scholarly journals Effect of Probability Distribution of the Response Variable in Optimal Experimental Design with Applications in Medicine

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1010
Author(s):  
Sergio Pozuelo-Campos ◽  
Víctor Casero-Alonso ◽  
Mariano Amo-Salas
Keyword(s):  
Experimental Design ◽  
Probability Distribution ◽  
Normal Distribution ◽  
Design Theory ◽  
Information Matrix ◽  
Optimal Experimental Design ◽  
Quadratic Model ◽  
Linear Quadratic ◽  
Hill Model ◽  
Response Variable

In optimal experimental design theory it is usually assumed that the response variable follows a normal distribution with constant variance. However, some works assume other probability distributions based on additional information or practitioner’s prior experience. The main goal of this paper is to study the effect, in terms of efficiency, when misspecification in the probability distribution of the response variable occurs. The elemental information matrix, which includes information on the probability distribution of the response variable, provides a generalized Fisher information matrix. This study is performed from a practical perspective, comparing a normal distribution with the Poisson or gamma distribution. First, analytical results are obtained, including results for the linear quadratic model, and these are applied to some real illustrative examples. The nonlinear 4-parameter Hill model is next considered to study the influence of misspecification in a dose-response model. This analysis shows the behavior of the efficiency of the designs obtained in the presence of misspecification, by assuming heteroscedastic normal distributions with respect to the D-optimal designs for the gamma, or Poisson, distribution, as the true one.

Optimal experimental design for machine learning using the Fisher information matrix

2018 ◽  
Vol 144 (3) ◽  
pp. 1730-1730 ◽  
Author(s):  
Tracianne B. Neilsen ◽  
Mark K. Transtrum ◽  
David F. Van Komen ◽  
David P. Knobles
Keyword(s):  
Machine Learning ◽  
Experimental Design ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Optimal Experimental Design

Multiple-objective criteria for optimal experimental design: application to ferrokinetics

1985 ◽  
Vol 248 (3) ◽  
pp. R378-R386 ◽  
Author(s):  
M. H. Nathanson ◽  
G. M. Saidel
Keyword(s):  
Experimental Design ◽  
Optimal Design ◽  
Objective Function ◽  
Information Matrix ◽  
Optimal Experimental Design ◽  
Multiple Objective ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Experimental Conditions ◽  
New Criterion

Optimal experimental design is used to predict the experimental conditions that will allow the "best" estimates of model parameters. A variety of criteria must be considered before an optimal design is chosen. Maximizing the determinant of the information matrix (D optimality), which tends to produce the most precise simultaneous estimates of all parameters, is commonly considered as the primary criterion. To complement this criterion, we present another whose effect is to reduce the interaction among the parameter estimates so that changes in any one parameter can be more distinct. This new criterion consists of maximizing the determinant of an appropriately scaled information matrix (M optimality). These criteria are applied jointly in a multiple-objective function. To illustrate the use of these concepts, we develop an optimal experimental design of blood sampling schedules using a detailed ferrokinetic model.

A numerical identifiability test for state-space models - application to optimal experimental design

2001 ◽  
Vol 43 (7) ◽  
pp. 339-346 ◽  
Author(s):  
M. E. Hidalgo ◽  
E. Ayesa
Keyword(s):  
Experimental Design ◽  
State Space ◽  
Information Matrix ◽  
Optimal Experimental Design ◽  
Mathematical Tool ◽  
Rigorous Analysis ◽  
Estimation Errors ◽  
Identifiability Analysis ◽  
Discrete Approach ◽  
Calibration Experiment

This paper describes a mathematical tool for identifiability analysis, easily applicable to high order non-linear systems modelled in state-space and implementable in simulators with a time-discrete approach. This procedure also permits a rigorous analysis of the expected estimation errors (average and maximum) in calibration experiments. The methodology is based on the recursive numerical evaluation of the information matrix during the simulation of a calibration experiment and in the setting-up of a group of information parameters based on geometric interpretations of this matrix. As an example of the utility of the proposed test, the paper presents its application to an optimal experimental design of ASM Model No.1 calibration, in order to estimate the maximum specific growth rate μH and the concentration of heterotrophic biomass XBH.

scholarly journals Introducing Parameter Clustering to the OED Procedure for Model Calibration of a Synthetic Inducible Promoter in S. cerevisiae

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 1053
Author(s):  
Zhaozheng Hou
Keyword(s):  
Experimental Design ◽  
Model Calibration ◽  
Linear Models ◽  
Estimation Error ◽  
Effective Means ◽  
Information Matrix ◽  
Optimal Experimental Design ◽  
Clustering Methods ◽  
Lower Estimation ◽  
Calibration Accuracy

In recent years, synthetic gene circuits for adding new cell features have become one of the most powerful tools in biological and pharmaceutical research and development. However, because of the inherent non-linearity and noisy experimental data, the experiment-based model calibration of these synthetic parts is perceived as a laborious and time-consuming procedure. Although the optimal experimental design (OED) based on the Fisher information matrix (FIM) has been proved to be an effective means to improve the calibration efficiency, the required calculation increases dramatically with the model size (parameter number). To reduce the OED complexity without losing the calibration accuracy, this paper proposes two OED approaches with different parameter clustering methods and validates the accuracy of calibrated models with in-silico experiments. A model of an inducible synthetic promoter in S. cerevisiae is adopted for bench-marking. The comparison with the traditional off-line OED approach suggests that the OED approaches with both of the clustering methods significantly reduce the complexity of OED problems (for at least 49.0%), while slightly improving the calibration accuracy (11.8% and 19.6% lower estimation error in average for FIM-based and sensitivity-based approaches). This study implicates that for calibrating non-linear models of biological pathways, cluster-based OED could be a beneficial approach to improve the efficiency of optimal experimental design.

Synthesis of optimal experiment designs under the conditions of Generalized Lambda-distribution of errors for models with errors in variables

2020 ◽  
pp. 130-141
Author(s):  
Владимир Семенович Тимофеев ◽  
Екатерина Алексеевна Хайленко
Keyword(s):  
Experimental Design ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Experimental Designs ◽  
Optimal Experimental Design ◽  
Efficiency Function ◽  
Explanatory Variables ◽  
Generalized Lambda Distribution ◽  
Optimal Experiment

Рассмотрена задача планирования эксперимента в условиях появления ошибок в объясняющих переменных. Сформулировано и доказано утверждение о способе вычисления элементов информационной матрицы Фишера с использованием обобщенного лямбда-распределения, доказано следствие о способе вычисления функции эффективности плана эксперимента. Сравнение результатов вычисления функции эффективности с использованием выведенного в следствии соотношения и с помощью известного соотношения для нормального распределения ошибок показало, что результаты совпадают. Построены оптимальные планы эксперимента для различных распределений случайных компонент. The problem of experimental design under conditions of errors in the explanatory variables is considered. The proposition of the method for calculating the Fisher information matrix elements using the Generalized Lambda-distribution is formulated and proved, the consequence of the method for calculating the efficiency function of the experimental design is proved. This method of calculating the Fisher information matrix takes into account the heterogeneity of the errors in random distribution throughout the planning area. In this paper, studies of the synthesis of optimal experimental designs using proven proposition and consequence under various conditions of computational experiments are presented. The results of calculating the efficiency function using the obtained relation and using the known relation for the normal distribution of errors are compared, it is found that the results coincide. Optimal experimental designs are constructed for various distributions of random components. The results of the synthesis of optimal experimental design showed that when function of efficiency is constant throughout the planning area then the optimal experimental design is equilibrium plan. When there are differences in the values of the efficiency function in the planning area, the optimal plan ceases to be equilibrium

scholarly journals Practical Identifiability Analysis and Optimal Experimental Design for the Parameter Estimation of the ASM2d-Based EBPR Anaerobic Submodel

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Zhenliang Li ◽  
Peili Lu ◽  
Daijun Zhang ◽  
Tian Zhang
Keyword(s):  
Parameter Estimation ◽  
Experimental Design ◽  
Information Matrix ◽  
Phosphorus Release ◽  
Optimal Experimental Design ◽  
Identifiability Analysis ◽  
Practical Identifiability ◽  
Optimal Experimental Condition ◽  
Reliable Parameter ◽  
Estimation Precision

Identifiability analysis is a precondition for reliable parameter estimation. Building on previous work on structural identifiability, this paper focuses on the practical identifiability and optimal experimental design (OED) of the EBPR anaerobic submodel. The nonnegative determinant of the Fisher information matrix (FIM) found in this study clearly demonstrates that the parametersYPO4,KA,qPHA, andXPAOin the submodel are practically identifiable usingSAandSPO4as the measured variables and fixingKPPas the default value. Furthermore, fixingKPPto study the practical identifiability of the other parameters and to estimate their values is shown to be valid. Subsequently, a modeling-based procedure for the OED for parameter estimation was proposed and applied successfully to anaerobic phosphorus release experiments. According to the FIMD-criterion, the optimal experimental condition was determined to be an initialSAconcentration of 300 mg/L. Under the optimal experimental condition, errors in the values ofYPO4,KA,qPHA, andXPAOare all below 20%, and the estimated values were 0.35 ± 0.02 mg P/mg COD, 3.88 ± 0.41 mg COD/L, 3.35 ± 0.27 mg P/(mgCOD⁎d-1), and 1500 ± 72 mg COD/L, respectively. Compared to the results from the nonoptimal experimental condition, the practical identifiability and the estimation precision of the four parameters were improved.

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