employed in the literature to account for the heterogeneity of the dataset. In the mixed effect model, often the random effect parameter has been assigned subjectively, and based on some attributes and engineering intuitions. Those assignments are expected to account for the heterogeneity in the dataset and enhancement of the model fit. However, a question might arise whether those factors could account for an optimum amount of the heterogeneity in the dataset. A more reasonable way might be to let the algorithm such as the finite mixture model (FMM) to identify those clusters based on parameters of the Gaussian model, means and covariance matrices of the dataset, and allocate each observation to the related clusters. Thus, in this study, to capture optimum amount of heterogeneity, first we implemented the finite mixture model in the context of maximum likelihood, due the label switching issue of the method in the context of the Bayesian method. After assignment of the parameters to the observation, the main method of Hamiltonian Monte Carlo (HMC) with random effect was implemented. The results highlighted a significant improvement in the model fit, in terms of Widely Applicable Information Criterion (WAIC). The results of this study highlighted factors such as older biker age, increased number of lanes, nighttime travelling, increased posted speed limit and driving while under emotional conditions are some factors contributing to an increased severity of bikers’ crash severity. Extensive discussion has been made regarding the methodological algorithms and model parameters estimations.

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