TY - JOUR

T1 - Inference for a discretized stochastic logistic differential equation and its application to biological growth

AU - Delgado-Vences, F.

AU - Baltazar-Larios, F.

AU - Vargas, A. Ornelas

AU - Morales-Bojórquez, E.

AU - Cruz-Escalona, V. H.

AU - Salomón Aguilar, C.

N1 - Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2022

Y1 - 2022

N2 - In this paper, we present a method to adjust a stochastic logistic differential equation (SLDE) to a set of highly sparse real data. We assume that the SLDE have two unknown parameters to be estimated. We calculate the Maximum Likelihood Estimator (MLE) to estimate the intrinsic growth rate. We prove that the MLE is strongly consistent and asymptotically normal. For estimating the diffusion parameter, the quadratic variation of the data is used. We validate our method with several types of simulated data. For more realistic cases in which we observe discretizations of the solution, we use diffusion bridges and the stochastic expectation-maximization algorithm to estimate the parameters. Furthermore, when we observe only one point for each path for a given number of trajectories we were still able to estimate the parameters of the SLDE. As far as we know, this is the first attempt to fit stochastic differential equations (SDEs) to these types of data. Finally, we apply our method to real data coming from fishery. The proposed adjustment method can be applied to other examples of SDEs and is highly applicable in several areas of science, especially in situations of sparse data.

AB - In this paper, we present a method to adjust a stochastic logistic differential equation (SLDE) to a set of highly sparse real data. We assume that the SLDE have two unknown parameters to be estimated. We calculate the Maximum Likelihood Estimator (MLE) to estimate the intrinsic growth rate. We prove that the MLE is strongly consistent and asymptotically normal. For estimating the diffusion parameter, the quadratic variation of the data is used. We validate our method with several types of simulated data. For more realistic cases in which we observe discretizations of the solution, we use diffusion bridges and the stochastic expectation-maximization algorithm to estimate the parameters. Furthermore, when we observe only one point for each path for a given number of trajectories we were still able to estimate the parameters of the SLDE. As far as we know, this is the first attempt to fit stochastic differential equations (SDEs) to these types of data. Finally, we apply our method to real data coming from fishery. The proposed adjustment method can be applied to other examples of SDEs and is highly applicable in several areas of science, especially in situations of sparse data.

KW - biological growth

KW - diffusion bridges

KW - EM algorithm

KW - Stochastic logistic differential equation

UR - http://www.scopus.com/inward/record.url?scp=85122863977&partnerID=8YFLogxK

U2 - 10.1080/02664763.2021.2024154

DO - 10.1080/02664763.2021.2024154

M3 - Artículo

AN - SCOPUS:85122863977

JO - Journal of Applied Statistics

JF - Journal of Applied Statistics

SN - 0266-4763

ER -