Modelling animal growth in random environments: An application using nonparametric estimation

Abstract

We study a stochastic differential equation growth model to describe individual growth in random environments. In particular, in this paper, we discuss the estimation of the drift and the diffusion coefficients using nonparametric methods for the case of nonequidistant data for several trajectories. We illustrate the methodology by using bovine growth data. Our goal is to assess: (i) if the parametric models (with specific functional forms for the drift and the diffusion coefficients) previously used by us to describe the evolution of bovine weight were adequate choices; (ii) whether some alternative specific parameterized functional forms of these coefficients might be suggested for further parametric analysis of this data. Modelling animal growth in random environments

Estimating reducible stochastic differential equations by conversion to a least-squares problem

“…Parameter estimation for linear SDEs, including multivariate and mixed-efects models with observation errors, has been implemented in the R packages PSM by Klim et al (2009) and ctsem by Driver et al (2017). Reducible SDEs have been used by García (1983), Lv and Pitchford (2007), Paige and Allen (2010), Filipe et al (2010), and Bu et al (2010Bu et al ( , 2016.…”

“…In addition to their traditional applications in physics and engineering (Gardiner 1985), SDEs are becoming routine in finance (Kunita 2010, Kloeden andPlaten 1992, Sec. 7.3) and pharmacokinetics (Kristensen et al 2005, Klim et al 2009, Donnet and Samson 2013, and are increasingly used in fields like econometrics (Paige and Allen 2010, Bu et al 2010, 2016, animal growth (Lv and Pitchford 2007, Strathe et al 2009, Filipe et al 2010, oncology (Sen 1989, Favetto and, and forestry (García 1983, Broad and Lynch 2006, Batho and García 2014. Other applications include Artzrouni and Reneke (1990), Cleur (2000), Driver et al (2017).…”

Profit optimization for cattle growing in a randomly fluctuating environment

“…We have used maximum likelihood estimation theory to estimate the parameter vector p = (α, β, σ). We describe details on this procedure, for instance, in [9,11] and [10]. In [11], we have seen that the best models for our data (using an AIC criterion), were the stochastic Bertalanffy-Richards model with c = 1/3, (SBRM) and the stochastic Gompertz model (SGM).…”

“…In earlier work we have studied a class of stochastic differential equation (SDE) models for individual growth in randomly fluctuating environments and we have applied such models using real data on the evolution of bovine weight (see, for instance, [8][9][10][11]). The Gompertz and the Bertalanffy-Richards stochastic models, are particular cases of this more general class of SDE models.…”

Profit Optimization of Cattle Growth with Variable Prices

“…In early work (see, for instance, Filipe et al (2012Filipe et al ( , 2010; Filipe and Braumann (2008); Filipe et al (2007)), we have studied stochastic versions of the class of deterministic models presented above where an adequate transformation of the size allows us to work with a general SDE model taking the form of a variant of the Ornstein-Uhlenbeck model. We have applied such class of models using real data on the evolution of bovine weight.…”