Unknown Model Parameters (unknown + model_parameter)

Distribution by Scientific Domains

Selected Abstracts

Modeling Longitudinal Data with Nonparametric Multiplicative Random Effects Jointly with Survival Data

BIOMETRICS, Issue 2 2008
Jimin Ding
Summary In clinical studies, longitudinal biomarkers are often used to monitor disease progression and failure time. Joint modeling of longitudinal and survival data has certain advantages and has emerged as an effective way to mutually enhance information. Typically, a parametric longitudinal model is assumed to facilitate the likelihood approach. However, the choice of a proper parametric model turns out to be more elusive than models for standard longitudinal studies in which no survival endpoint occurs. In this article, we propose a nonparametric multiplicative random effects model for the longitudinal process, which has many applications and leads to a flexible yet parsimonious nonparametric random effects model. A proportional hazards model is then used to link the biomarkers and event time. We use B-splines to represent the nonparametric longitudinal process, and select the number of knots and degrees based on a version of the Akaike information criterion (AIC). Unknown model parameters are estimated through maximizing the observed joint likelihood, which is iteratively maximized by the Monte Carlo Expectation Maximization (MCEM) algorithm. Due to the simplicity of the model structure, the proposed approach has good numerical stability and compares well with the competing parametric longitudinal approaches. The new approach is illustrated with primary biliary cirrhosis (PBC) data, aiming to capture nonlinear patterns of serum bilirubin time courses and their relationship with survival time of PBC patients. [source]

A Probabilistic Framework for Bayesian Adaptive Forecasting of Project Progress

Paolo Gardoni
An adaptive Bayesian updating method is used to assess the unknown model parameters based on recorded data and pertinent prior information. Recorded data can include equality, upper bound, and lower bound data. The proposed approach properly accounts for all the prevailing uncertainties, including model errors arising from an inaccurate model form or missing variables, measurement errors, statistical uncertainty, and volitional uncertainty. As an illustration of the proposed approach, the project progress and final time-to-completion of an example project are forecasted. For this illustration construction of civilian nuclear power plants in the United States is considered. This application considers two cases (1) no information is available prior to observing the actual progress data of a specified plant and (2) the construction progress of eight other nuclear power plants is available. The example shows that an informative prior is important to make accurate predictions when only a few records are available. This is also the time when forecasts are most valuable to the project manager. Having or not having prior information does not have any practical effect on the forecast when progress on a significant portion of the project has been recorded. [source]

Back analysis of model parameters in geotechnical engineering by means of soft computing

B. Pichler
Abstract In this paper, a parameter identification (PI) method for determination of unknown model parameters in geotechnical engineering is proposed. It is based on measurement data provided by the construction site. Model parameters for finite element (FE) analyses are identified such that the results of these calculations agree with the available measurement data as well as possible. For determination of the unknown model parameters, use of an artificial neural network (ANN) is proposed. The network is trained to approximate the results of FE simulations. A genetic algorithm (GA) uses the trained ANN to provide an estimate of optimal model parameters which, finally, has to be assessed by an additional FE analysis. The presented mode of PI renders back analysis of model parameters feasible even for large-scale models as used in geotechnical engineering. The advantages of theoretical developments concerning both the structure and the training of the ANN are illustrated by the identification of material properties from experimental data. Finally, the performance of the proposed PI method is demonstrated by two problems taken from geotechnical engineering. The impact of back analysis on the actual construction process is outlined. Copyright 2003 John Wiley & Sons, Ltd. [source]

Kalman filter-based adaptive control for networked systems with unknown parameters and randomly missing outputs

Y. Shi
Abstract This paper investigates the problem of adaptive control for networked control systems with unknown model parameters and randomly missing outputs. In particular, for a system with the autoregressive model with exogenous input placed in a network environment, the randomly missing output feature is modeled as a Bernoulli process. Then, an output estimator is designed to online estimate the missing output measurements, and further a Kalman filter-based method is proposed for parameter estimation. Based on the estimated output and the available output, and the estimated model parameters, an adaptive control is designed to make the output track the desired signal. Convergence properties of the proposed algorithms are analyzed in detail. Simulation examples illustrate the effectiveness of the proposed method. Copyright 2008 John Wiley & Sons, Ltd. [source]

The analysis of indexed astronomical time series , X. Significance testing of O,C data

Chris Koen
ABSTRACT It is assumed that O,C (,observed minus calculated') values of periodic variable stars are determined by three processes, namely measurement errors, random cycle-to-cycle jitter in the period, and possibly long-term changes in the mean period. By modelling the latter as a random walk, the covariances of all O,C values can be calculated. The covariances can then be used to estimate unknown model parameters, and to choose between alternative models. Pseudo-residuals which could be used in model fit assessment are also defined. The theory is illustrated by four applications to spotted stars in eclipsing binaries. [source]

Cell Population Modeling and Parameter Estimation for Continuous Cultures of Saccharomyces cerevisiae

Prashant Mhaskar
Saccharomyces cerevisiae is known to exhibit sustained oscillations in chemostats operated under aerobic and glucose-limited growth conditions. The oscillations are reflected both in intracellular and extracellular measurements. Our recent work has shown that unstructured cell population balance models are capable of generating sustained oscillations over an experimentally meaningful range of dilution rates. A disadvantage of such unstructured models is that they lack variables that can be compared directly to easily measured extracellular variables. Thus far, most of our work in model development has been aimed at achieving qualitative agreement with experimental data. In this paper, a segregated model with a simple structured description of the extracellular environment is developed and evaluated. The model accounts for the three most important metabolic pathways involved in cell growth with glucose substrate. As compared to completely unstructured models, the major advantage of the proposed model is that predictions of extracellular variables can be compared directly to experimental data. Consequently, the model structure is well suited for the application of estimation techniques aimed at determining unknown model parameters from available extracellular measurements. A steady-state parameter selection method developed in our group is extended to oscillatory dynamics to determine the parameters that can be estimated most reliably. The chosen parameters are estimated by solving a nonlinear programming problem formulated to minimize the difference between predictions and measurements of the extracellular variables. The efficiency of the parameter estimation scheme is demonstrated using simulated and experimental data. [source]