Stanford & Smith nonlinear model in the description of CO2 evolved from soil treated with swine manure: maximum entropy prior

Abstract

The dynamics of organic waste decomposition in the soil can be described by nonlinear regression models, however, the theory for regression models is valid for sufficiently large samples, and in general, in small samples, these properties are unknown. One of the methods for data analysis that has been widely used to overcome this problem is the bayesian inference, as it has the advantage of being able to work with small samples, in addition to allowing the incorporation of information from previous studies, and even having a probability distribution for the parameters, consequently, to present a direct interpretation for the credibility interval. However, criticism has been made because of the effect that a prior subjective distribution can have on posterior distribution. One way of determining objective prior is through of maximum entropy prior distributions. For data of organic waste decomposition in the soil, little is known about the probability distributions of the parameters. The present study aimed to use of maximum entropy prior distributions to the parameters of the Stanford & Smith nonlinear model. In addition, using simulated data, to understand the effect that hyperparameters of prior distribution has on the posterior curve, and also to apply the methodology in the description of CO2 mineralization data from swine manure applied to the soil surface. Data analyzed came from an experiment conducted in a laboratory that evaluated the carbon mineralization of swine manure on the soil surface over time. The posterior distributions were obtained, so the bayesian methodology with maximum entropy prior was efficient in the study of the Stanford & Smith nonlinear model to the data of carbon mineralization of swine manure on the soil surface.