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

Parameter Estimation and Model Selection for Stochastic Differential Equations for Biological Growth

“…For this model, we use the quadratic variations to obtain an estimator of σ. The MLE for r is presented in [9], where the authors proved that the MLE is strongly consistent and asymp-totically normal. Let P t0 = p 0 , P t1 = p 1 , .…”

“…, P tn = p n be the observations in the interval time [0, T ]. Following [9], we have that an estimator of σ is given by σ2…”

“…We follow [9] to estimate σ, and as in the previous models, r is estimated using diffusion bridges to complete information. The expressions (18) and (19) are used in the following EM algorithm.…”

“…In this work, we calculate the likelihood function of the transition probabilities for the parameter of Gompertz and Von Bertalanffy models and obtain the MLEs for the parameters in the continuous case and use the EM algorithm to obtain the corresponding MLEs for the case of incomplete information (discrete observation). For the Logistic model, we follow the method for estimating the parameters described in [9], where the estimation combines quadratic variation of the observations and MLE via EM algorithm. For the case where only a data set corresponding to one record for each individual, but with observations of several different individuals at different points in time, we propose a novel algorithm to simulate paths of the SDEs and obtained the corresponding parameters.…”

“…Since we know that by maximizing the log-likelihood, it is possible to obtain the estimators and we conclude that we have good estimators for Gompertz and Von Bertalanffy models. For the Logistic model, the properties of the estimators were proved in [9].…”