Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach

Abstract In this communication, based upon the stochastic Gompertz law of population growth, we have reformulated the Leaky Competing Accumulator (LCA) model with multiple alternatives such that the positive-definiteness of evidence accumulation is automatically satisfied. By exploiting the Lie symm...

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Autores principales:	Chi-Fai Lo, Ho-Yan Ip
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/b4f69b4814954f83948fbb101210802f
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spelling	oai:doaj.org-article:b4f69b4814954f83948fbb101210802f2021-12-02T15:49:31ZModified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach10.1038/s41598-021-90356-72045-2322https://doaj.org/article/b4f69b4814954f83948fbb101210802f2021-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-90356-7https://doaj.org/toc/2045-2322Abstract In this communication, based upon the stochastic Gompertz law of population growth, we have reformulated the Leaky Competing Accumulator (LCA) model with multiple alternatives such that the positive-definiteness of evidence accumulation is automatically satisfied. By exploiting the Lie symmetry of the backward Kolmogorov equation (or Fokker–Planck equation) assoicated with the modified model and applying the Wei–Norman theorem, we have succeeded in deriving the N-dimensional joint probability density function (p.d.f.) and marginal p.d.f. for each alternative in closed form. With this joint p.d.f., a likelihood function can be constructed and thus model-fitting procedures become feasible. We have also demonstrated that the calibration of model parameters based upon the Monte Carlo simulated time series is indeed both efficient and accurate. Moreover, it should be noted that the proposed Lie-algebraic approach can also be applied to tackle the modified LCA model with time-varying parameters.Chi-Fai LoHo-Yan IpNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-7 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Chi-Fai Lo Ho-Yan Ip Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach
description	Abstract In this communication, based upon the stochastic Gompertz law of population growth, we have reformulated the Leaky Competing Accumulator (LCA) model with multiple alternatives such that the positive-definiteness of evidence accumulation is automatically satisfied. By exploiting the Lie symmetry of the backward Kolmogorov equation (or Fokker–Planck equation) assoicated with the modified model and applying the Wei–Norman theorem, we have succeeded in deriving the N-dimensional joint probability density function (p.d.f.) and marginal p.d.f. for each alternative in closed form. With this joint p.d.f., a likelihood function can be constructed and thus model-fitting procedures become feasible. We have also demonstrated that the calibration of model parameters based upon the Monte Carlo simulated time series is indeed both efficient and accurate. Moreover, it should be noted that the proposed Lie-algebraic approach can also be applied to tackle the modified LCA model with time-varying parameters.
format	article
author	Chi-Fai Lo Ho-Yan Ip
author_facet	Chi-Fai Lo Ho-Yan Ip
author_sort	Chi-Fai Lo
title	Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach
title_short	Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach
title_full	Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach
title_fullStr	Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach
title_full_unstemmed	Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach
title_sort	modified leaky competing accumulator model of decision making with multiple alternatives: the lie-algebraic approach
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/b4f69b4814954f83948fbb101210802f
work_keys_str_mv	AT chifailo modifiedleakycompetingaccumulatormodelofdecisionmakingwithmultiplealternativestheliealgebraicapproach AT hoyanip modifiedleakycompetingaccumulatormodelofdecisionmakingwithmultiplealternativestheliealgebraicapproach
_version_	1718385713590829056

Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach

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