scholarly journals A REMARK ON L2 DISTANCE FUNCTION AND NON-IDENTIFIABILITY PROBLEM OF FINITE MIXTURE DISTRIBUTION MODELS IN MODEL-BASED CLASSIFICATION

2019 ◽  
Vol 14 (4) ◽  
pp. 139-146
Author(s):  
Yüksel Öner ◽  
Fikriye Kabakçı ◽  
Burçin Öner ◽  
Mehmet Gürcan
Keyword(s):  
Distance Function ◽  
Mixture Distribution ◽  
Finite Mixture ◽  
Distribution Models ◽  
Model Based ◽  
Identifiability Problem

Modeling Structure and Chance in Transitions: Mixed Latent Partial Markov-Chain Models

1996 ◽  
Vol 21 (2) ◽  
pp. 91-109 ◽  
Author(s):  
Thorsten Meiser ◽  
Barbara Ohrt
Keyword(s):  
Developmental Trajectories ◽  
Mixture Distribution ◽  
Finite Mixture ◽  
Therapeutic Interventions ◽  
Model Specification ◽  
Random Fluctuation ◽  
Distribution Models ◽  
Multiple Indicators ◽  
Markov Chain Models ◽  
Infancy And Early Childhood

A family of finite mixture distribution models is presented which allows specification of basically different developmental processes in distinct latent subpopulations. In particular, random fluctuation between states for one latent subpopulation can be modeled together with stability or coherent developmental trajectories for others. Formally, these models are introduced within the framework of mixed latent Markov chains with multiple indicators per occasion. Identifiability conditions which become necessary because of the random fluctuation assumption for a part of the population are discussed. Model specification and interpretation are illustrated by an application to empirical data on therapeutic interventions in infancy and early childhood.

scholarly journals Performance of finite mixture distribution models to estimate nursery habitat contributions to fish stocks

2016 ◽  
Author(s):  
Edwin J Niklitschek ◽  
Audrey M Darnaude
Keyword(s):  
Sparus Aurata ◽  
Mixture Distribution ◽  
Finite Mixture ◽  
Data Availability ◽  
Mixed Data ◽  
Distribution Models ◽  
Elemental Ratios ◽  
Fish Stocks ◽  
Mixed Stock ◽  
Mixed Samples

Background. Otolith microchemistry applications of finite mixture distribution models (FMDM) describe mixed stocks using three sets of parameters: proportional contributions (pi), baseline parameters (θi) and number of contributing nursery origins (c#). Under ideal scenarios, c# is known and all potential sources are sampled to produce source-based ^θi estimates. Hence, ^pi is the only parameter vector estimated by FMDM from the mixed-data. If some/all nursery areas are unknown or not sampled, some or all θi and c# need to be also estimated from the mixed-data. Our goal here was to assess bias and variability in ^pi, ^θi and ^c# when estimated by FMDM, under a range of data availability scenarios. Methods. We used a comprehensive Sparus aurata dataset, tat contained otolith elemental ratios from 301 young of the year, sampled at four nursery origins, in three highly contrasting years. Using bootstrap resampling (n=1000) we produced artificial source- and mixed-samples. Source-samples simulated different scenarios where KU=0-4 nursery sources were excluded. We evaluated bias (BI) and variability (VI) in ^pi by fitting FMDM to mixed-samples with true pi=0.1-0.4. Bias and variability in ^θi and ^c# were, instead, assessed on balanced mixed stock-samples (pi=0.25). Estimations of ^c# were obtained by fitting and comparing multiple FMDMs with c#=1-9. Results. Accurate and precise ^pi estimates (BI<0.03, VI<0.07) were produced by FMDM when samples from all origins were available (KU=0). BI and VI in ^pi tended to increase rapidly as KU increased, yielding unreliable results for KU>1. BI and VI in ^θi were highly heterogeneous among cohorts and less sensitive to KU. Relatively accurate ^θi estimates (BI<0.3) were produced for cohorts 2008 and 2010, but highly biased ones for cohort 2011 (VI>0.53), at all scenarios. Variability in ^θi was relatively low (VI<0.3) and insensitive to KU, across all cohorts. While ^c# tended to underestimate c# (BI=0.05 to -2.06), its variability was relatively high (VI=0.24-1.14) across scenarios and cohorts. Both bias and variability in ^c# were highly sensitive to KU. Discussion. FMDM estimated accurate and unbiased ^pi and ^θi parameters when all origins were known and sampled. FMDM performance decreased rapidly and all three set of estimated parameters became unreliable when ≥2 origins were missing from nursery-samples. Large differences in BI and VI among cohorts emphasized the need for extensive sampling of nursery origins. Being FMDM one default method for mixed stock analysis, we strongly recommend exploring alternative FMDM implementations and extreme caution when using results from FMDM, under incomplete sampling scenarios.

scholarly journals Finite mixture distribution models of simple discrimination learning

2001 ◽  
Vol 29 (5) ◽  
pp. 659-677 ◽  
Author(s):  
Maartje E. J. Raijmakers ◽  
Conor V. Dolan ◽  
Peter C. M. Molenaar
Keyword(s):  
Discrimination Learning ◽  
Mixture Distribution ◽  
Finite Mixture ◽  
Simple Discrimination ◽  
Distribution Models

scholarly journals Performance of finite mixture distribution models to estimate nursery habitat contributions to fish stocks

2016 ◽  
Author(s):  
Edwin J Niklitschek ◽  
Audrey M Darnaude
Keyword(s):  
Sparus Aurata ◽  
Mixture Distribution ◽  
Finite Mixture ◽  
Data Availability ◽  
Mixed Data ◽  
Distribution Models ◽  
Elemental Ratios ◽  
Fish Stocks ◽  
Mixed Stock ◽  
Mixed Samples

Background. Otolith microchemistry applications of finite mixture distribution models (FMDM) describe mixed stocks using three sets of parameters: proportional contributions (pi), baseline parameters (θi) and number of contributing nursery origins (c#). Under ideal scenarios, c# is known and all potential sources are sampled to produce source-based ^θi estimates. Hence, ^pi is the only parameter vector estimated by FMDM from the mixed-data. If some/all nursery areas are unknown or not sampled, some or all θi and c# need to be also estimated from the mixed-data. Our goal here was to assess bias and variability in ^pi, ^θi and ^c# when estimated by FMDM, under a range of data availability scenarios. Methods. We used a comprehensive Sparus aurata dataset, tat contained otolith elemental ratios from 301 young of the year, sampled at four nursery origins, in three highly contrasting years. Using bootstrap resampling (n=1000) we produced artificial source- and mixed-samples. Source-samples simulated different scenarios where KU=0-4 nursery sources were excluded. We evaluated bias (BI) and variability (VI) in ^pi by fitting FMDM to mixed-samples with true pi=0.1-0.4. Bias and variability in ^θi and ^c# were, instead, assessed on balanced mixed stock-samples (pi=0.25). Estimations of ^c# were obtained by fitting and comparing multiple FMDMs with c#=1-9. Results. Accurate and precise ^pi estimates (BI<0.03, VI<0.07) were produced by FMDM when samples from all origins were available (KU=0). BI and VI in ^pi tended to increase rapidly as KU increased, yielding unreliable results for KU>1. BI and VI in ^θi were highly heterogeneous among cohorts and less sensitive to KU. Relatively accurate ^θi estimates (BI<0.3) were produced for cohorts 2008 and 2010, but highly biased ones for cohort 2011 (VI>0.53), at all scenarios. Variability in ^θi was relatively low (VI<0.3) and insensitive to KU, across all cohorts. While ^c# tended to underestimate c# (BI=0.05 to -2.06), its variability was relatively high (VI=0.24-1.14) across scenarios and cohorts. Both bias and variability in ^c# were highly sensitive to KU. Discussion. FMDM estimated accurate and unbiased ^pi and ^θi parameters when all origins were known and sampled. FMDM performance decreased rapidly and all three set of estimated parameters became unreliable when ≥2 origins were missing from nursery-samples. Large differences in BI and VI among cohorts emphasized the need for extensive sampling of nursery origins. Being FMDM one default method for mixed stock analysis, we strongly recommend exploring alternative FMDM implementations and extreme caution when using results from FMDM, under incomplete sampling scenarios.

A Segmentation Model for the Targeted Marketing of Consumer Durables

1995 ◽  
Vol 32 (4) ◽  
pp. 463-469 ◽  
Author(s):  
Barry L. Bayus ◽  
Raj Mehta
Keyword(s):  
Mixture Distribution ◽  
Finite Mixture ◽  
Consumer Durables ◽  
Empirical Application ◽  
Household Characteristics ◽  
Household Data ◽  
Potential Consumer ◽  
Consumer Durable ◽  
Managerial Implications ◽  
Targeted Marketing

The authors use finite mixture distribution theory to develop a segmentation model for targeting potential consumer durable buyers. The model enables them to identify simultaneously durable replacer segments on the basis of household characteristics and product ages and determine which of the household characteristics are significant predictors of segment membership. Using household data for five home appliances, the authors present an empirical application of the model. They also discuss managerial implications and uses of this approach.

FUZZY C-MEANS AND MIXTURE DISTRIBUTION MODELS IN THE PRESENCE OF NOISE CLUSTERS

2002 ◽  
Vol 02 (04) ◽  
pp. 573-586 ◽  
Author(s):  
SADAAKI MIYAMOTO ◽  
ARNOLD C. ALANZADO
Keyword(s):  
Em Algorithm ◽  
Statistical Model ◽  
Fuzzy Model ◽  
Mixture Distribution ◽  
Distribution Model ◽  
Distribution Models ◽  
The Em Algorithm ◽  
Mixture Distribution Model ◽  
The Relationship ◽  
Noise Cluster

This paper discusses the relationship between the K-L information based FCM method and a mixture distribution model with the EM algorithm when a noise cluster is assumed. Equivalence between the two methods in the sense that the derived solutions are the same is proved. From the equivalence a parameter in the fuzzy model can be estimated by using the mixture distribution model. A regularized FCM algorithm with the noise cluster is moreover derived for which the equivalent statistical model with the EM algorithm does not exist.

scholarly journals Genetic Algorithms for Finite Mixture Model Based Voxel Classification in Neuroimaging

2007 ◽  
Vol 26 (5) ◽  
pp. 696-711 ◽  
Author(s):  
J. Tohka ◽  
E. Krestyannikov ◽  
I.D. Dinov ◽  
A.M. Graham ◽  
D.W. Shattuck ◽  
...  
Keyword(s):  
Genetic Algorithms ◽  
Mixture Model ◽  
Finite Mixture Model ◽  
Finite Mixture ◽  
Model Based ◽  
Voxel Classification
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