Parameter estimation and estimability analysis in pharmaceutical models with uncertain inputs

Undirected graphical models such as Markov random fields or Boltzmann machines prove useful in many signal processing and machine learning tasks. However, parameter estimation in these models is difficult due to the intractable normalising constant in their probability density functions. One powerful technique for parameter estimation in such models is score matching. This technique makes use of an objective function which is independent of the normalising constant and constitutes locally consistent estimators for the parameters of such models. However, score matching is only applicable to fully-observed models. In this paper, we extend the applicability of score matching to models with latent variables. Our estimators are unbiased, based on Monte Carlo integration. Unbiased gradient estimators open the way to optimisation through stochastic approximation. We demonstrate the performance of our methodology on two synthetic problems.

In order to solve the problem of parameter estimation of nonlinear model in chemical engineering, a novel heuristic optimization approach is presented. The proposed approach develops and employs particle swarm optimization (PSO) technique to search for optimal solution of the parameter estimation. Firstly, the proposed approach converts the problem of parameter estimation of nonlinear model into an equation solving problem that is prone to be optimized. Secondly, two extrema of PSO are used as the target, and all the particles synchronously move through the solution space roundly and efficiently to find the optimum parameter estimation. The feasibility of the proposed method is demonstrated by the parameter estimation example of the pyrolysis model for fir.

Parameter estimation in blood flow models from measured velocity data—as e.g. velocity-encoded MRI—is a key step for patient-specific hemodynamic analysis. However, velocity encoding suffers from competing noise and aliasing artifacts, which negatively impact the parameter estimation results. The aim of this work is to propose a new inverse problem formulation capable of tackling aliased and noisy velocity MRI measurements in parameter estimation in flows. The formulation is based on a modification of the quadratic cost function for velocity measurements. This allows for a correct parameter estimation when they have influence on the whole measurement domain, in spite of aliasing artifacts. The new inverse problem can be solved numerically using any standard solver, and we show how a popular sequential approach can be applied. Numerical results in an aortic flow show robust parameter estimation for velocity encoding ranges until 30% of the maximal velocity of the problem, while the standard inverse problem fails already for any encoding velocity smaller than the true one. Moreover, the parameter estimation results are even improved for reduced velocity encoding ranges when using the new cost function. The presented approach allows therefore for great flexibility in personalization of blood flows models from MRI data commonly encountered in the clinical context.

This paper presents a new methodology for parameter estimation of models with limit cycle and Hopf bifurcation. By calculating average cycle values for the process signal, a convex objective function can be produced using a maximum likelihood approach. This methodology allows for the proper statistical analysis of the results and the usage of local optimization algorithms for fast and efficient estimation. A case study is presented for a simplified well model of slugging oil systems, for which parameter estimation is crucial to correctly represent any system of interest. Two other objective functions from the literature are compared through Particle Swarm Optimization. The proposed method outperformed those of previous works as determined by a rigorous statistical assessment.

Data assimilation is predominantly used for state estimation, combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts, we need good estimates of both the current system state and the model parameters. This article presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three‐dimensional variational (3D‐Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from synthetic aperture radar (SAR) satellite imagery and a ship‐borne survey is shown to significantly improve the predictive capability of the model over a 2‐year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this article considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D‐Var data assimilation algorithm for joint state‐parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation‐based state‐parameter estimation in coastal morphodynamic modelling. Copyright © 2012 Royal Meteorological Society

Distribution mixtures are used as models to analyze grouped data. The estimation of parameters is an important step for mixture distributions. The latent class model is generally used as the analysis of mixture distributions for discrete data. In this paper, we consider the parameter estimation for a mixture of logistic regression models. We know that the expectation maximization (EM) algorithm was most used for estimating the parameters of logistic regression mixture models. In this paper, we propose a new type of fuzzy class model and then derive an algorithm for the parameter estimation of a fuzzy class logistic regression model. The effects of the explanatory variables on the response variables are described. The focus is on binary responses for the logistic regression mixture analysis with a fuzzy class model. An algorithm, called a fuzzy classification maximum likelihood (FCML), is then created. The mean squared error (MSE) based accuracy criterion for the FCML and EM algorithms to the parameter estimation of logistic regression mixture models are compared using the samples drawn from logistic regression mixtures of two classes. Numerical results show that the proposed FCML algorithm presents good accuracy and is recommended as a new tool for the parameter estimation of the logistic regression mixture models.

The primary challenge of software reliability growth model is to find the unknown model parameters that are used to validate on software failure dataset. Though, numerical estimation technique plays a vital role in parameter estimation of software reliability growth models, they are not optimal as they suffer from constraints sucha as sample size, biasing, and initialisation of parameters. In this study, a parameter estimation of software reliability growth model that utilises a variant of harmony search is proposed. Extensive experiments are conducted on seven different software datasets of varying complexity. A robust experimental setup is developed employing an orthogonal array and Taguchi method. Two‐fold performance comparisons are performed. First, the authors tested their proposed approach against Cuckoo search and numerical method (least square estimation) considering mean square error and Theil's statistics as a quality measure. Second, the authors applied statistical tests are performed that demonstrate the superiority of their approach over the others. The underlying motivation to conduct this study is to motivate researchers to utilise their approach for a better estimation of model parameters.

Parameter and uncertainty estimation in stochastic differential equation models with multi-rate data and nonstationary disturbances

The Bayes principle is applied to the joint model selection and parameter estimation of GTD model to explore the prior information. An algorithm using RJ-MCMC is designed. It not only has better model selection and parameter estimation performance than the non-Bayes algorithms, but also solves the mixed parameter estimation problem in GTD model effectively. The advantage of this algorithm is especially evident at low SNR, for short data and with closely-spaced components. Simulations verify the effectiveness of this algorithm.

The Sacramento model is widely utilized in hydrological forecast, of which the accuracy and performance are primarily determined by the model parameters, indicating the key role of parameter estimation. This paper presents a multi-step parameter estimation method, which divides the parameter estimation of Sacramento model into three steps and realizes optimization step by step. We firstly use the immune clonal selection algorithm (ICSA) to solve the non-liner objective function of parameter estimation, and compare the parameter calibration result of ideal artificial data with Shuffled Complex Evolution (SCE-UA), Parallel Genetic Algorithm (PGA), and Serial Master-slaver Swarms Shuffling Evolution Algorithm Based on Particle Swarms Optimization (SMSE-PSO). The comparison result shows that ICSA has the best convergence, efficiency and precision. Then we apply ICSA to the parameter estimation of single-step and multi-step Sacramento model and simulate 32 floods based on application examples of Dongyang and Tantou river basins for validation. It is clearly shown that the results of multi-step method based on ICSA show higher accuracy and 100% qualified rate, indicating its higher precision and reliability, which has great potential to improve Sacramento model and hydrological forecast.

The efficacy of the compound Gauss-Markov (CGM) model, initially proposed by Jeng and Woods (1990), has been demonstrated in several image processing applications. However, parameter estimation for the CGM model is difficult since it is not clear as to how the constraints or interdependence amongst the model parameters can be incorporated into the estimation procedures. As result, the parameter estimates tend to be inconsistent. It is shown that, under some reasonable symmetry constraints, the 80 interdependent parameters of the CGM model can be reduced to seven independent ones. This guarantees the consistency of model parameters obtained from parameter estimation algorithms, thereby removing a main obstacle for the parameter estimation of the CGM model.

BackgroundThe development of large-scale kinetic models is one of the current key issues in computational systems biology and bioinformatics. Here we consider the problem of parameter estimation in nonlinear dynamic models. Global optimization methods can be used to solve this type of problems but the associated computational cost is very large. Moreover, many of these methods need the tuning of a number of adjustable search parameters, requiring a number of initial exploratory runs and therefore further increasing the computation times.Here we present a novel parallel method, self-adaptive cooperative enhanced scatter search (saCeSS), to accelerate the solution of this class of problems. The method is based on the scatter search optimization metaheuristic and incorporates several key new mechanisms: (i) asynchronous cooperation between parallel processes, (ii) coarse and fine-grained parallelism, and (iii) self-tuning strategies.ResultsThe performance and robustness of saCeSS is illustrated by solving a set of challenging parameter estimation problems, including medium and large-scale kinetic models of the bacterium E. coli, bakerés yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network.The results consistently show that saCeSS is a robust and efficient method, allowing very significant reduction of computation times with respect to several previous state of the art methods (from days to minutes, in several cases) even when only a small number of processors is used.ConclusionsThe new parallel cooperative method presented here allows the solution of medium and large scale parameter estimation problems in reasonable computation times and with small hardware requirements. Further, the method includes self-tuning mechanisms which facilitate its use by non-experts. We believe that this new method can play a key role in the development of large-scale and even whole-cell dynamic models.

Functional relationship model is used to study the data that are subjected to errors. In this paper, we consider the linear functional relationship model with bivariate circular data where the pair of errors is with unequal concentration parameters. The parameter estimation of the model for circular data is different from linear data due to its wrapped around nature. We propose some improvements on the parameter estimation where some iterative procedures are considered. The concentration parameters are estimated based on the Bessel function. Also, we derive the corresponding covariance matrix of the model based on the Fisher Information matrix. Monte Carlo simulation studies were performed to study the suitability of the estimation method. It is found that the biasness of the estimates is small. Practical application of the method is illustrated by using real data set. Keywords: circular data; covariance matrix; Von Mises distribution; simulation study

Parameter estimation in complicated rational functions

Modeling and Identification of a Nuclear Reactor