Values Of Unknown Model Parameters Research Articles

ПРИМЕНЕНИЕ ФУНКЦИОНАЛА КВАЗИПРОТЯЖЕННОСТИ В ЗАДАЧАХ АППРОКСИМАЦИИ ИСКАЖЕННЫХ ДАННЫХ

Исследована эффективность применения функционала квазипротяженности для решения задач аппроксимации данных, описываемых параметрической моделью. Представлены результаты теоретического и численного анализа, которые демонстрируют особенности поведения этого функционала как целевой функции линейного и нелинейного параметров модели данных для разных уровней шума в предположении, что параметры модели принимают одно или несколько значений. Сформулированы рекомендации по эффективному использованию функционала квазипротяженности для решения задач аппроксимации данных.

Statistical models of tumour onset and growth for modern breast cancer screening cohorts

Historically, multi-state Markov models have been used to study breast cancer incidence and mammography screening effectiveness. In recent years, more biologically motivated continuous tumour growth models have emerged as alternatives. However, a number of challenges remain for these models to make use of the wealth of information available in large mammography cohort data. In particular, methodology is needed to address random left truncation and individual, asynchronous screening. We present a comprehensive continuous random effects model for the natural history of breast cancer. It models the unobservable processes of tumour onset, tumour growth, screening sensitivity, and symptomatic detection. We show how the unknown model parameter values can be jointly estimated using a prospective cohort with diagnostic data on age and tumour size at diagnosis, and individual screening histories. We also present a microsimulation study calibrated to population breast cancer incidence data, and to data on mode of detection and tumour size. We highlight the importance of adjusting for random left truncation, derive tumour doubling time distributions for screen-detected and interval cancers, and present results concerning the relationship between tumour presence time and age at diagnosis.

A Bayesian Optimal Design for Sequential Accelerated Degradation Testing

When optimizing an accelerated degradation testing (ADT) plan, the initial values of unknown model parameters must be pre-specified. However, it is usually difficult to obtain the exact values, since many uncertainties are embedded in these parameters. Bayesian ADT optimal design was presented to address this problem by using prior distributions to capture these uncertainties. Nevertheless, when the difference between a prior distribution and actual situation is large, the existing Bayesian optimal design might cause some over-testing or under-testing issues. For example, the implemented ADT following the optimal ADT plan consumes too much testing resources or few accelerated degradation data are obtained during the ADT. To overcome these obstacles, a Bayesian sequential step-down-stress ADT design is proposed in this article. During the sequential ADT, the test under the highest stress level is firstly conducted based on the initial prior information to quickly generate degradation data. Then, the data collected under higher stress levels are employed to construct the prior distributions for the test design under lower stress levels by using the Bayesian inference. In the process of optimization, the inverse Gaussian (IG) process is assumed to describe the degradation paths, and the Bayesian D-optimality is selected as the optimal objective. A case study on an electrical connector’s ADT plan is provided to illustrate the application of the proposed Bayesian sequential ADT design method. Compared with the results from a typical static Bayesian ADT plan, the proposed design could guarantee more stable and precise estimations of different reliability measures.

An online spatiotemporal prediction model for dengue fever epidemic inKaohsiung (Taiwan)

The emergence and re-emergence of disease epidemics is a complex question that may be influenced by diverse factors, including the space-time dynamics of human populations, environmental conditions, and associated uncertainties. This study proposes a stochastic framework to integrate space-time dynamics in the form of a Susceptible-Infected-Recovered (SIR) model, together with uncertain disease observations, into a Bayesian maximum entropy (BME) framework. The resulting model (BME-SIR) can be used to predict space-time disease spread. Specifically, it was applied to obtain a space-time prediction of the dengue fever (DF) epidemic that took place in Kaohsiung City (Taiwan) during 2002. In implementing the model, the SIR parameters were continually updated and information on new cases of infection was incorporated. The results obtained show that the proposed model is rigorous to user-specified initial values of unknown model parameters, that is, transmission and recovery rates. In general, this model provides a good characterization of the spatial diffusion of the DF epidemic, especially in the city districts proximal to the location of the outbreak. Prediction performance may be affected by various factors, such as virus serotypes and human intervention, which can change the space-time dynamics of disease diffusion. The proposed BME-SIR disease prediction model can provide government agencies with a valuable reference for the timely identification, control, and prevention of DF spread in space and time.

Investigation of flow and transport processes at the MADE site using ensemble Kalman filter

In this work the ensemble Kalman filter (EnKF) is applied to investigate the flow and transport processes at the macro-dispersion experiment (MADE) site in Columbus, MS. The EnKF is a sequential data assimilation approach that adjusts the unknown model parameter values based on the observed data with time. The classic advection–dispersion (AD) and the dual-domain mass transfer (DDMT) models are employed to analyze the tritium plume during the second MADE tracer experiment. The hydraulic conductivity ( K), longitudinal dispersivity in the AD model, and mass transfer rate coefficient and mobile porosity ratio in the DDMT model, are estimated in this investigation. Because of its sequential feature, the EnKF allows for the temporal scaling of transport parameters during the tritium concentration analysis. Inverse simulation results indicate that for the AD model to reproduce the extensive spatial spreading of the tritium observed in the field, the K in the downgradient area needs to be increased significantly. The estimated K in the AD model becomes an order of magnitude higher than the in situ flowmeter measurements over a large portion of media. On the other hand, the DDMT model gives an estimation of K that is much more comparable with the flowmeter values. In addition, the simulated concentrations by the DDMT model show a better agreement with the observed values. The root mean square (RMS) between the observed and simulated tritium plumes is 0.77 for the AD model and 0.45 for the DDMT model at 328 days. Unlike the AD model, which gives inconsistent K estimates at different times, the DDMT model is able to invert the K values that consistently reproduce the observed tritium concentrations through all times.

Gamma-ray burst neutrino background and star formation history in the universe

We estimate the flux of the GRB neutrino background and compute the event rate at SK and TITAND in the collapsar model, assuming that GRB formation rate is proportional to the star formation rate. We find that the predicted background neutrino flux is highly sensitive to unknown model parameters, mainly to the mass accretion rate, to the fraction of disk energy emitted in thermal neutrinos (as opposed to emission through electromagnetic processes), and to the fraction of collapsar events leading to GRBs. The predicted neutrino flux varies over many orders of magnitude as the values of unknown model parameters are varied. We investigate the detection possibility of thermal neutrinos from collapsars which lead to GRBs by TITAND. We find that the GRB neutrino background might be detected by TITAND within ∼ 10 yrs only for the optimistic cases in which the average mass-accretion rate is high (≥ a few M ⊙ s −1), and the probability that one collapsar generates a GRB is high ( φ = 0.5 − 1.0).

Monte Carlo Simulation of an Ethanol Pharmacokinetic Model

Background One challenge of using even relatively simple pharmacokinetic models is valuation of model parameters. Unknown model parameter values can be determined by fitting the model to measured data. Goals of the present study were to (1) obtain ethanol pharmacokinetic data from a cohort of dogs, (2) propose a physiologic ethanol pharmacokinetic model, (3) and perform Monte Carlo simulation to determine model parameter values. The rationale for the particular model proposed here was to account for the interrelationship between blood ethanol concentration and gastrointestinal physiology. Methods To each of five fasted dogs, 1 g of ethanol/kg body weight was administered as a gavage of 20% w/v ethanol solution. Developed was an ethanol pharmacokinetic model that comprised a gastric emptying mechanism, a body water compartment, ethanol diffusion through the stomach mucosa, gastric alcohol dehydrogenase (GADH) oxidation of ethanol, diffusion through the small intestine epithelia to the villi, a countercurrent exchanger model of the villi, and liver alcohol dehydrogenase oxidation of ethanol. Monte Carlo simulation was used to estimate model parameter values and standard deviations by minimization of the χ2 function. Results Fitting the experimental data to the model using Monte Carlo simulation yielded reasonable values for model parameters. The model predicted that the capacity for ethanol absorption in the intestine was 6.79-fold greater than the ethanol absorption capacity in the stomach. The model indicated that 23.8 ± 8.3% of the ethanol dose was actually absorbed in the stomach, and an insignificant amount of ethanol was metabolized by GADH. Conclusions Ethanol metabolism by GADH is insignificant in the present case. The blood ethanol profile was strongly determined by gastric emptying. Differences between experimental data and simulation results largely result from the gastric emptying model selected. Therefore, accuracy of the complete pharmacokinetic model can be improved significantly by improving the gastric emptying model.

Monte Carlo Simulation of an Ethanol Pharmacokinetic Model

Background One challenge of using even relatively simple pharmacokinetic models is valuation of model parameters. Unknown model parameter values can be determined by fitting the model to measured data. Goals of the present study were to (1) obtain ethanol pharmacokinetic data from a cohort of dogs, (2) propose a physiologic ethanol pharmacokinetic model, (3) and perform Monte Carlo simulation to determine model parameter values. The rationale for the particular model proposed here was to account for the interrelationship between blood ethanol concentration and gastrointestinal physiology.Methods To each of five fasted dogs, 1 g of ethanol/kg body weight was administered as a gavage of 20% w/v ethanol solution. Developed was an ethanol pharmacokinetic model that comprised a gastric emptying mechanism, a body water compartment, ethanol diffusion through the stomach mucosa, gastric alcohol dehydrogenase (GADH) oxidation of ethanol, diffusion through the small intestine epithelia to the villi, a countercurrent exchanger model of the villi, and liver alcohol dehydrogenase oxidation of ethanol. Monte Carlo simulation was used to estimate model parameter values and standard deviations by minimization of the χ2 function.Results Fitting the experimental data to the model using Monte Carlo simulation yielded reasonable values for model parameters. The model predicted that the capacity for ethanol absorption in the intestine was 6.79‐fold greater than the ethanol absorption capacity in the stomach. The model indicated that 23.8 ± 8.3% of the ethanol dose was actually absorbed in the stomach, and an insignificant amount of ethanol was metabolized by GADH.Conclusions Ethanol metabolism by GADH is insignificant in the present case. The blood ethanol profile was strongly determined by gastric emptying. Differences between experimental data and simulation results largely result from the gastric emptying model selected. Therefore, accuracy of the complete pharmacokinetic model can be improved significantly by improving the gastric emptying model.

Gamma-ray burst neutrino background and star formation history in the universe

We estimate the flux of the gamma-ray burst (GRB) neutrino background and compute the event rate at SK and TITAND in the collapsar model, assuming that GRB formation rate is proportional to the star formation rate. We find that the predicted background neutrino flux is highly sensitive to unknown model parameters, mainly to the mass–accretion rate, to the fraction of disk energy emitted in thermal neutrinos (as opposed to emission through electromagnetic processes), and to the fraction of collapsar events leading to GRBs. The predicted neutrino flux varies over many orders of magnitude as the values of unknown model parameters are varied. We investigate the detection possibility of thermal neutrinos from collapsars which lead to GRBs by TITAND. We find that the GRB neutrino background might be detected by TITAND within ∼10 yrs only for the optimistic cases in which the average mass–accretion rate is high (≳ a few M ⊙ s −1), and the probability that one collapsar generates a GRB is high ( f=0.5–1.0).

A physiologically based mathematical model of dermal absorption in man.

A sound understanding of the mechanisms determining percutaneous absorption is necessary for toxicological risk assessment of chemicals contacting the skin. As part of a programme investigating these mechanisms we have developed a physiologically based mathematical model. The structure of the model parallels the multi-layer structure of the skin, with separate surface, stratum corneum and viable tissue layers. It simulates the effects of partitioning and diffusive transport between the sub-layers, and metabolism in the viable epidermis. In addition the model describes removal processes on the surface of the skin, including the effects of washing and desquamation, and rubbing off onto clothing. This model is applied to data on the penetration of the herbicide fluazifop-butyl through human skin in vivo and in vitro. Part of this dataset is used to estimate unknown model parameter values and the remainder is used to provide a partial validation of the model. Only a small fraction of the applied dose was absorbed through the skin; most of it was removed by washing or onto clothing. The model provides a quantitative description of these loss processes on the skin surface.

A validated mathematical model for a zinc electrowinning cell

A set of (95) equations forming a dynamic, nonlinear model of an industrial pilot-plant scale zinc electrowinning cell fed with high purity electrolyte is presented. Only the solution of the steady-state model is considered in this paper. Values for unknown model parameters have either been obtained from the literature or else estimated using experimental data taken from the pilot-plant cell. Sensitivity studies showed that uncertainties in the temperature dependency of the zinc and hydrogen reaction exchange current densities and the exchange coefficient for the hydrogen reaction have a major effect on the model predictions. Excellent agreement between predicted and experimental results was obtained, provided that cathodic mass transfer effects were included in the model. Both parameter estimation and solution of the steady-state model were carried out using the SPEEDUP flowsheeting package.