Analysis of steady-state carbon tracer experiments using akaike information criteria

Simultaneous Equations Models (SEM) is a statistical technique widely used in economic science to model the simultaneity relationship between variables. In the past years, this technique has also been used in other fields such as psychology or medicine. Thus, the development of new estimating methods is an important line of research. In fact, if we want to apply the SEM to medical problems with the main goal being to obtain the best approximation between the parameters of model and their estimations. This paper shows a computational study between different methods for estimating simultaneous equations models as well as a new method which allows the estimation of those parameters based on the optimization of the Bayesian Method of Moments and minimizing the Akaike Information Criteria. In addition, an entropy measure has been calculated as a parameter criteria to compare the estimation methods studied. The comparison between those methods is performed through an experimental study using randomly generated models. The experimental study compares the estimations obtained by the different methods as well as the efficiency when comparing solutions by Akaike Information Criteria and Entropy Measure. The study shows that the proposed estimation method offered better approximations and the entropy measured results more efficiently than the rest.

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Estimates of Michaelis-Menten Constants for the Two Membranes of the Brain Endothelium

Journal of Cerebral Blood Flow & Metabolism ◽

10.1038/jcbfm.1984.33 ◽

1984 ◽

Vol 4 (2) ◽

pp. 241-249 ◽

Cited By ~ 65

Author(s):

Albert Gjedde ◽

Ove Christensen

Keyword(s):

Steady State ◽

Endothelial Cell ◽

Transport Properties ◽

Glucose Transport ◽

Cell Membranes ◽

Experimental Studies ◽

Facilitated Diffusion ◽

Capillary Endothelial Cells ◽

The Individual ◽

Tracer Experiments

Tracer studies on facilitated diffusion across the blood–brain barrier lead to the calculation of Michaelis-Menten constants that describe the rate of transport. However, the barrier consists of two endothelial cell membranes, and the relevance of single Michaelis-Menten constants in relation to the two cell membranes is unknown. We have formulated a model of two endothelial cell membranes and show that the measured Michaelis-Menten constants are simple functions of the properties of the individual membranes when transport across the endothelium is rapid ( P1 > 10−6 cm s−1). We also show that the Michaelis-Menten constants determined in tracer experiments describe facilitated diffusion in the steady state only if the two membranes have similar transport properties. As an application of this observation, we have examined three experimental studies that measure glucose transport in the steady state and show that the Michaelis-Menten constants for glucose transport calculated from the tracer experiments are equal to the constants calculated from the steady-state experiments. We conclude that the luminal and abluminal membranes of brain capillary endothelial cells have equal glucose transport properties.

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Indian COVID-19 dynamics: Prediction using autoregressive integrated moving average modelling

SCRIPTA MEDICA ◽

10.5937/scriptamed52-29893 ◽

2021 ◽

Vol 52 (1) ◽

pp. 6-14

Author(s):

Amit Tak ◽

Sunita Dia ◽

Mahendra Dia ◽

Todd Wehner

Keyword(s):

Root Mean Square Error ◽

Real Time ◽

Mean Square Error ◽

Root Mean Square ◽

Moving Average ◽

Information Criteria ◽

Evidence Based ◽

Mean Square ◽

Autoregressive Integrated Moving Average ◽

Akaike Information Criteria

Background: The forecasting of Coronavirus Disease-19 (COVID-19) dynamics is a centrepiece in evidence-based disease management. Numerous approaches that use mathematical modelling have been used to predict the outcome of the pandemic, including data-driven models, empirical and hybrid models. This study was aimed at prediction of COVID-19 evolution in India using a model based on autoregressive integrated moving average (ARIMA). Material and Methods: Real-time Indian data of cumulative cases and deaths of COVID-19 was retrieved from the Johns Hopkins dashboard. The dataset from 11 March 2020 to 25 June 2020 (n = 107 time points) was used to fit the autoregressive integrated moving average model. The model with minimum Akaike Information Criteria was used for forecasting. The predicted root mean square error (PredRMSE) and base root mean square error (BaseRMSE) were used to validate the model. Results: The ARIMA (1,3,2) and ARIMA (3,3,1) model fit best for cumulative cases and deaths, respectively, with minimum Akaike Information Criteria. The prediction of cumulative cases and deaths for next 10 days from 26 June 2020 to 5 July 2020 showed a trend toward continuous increment. The PredRMSE and BaseRMSE of ARIMA (1,3,2) model were 21,137 and 166,330, respectively. Similarly, PredRMSE and BaseRMSE of ARIMA (3,3,1) model were 668.7 and 5,431, respectively. Conclusion: It is proposed that data on COVID-19 be collected continuously, and that forecasting continue in real time. The COVID-19 forecast assist government in resource optimisation and evidence-based decision making for a subsequent state of affairs.

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Perbandingan Model GAM dan Gamboost dalam Fitting Dataset Sea Surface Temperature

STATISTIKA: Journal of Theoretical Statistics and Its Applications ◽

10.29313/jstat.v18i1.3875 ◽

2018 ◽

Vol 18 (1) ◽

pp. 39-50

Author(s):

Miftahuddin Miftahuddin

Keyword(s):

Surface Temperature ◽

Sea Surface Temperature ◽

Risk Model ◽

Generalized Additive Models ◽

Information Criteria ◽

Additive Models ◽

Sea Surface ◽

Akaike Information Criteria ◽

Fitting Model

Fitting model GAM (generalized additive models) dan Gamboost (generalized additive models by boosting) untuk dataset SST (sea surface temperature) dimaksudkan sebagai upaya mencapai perbaikan fitting model terhadap data SST. Secara umum, model GAM dapat memvisualisasikan masing-masing kovariat, sedangkan model gamboost dapat memvisualisasikan lebih detail kovariatnya dalam beberapa bentuk, baik secara linier dan nonlinier. Pengukuran performance yang digunakan terhadap model adalah nilai AIC (Akaike Information Criteria) dan CV-risk. Model GAM dengan boosting menunjukkan lebih sesuai dalam struktur model, pemilihan model terbaik dan seleksi variabel pada dataset SST. Fitting model GAM dapat menghasilkan pola dan trend masing-masing kovariat meskipun memiliki beberapa gap, sedangkan pada model gamboost memiliki lebih banyak pilihan simultan dalam bentuk linier, nonlinier dan smooth untuk masing-masing kovariat. Kedua pendekatan fitting memiliki kelebihan yang dapat saling melengkapi dalam memodelkan dataset SST.

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The Mathematical Basis of the Interpretation of Tracer Experiments in Closed Steady‐State Systems

Journal of Applied Physics ◽

10.1063/1.1699992 ◽

1951 ◽

Vol 22 (4) ◽

pp. 510-520 ◽

Cited By ~ 144

Author(s):

C. W. Sheppard ◽

A. S. Householder

Keyword(s):

Steady State ◽

Mathematical Basis ◽

Tracer Experiments

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Simplified large African carnivore density estimators from track indices

PeerJ ◽

10.7717/peerj.2662 ◽

2016 ◽

Vol 4 ◽

pp. e2662 ◽

Cited By ~ 10

Author(s):

Christiaan W. Winterbach ◽

Sam M. Ferreira ◽

Paul J. Funston ◽

Michael J. Somers

Keyword(s):

Linear Regression ◽

Confidence Interval ◽

Population Size ◽

Linear Model ◽

Standard Error ◽

Linear Models ◽

Information Criteria ◽

Large Carnivores ◽

Simple Linear Regression ◽

Akaike Information Criteria

BackgroundThe range, population size and trend of large carnivores are important parameters to assess their status globally and to plan conservation strategies. One can use linear models to assess population size and trends of large carnivores from track-based surveys on suitable substrates. The conventional approach of a linear model with intercept may not intercept at zero, but may fit the data better than linear model through the origin. We assess whether a linear regression through the origin is more appropriate than a linear regression with intercept to model large African carnivore densities and track indices.MethodsWe did simple linear regression with intercept analysis and simple linear regression through the origin and used the confidence interval for ß in the linear modely = αx + ß, Standard Error of Estimate, Mean Squares Residual and Akaike Information Criteria to evaluate the models.ResultsThe Lion on Clay and Low Density on Sand models with intercept were not significant (P > 0.05). The other four models with intercept and the six models thorough origin were all significant (P < 0.05). The models using linear regression with intercept all included zero in the confidence interval for ß and the null hypothesis that ß = 0 could not be rejected. All models showed that the linear model through the origin provided a better fit than the linear model with intercept, as indicated by the Standard Error of Estimate and Mean Square Residuals. Akaike Information Criteria showed that linear models through the origin were better and that none of the linear models with intercept had substantial support.DiscussionOur results showed that linear regression through the origin is justified over the more typical linear regression with intercept for all models we tested. A general model can be used to estimate large carnivore densities from track densities across species and study areas. The formulaobserved track density = 3.26 × carnivore densitycan be used to estimate densities of large African carnivores using track counts on sandy substrates in areas where carnivore densities are 0.27 carnivores/100 km2or higher. To improve the current models, we need independent data to validate the models and data to test for non-linear relationship between track indices and true density at low densities.

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Transport of bromide in the Bainsvlei soil: Field experiment and deterministic/stochastic model simulation. II. Intermittent water application

Soil Research ◽

10.1071/sr03015 ◽

2005 ◽

Vol 43 (1) ◽

pp. 81 ◽

Cited By ~ 1

Author(s):

Ketema Tilahun ◽

J. F. Botha ◽

A. T. P. Bennie

Keyword(s):

Steady State ◽

Model Simulation ◽

Soil Core ◽

Water Fluxes ◽

Water Application ◽

Concentration Data ◽

Average Pore ◽

Continuous Application ◽

Average Dispersion ◽

Tracer Experiments

Despite the fact that non-uniform soil water content and variable input water fluxes are usually encountered in the field, tracer experiments have usually been carried out under steady-state conditions. The objective of this study was to analyse solute transport in a Bainsvlei soil under intermittent water application using Br– as a tracer. Sprinkler was used to apply water on a plot 200 by 200 cm. Soil core samples were taken every 20 cm to a depth of 160 cm several times during the experiment. The soil Br– concentration data were fitted to the steady-state convection–dispersion analytical model in the CXTFIT package. The average coefficients of determination yielded by this fit (r2 = 0.810) clearly support that the data could be analysed successfully with CXTFIT. The average pore-water velocity of 1.72 cm/day and average dispersion coefficient of 26.19 cm2/day determined from this fit are lower than the fitted values of the steady-state experiments. The Br– moved slower under the intermittent application of water than in the steady case, a conclusion supported by the deeper location of Br– peaks under continuous application than intermittent application after the same amount of water is applied.

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