Fisher Identifiability Analysis of Longitudinal Vehicle Dynamics

This paper investigates the theoretical Cram´er-Rao bounds on estimation accuracy of longitudinal vehicle dynamics parameters. This analysis is motivated by the value of parameter estimation in various applications, including chassis model validation and active safety. Relevant literature addresses this demand through algorithms capable of estimating chassis parameters for diverse conditions. While the implementation of such algorithms has been studied, the question of fundamental limits on their accuracy remains largely unexplored. We address this question by presenting two contributions. First, this paper presents theoretical findings which reveal the prevailing effects underpinning vehicle chassis parameter identifiability. We then validate these findings with data from on-road experiments. Our results demonstrate, among a variety of effects, the strong relevance of road grade variability in determining parameter identifiability from a drive cycle. These findings can motivate improved experimental designs in the future.

Combined State and Parameter Identifiability for a Model of Drug-Resistant Cancer Dynamics

This article analyzes the combined parameter and state identifiability for a model of a cancerous tumor's growth dynamics. The model describes the impact of drug administration on the growth of two populations of cancer cells: a drug-sensitive population and a drug-resistant population. The model's dynamic behavior depends on the underlying values of its state variables and parameters, including the initial sizes and growth rates of the drug sensitive and drug-resistant populations, respectively. The article's primary goal is to use Fisher identifiability analysis to derive and analyze the Cram´er-Rao theoretical bounds on the best-achievable accuracy with which this estimation can be performed locally. This extends previous work by the authors, which focused solely on state estimation accuracy. This analysis highlights two key scenarios where estimation accuracy is particularly poor. First, a critical drug administration rate exists where the model's state observability is lost, thereby making the independent estimation of the drug-sensitive and drug-resistant population sizes impossible. Second, a different critical drug administration rate exists that brings the overall growth rate of the drug-sensitive population to zero, thereby worsening model parameter identifiability.

Parameter identifiability and model selection for sigmoid population growth models

Sigmoid growth models, such as the logistic and Gompertz growth models, are widely used to study various population dynamics ranging from microscopic populations of cancer cells, to continental-scale human populations. Fundamental questions about model selection and precise parameter estimation are critical if these models are to be used to make useful inferences about underlying ecological mechanisms. However, the question of parameter identifiability for these models -- whether a data set contains sufficient information to give unique or sufficiently precise parameter estimates for the given model -- is often overlooked; We use a profile-likelihood approach to systematically explore practical parameter identifiability using data describing the re-growth of hard coral cover on a coral reef after some ecological disturbance. The relationship between parameter identifiability and checks of model misspecification is also explored. We work with three standard choices of sigmoid growth models, namely the logistic, Gompertz, and Richards' growth models; We find that the logistic growth model does not suffer identifiability issues for the type of data we consider whereas the Gompertz and Richards' models encounter practical non-identifiability issues, even with relatively-extensive data where we observe the full shape of the sigmoid growth curve. Identifiability issues with the Gompertz model lead us to consider a further model calibration exercise in which we fix the initial density to its observed value, neglecting its uncertainty. This is a common practice, but the results of this exercise suggest that parameter estimates and fundamental statistical assumptions are extremely sensitive under these conditions; Different sigmoid growth models are used within subdisciplines within the biology and ecology literature without necessarily considering whether parameters are identifiable or checking statistical assumptions underlying model family adequacy. Standard practices that do not consider parameter identifiability can lead to unreliable or imprecise parameter estimates and hence potentially misleading interpretations of the underlying mechanisms of interest. While tools in this work focus on three standard sigmoid growth models and one particular data set, our theoretical developments are applicable to any sigmoid growth model and any relevant data set. MATLAB implementations of all software available on GitHub.

Identifiability analysis for models of the translation kinetics after mRNA transfection

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.