Information content in data sets: A review of methods for interrogation and model comparison

Banks, Harvey Thomas; Joyner, Michele L.

doi:10.1515/jiip-2017-0096

Cited by 6 publications

(11 citation statements)

References 63 publications

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“…When an absolute statistical error model is used, we estimateθ OLS using Matlab's built-in optimization solver fmincon directly to minimize the cost function in (3). In the case when γ > 0, we use the numerical algorithm provided in [5,7] to estimateθ IRWLS which is summarized below.…”

Section: Methodsmentioning

confidence: 99%

“…For a detailed discussion on the subject, we refer the reader to [5,6,7,10] and the references therein.…”

Section: Methods For Selection Of a Mathematical Modelmentioning

confidence: 99%

“…Following the expositions in [5,7,8], we present a short description of the methodology of the inverse problem for the following general 1-dimensional dynamical model:…”

Section: Components Of Inverse Problem Studies: Mathematical and Statmentioning

confidence: 99%

“…For further and more in depth discussion on inverse problem methodology, we refer the reader to [5,7,8,11,12,22].…”

Section: Components Of Inverse Problem Studies: Mathematical and Statmentioning

confidence: 99%

See 3 more Smart Citations

The Effect of Statistical Error Model Formulation on the Fit and Selection of Mathematical Models of Tumor Growth for Small Sample Sizes

Bekele-Maxwell¹,

Noorman²,

Menda³

et al. 2018

Int. J. of Pure and Appl. Math.

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When fitting a mathematical model to a given data set using inverse problems, the correctness of both the mathematical model and the statistical error models are important since an incorrect statistical or observational model directly affects both the estimates and their corresponding standard errors. The effects of these models, among many other factors, are dependent on the sample size and the information content of the data set.In this article, we investigate how the choice of the statistical error model affects the mathematical model fit and accuracy of parameter estimates in small sample size tumor growth data sets. We specifically seek to determine the appropriate statistical error model for small sample size breast, lung and HPV tumor growth data sets obtained from studies on mice. T. Banks et alWe find that for small sample sizes the selection of the best statistical error model is not straightforward and requires the examination of multiple criteria for model fit and uncertainty.Therefore, selection of the best mathematical model is not an easy process for small sample size tumor data and selection of a model based on few data points may not prove accurate.We encourage further research on the optimal design of experiments (duration and number of observations) in order to best fit mathematical models to tumor growth data.

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Section: Methodsmentioning

confidence: 99%

“…For a detailed discussion on the subject, we refer the reader to [5,6,7,10] and the references therein.…”

Section: Methods For Selection Of a Mathematical Modelmentioning

confidence: 99%

“…Following the expositions in [5,7,8], we present a short description of the methodology of the inverse problem for the following general 1-dimensional dynamical model:…”

Section: Components Of Inverse Problem Studies: Mathematical and Statmentioning

confidence: 99%

“…For further and more in depth discussion on inverse problem methodology, we refer the reader to [5,7,8,11,12,22].…”

Section: Components Of Inverse Problem Studies: Mathematical and Statmentioning

confidence: 99%

See 2 more Smart Citations

The Effect of Statistical Error Model Formulation on the Fit and Selection of Mathematical Models of Tumor Growth for Small Sample Sizes

Bekele-Maxwell¹,

Noorman²,

Menda³

et al. 2018

Int. J. of Pure and Appl. Math.

View full text Add to dashboard Cite

show abstract

“…With accurate parameter estimates, a model solution can then realistically capture population trends, which can help, for example, investigate the minimum pesticide amount needed to reduce pest populations below an economic threshold. Examples of previous works using dynamical models to investigate information content in ecological data include [1,2,3,7].…”

mentioning

confidence: 99%

Optimal design for dynamical modeling of pest populations

Banks

Everett²,

Murad³

et al. 2018

Mathematical Biosciences &Amp; Engineering

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We apply SE-optimal design methodology to investigate optimal data collection procedures as a first step in investigating information content in ecoinformatics data sets. To illustrate ideas we use a simple phenomenological citrus red mite population model for pest dynamics. First the optimal sampling distributions for a varying number of data points are determined. We then analyze these optimal distributions by comparing the standard errors of parameter estimates corresponding to each distribution. This allows us to investigate how many data are required to have confidence in model parameter estimates in order to employ dynamical modeling to infer population dynamics. Our results suggest that a field researcher should collect at least 12 data points at the optimal times. Data collected according to this procedure along with dynamical modeling will allow us to estimate population dynamics from presence/absence-based data sets through the development of a scaling relationship. These Likert-type data sets are commonly collected by agricultural pest management consultants and are increasingly being used in ecoinformatics studies. By applying mathematical modeling with the relationship scale from the new data, we can then explore important integrated pest management questions using past and future presence/absence data sets.

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Transmission dynamics of COVID-19 in Nepal: Mathematical model uncovering effective controls

Adhikari

Gautam

Pokharel

et al. 2021

Journal of Theoretical Biology

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While most of the countries around the globe are combating the pandemic of COVID-19, the level of its impact is quite variable among different countries. In particular, the data from Nepal, a developing country having an open border provision with highly COVID-19 affected country India, has shown a biphasic pattern of epidemic, a controlled phase (until July 21, 2020) followed by an outgrown phase (after July 21, 2020). To uncover the effective strategies implemented during the controlled phase, we develop a mathematical model that is able to describe the data from both phases of COVID-19 dynamics in Nepal. Using our best parameter estimates with 95% confidence interval, we found that during the controlled phase most of the recorded cases were imported from outside the country with a small number generated from the local transmission, consistent with the data. Our model predicts that these successful strategies were able to maintain the reproduction number at around 0.21 during the controlled phase, preventing 442,640 cases of COVID-19 and saving more than 1,200 lives in Nepal. However, during the outgrown phase, when the strategies such as border screening and quarantine, lockdown, and detection and isolation, were altered, the reproduction number raised to 1.8, resulting in exponentially growing cases of COVID-19. We further used our model to predict the long-term dynamics of COVID-19 in Nepal and found that without any interventions the current trend may result in about 18.76 million cases (10.70 million detected and 8.06 million undetected) and 89 thousand deaths in Nepal by the end of 2021. Finally, using our predictive model, we evaluated the effects of various control strategies on the long-term outcome of this epidemics and identified ideal strategies to curb the epidemic in Nepal.

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Information content in data sets: A review of methods for interrogation and model comparison

Cited by 6 publications

References 63 publications

The Effect of Statistical Error Model Formulation on the Fit and Selection of Mathematical Models of Tumor Growth for Small Sample Sizes

The Effect of Statistical Error Model Formulation on the Fit and Selection of Mathematical Models of Tumor Growth for Small Sample Sizes

Optimal design for dynamical modeling of pest populations

Transmission dynamics of COVID-19 in Nepal: Mathematical model uncovering effective controls

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