# An ANOVA test for parameter estimability using data cloning with application to statistical inference for dynamic systems

@article{Campbell2014AnAT, title={An ANOVA test for parameter estimability using data cloning with application to statistical inference for dynamic systems}, author={David A. Campbell and Subhash R. Lele}, journal={Comput. Stat. Data Anal.}, year={2014}, volume={70}, pages={257-267} }

## 16 Citations

### Parameter redundancy and identifiability in hidden Markov models

- MathematicsMETRON
- 2019

An exhaustive summary for hidden Markov models is provided and it is shown how it can be used to investigate identifiability.

### A model‐based initial guess for estimating parameters in systems of ordinary differential equations

- Mathematics, Computer ScienceBiometrics
- 2015

A novel technique for generating good initial guesses that can be used by any estimation method on a fairly general and often applied class of systems linear in the parameters is introduced.

### Study design and parameter estimability for spatial and temporal ecological models

- Environmental ScienceEcology and evolution
- 2017

It is shown how a new statistical computing method called data cloning can be used to inform study design by assessing the estimability of parameters under different spatial and temporal scales of sampling.

### Bayesian Solution Uncertainty Quantification for Differential Equations

- Computer Science
- 2013

A formalism is proposed for inferring a fixed but a priori unknown model trajectory through Bayesian updating of a prior process conditional on model information, and a Markov chain Monte Carlo algorithm that targets this posterior distribution is presented.

### State-space models’ dirty little secrets: even simple linear Gaussian models can have estimation problems

- Environmental ScienceScientific reports
- 2016

It is demonstrated that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems, and it is urged to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.

### Application of one‐step method to parameter estimation in ODE models

- Mathematics, Computer ScienceStatistica Neerlandica
- 2018

This computationally simple technique can serve as an alternative to numerical evaluation of the popular non‐linear least squares estimator, which typically requires the use of a multistep iterative algorithm and repetitive numerical integration of the ordinary differential equation system.

### Bayesian Uncertainty Quantication for Dierential Equations

- Computer Science
- 2014

This paper develops a general methodology for the probabilistic integration of dierential equations via model based updating of a joint prior measure on the space of functions and their temporal and spatial derivatives and provides a fully Bayesian approach to model calibration.

### A guide to state–space modeling of ecological time series

- Environmental ScienceEcological Monographs
- 2021

A review of SSMs is presented that will provide a strong foundation to ecologists interested in learning about SSMs, introduce new tools to veteran SSM users, and highlight promising research directions for statisticians interested in ecological applications.

### An introduction to state-space modeling of ecological time series

- Environmental Science
- 2020

A review of SSMs is presented that will provide a strong foundation to ecologists interested in learning about SSMs, introduce new tools to veteran SSM users, and highlight promising research directions for statisticians interested in ecological applications.

## References

SHOWING 1-10 OF 25 REFERENCES

### Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning

- Mathematics
- 2010

Maximum likelihood estimation for Generalized Linear Mixed Models (GLMM), an important class of statistical models with substantial applications in epidemiology, medical statistics, and many other…

### Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood

- Computer ScienceBioinform.
- 2009

This work suggests an approach that exploits the profile likelihood that enables to detect structural non-identifiabilities, which manifest in functionally related model parameters, that might arise due to limited amount and quality of experimental data.

### Selection of optimal parameter set using estimability analysis and MSE-based model-selection criterion

- Mathematics
- 2011

Parameter estimation in complex mathematical models is difficult, especially when there are too many unknown parameters to estimate, and the available data for parameter estimation are limited.…

### Approximate Maximum Likelihood Parameter Estimation for Nonlinear Dynamic Models: Application to a Laboratory-Scale Nylon Reactor Model

- Mathematics
- 2008

Approximate maximum likelihood parameter estimation (AMLE) is a novel parameter estimation algorithm that is recently developed to address the problem of parameter estimation in continuous-time nonlinear dynamic models, in which model discrepancies are significant.

### Nonlinear parameter estimation: A case study comparison

- Computer Science
- 1986

A case study of the difficulties of parameter estimation in the industrial environment and the limitations of existing methods, a parameter estimation problem formulated by the Dow Chemical Company is presented and solved.

### Hierarchical models in ecology: confidence intervals, hypothesis testing, and model selection using data cloning.

- BiologyEcology
- 2009

This work reanalyzes part of Gause's classic Paramecium data with state-space population models containing both environmental noise and sampling error to demonstrate the use of these tools with complex ecological models in a frequentist context.

### Parameter Identifiability and Estimation of HIV/AIDS Dynamic Models

- MathematicsBulletin of mathematical biology
- 2008

It is concluded that the initial values of output (observable) variables are part of the data that can be used to estimate the unknown parameters, but the identifiability of unknown parameters is not affected if the exact initial values are measured with error.

### Experimental Design Tools for Ordinary and Algebraic Differential Equations

- Computer Science
- 2007

A heuristic procedure to compute significance levels of model parameters and allow successive elimination of redundant ones is presented and the A-criterion is chosen to evaluate the performance of the system and to compute the optimal experimental designs.