Derivation of ISRP using localized MLE method
Bhowmick et al. (2014) proposed the derivation method of ISRP but it has some serious limitations. For non-monotonic data and highly nonlinear models, the computation of interval estimates using Bhowmick et al. (2014)’s method is almost impossible and may suffer from significant approximation errors. To address these limitations Karim and Bhowmick (2023) proposed a computational approach based on the maximum likelihood estimation method to obtain interval estimates of parameters. The new methodology of ISRP is more stable and efficient compared to the previous approach. The most important advantage is that it can be implemented using existing optimizers in software packages efficiently, therefore, giving more accessibility to the practitioners. The simulation studies for the theoretical validation of the computational-based proposed estimation process and comparison between existing and new proposed method has been carried out in Karim and Bhowmick (2023). Also, the proposed method has been applied to derive the ISRP from real data sets (Karim and Bhowmick, 2023).
Here, we will demonstrate the derivation of ISRP by using the localized MLE method provided by Karim and Bhowmick (2023) with the help of R software.
References:
Bhowmick A.R., Chattopadhyay G., Bhattacharya S., 2014. Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach. J Biol Phys; 40(1):71–95.
Karim, M.A.U., Bhowmick, A.R., 2023+. An improved approximation of interval-specific estimates of parameters for biological growth models. Journal of Biological Physics (Under review).