Model comparison tests to determine data information content

Abstract

In the context of inverse or parameter estimation problems we demonstrate the use of statistically based model comparison tests in several examples of practical interest. In these examples we are interested in questions related to information content of a particular given data set and whether the data will support a more complicated model to describe it. In the first example we compare fits for several different models to describe simple decay in a size histogram for aggregates in amyloid fibril formation. In a second example we investigate whether the information content in data sets for the pest Lygus hesperus in cotton fields as it is currently collected is sufficient to support a model in which one distinguishes between nymphs and adults. Finally in a third example with data for patients having undergone an organ transplant, we question whether the data content is sufficient to estimate more than 5 of the fundamental parameters in a particular dynamic model.

Modelling populations ofLygus hesperuson cotton fields in the San Joaquin Valley of California: the importance of statistical and mathematical model choice

“…In other words, it is a beneficial exercise to determine if there is a correlation between parameter estimation accuracy/data information content (see also [8] for examples) and frequency of pesticide application. In addition, we would like to consider a 2-D compartmental model, as in previous research [9] and use the model comparison test to determine if the data can support time-dependent parameters for each age class. This could not only shed light on the class-specific effects of pesticides (on both nymphs and adults), but could also provide further insight into whether distinguishing between nymph and adult age classes during data collection is beneficial to understanding population dynamics, in the case of pesticide-treated fields.…”

“…In previous modelling attempts of L. hesperus population in untreated fields, an exponential model adequately described the total population growth [9]. However, manipulations of the system, such as pesticide applications, time-varying presence of predators or prey, or resource changes, can be mathematically represented with time-varying parameters.…”

“…This can be described as an understanding of how strongly one can carry out model validation given a particular data set. There are many ways to quantify the content of a data set, including use of sensitivities, the Fisher Information Matrix and Akaike Information Criteria methods [4,8,9,13,38]. Simple mathematical models, parameterized with field data, are often used to then predict the consequences of increasing or decreasing pesticide exposure in the field.…”

Modelling Pesticide Treatment Effects on Lygus hesperus in Cotton Fields

“…In most cases, this includes selection of both statistical and mathematical models in fits-to-data -something that is not always fully explicitly addressed in the ecological literature. We first addressed this gap in [1,2] using data from pest population counts of Lygus hesperus Knight (Hemiptera: Meridae) feeding on pesticide-treated cotton fields in the San Joaquin Valley of California [22].…”

“…In particular, in [1,2] we investigated the effect of pesticide treatments on the growth dynamics of Lygus hesperus. This was done by constructing mathematical models and then fitting these models to field data so as to estimate growth rate parameters of Lygus hesperus both in the absence and in the presence of pesticide application.…”