Cross-validation:a review

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

Cancer is one of the most fatal diseases in the world. Governments and researchers from various areas have continuously concentrated efforts to better understand the disease and propose diagnostic and treatment techniques. The use of mathematical models of tumor growth is of great importance for the development of such techniques. Due to the variety of models nowadays available in the literature, the problems of model selection and parameter estimation come into picture, aiming at suitably predicting the patient’s status of the disease. As the available data on dependent variables of existing models might not justify the use of common likelihood functions, approximate Bayesian computation (ABC) becomes a very attractive tool for model selection and model calibration (parameter estimation) in tumor growth models. In the present study, a Monte Carlo approximate Bayesian computation (ABC) algorithm is applied to select among competing models of tumor growth, with and without chemotherapy treatment. Simulated measurements are used in this work. The results obtained show that the algorithm correctly selects the model and estimates the parameters used to generate the simulated measurements.

General frequency-modulated (GFM) signals can be used to characterize many vibrations in dynamic environments, with applications to engine monitoring and sonar. Most work into parameter estimation of such signals assumes knowledge of the number of carrier frequencies. In this paper, we make no such assumption and use Bayesian techniques to address jointly the problem of model selection and parameter estimation. Following the work of Andrieu and Doucet (see ibid., vol.47, p.2667-76, 1999), who addressed the problem for nonmodulated sinusoids, a posterior distribution for the parameters and model order is obtained. This distribution is too complicated for analytical extraction of moments and to sample from directly; therefore, we use a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to draw samples from the distribution. Some simulated examples are presented to illustrate the algorithm's performance.

Motivated by a certain type of infinite-patch metapopulation model, we propose an extension to the popular Poisson INAR(1) model, where the innovations are assumed to be serially dependent in such a way that their mean is increased if the current population is large. We shall recognize that this new model forms a bridge between the Poisson INAR(1) model and the INARCH(1) model. We analyze the stochastic properties of the observations and innovations from an extended Poisson INAR(1) process, and we consider the problem of model identification and parameter estimation. A real-data example about iceberg counts shows how to benefit from the new model.

Retail forecasting is a diverse and dynamic research area encompassing a variety of different topics. The advent of online channels, the increasing complexity of product ranges, and the shortening lifespan of many items are as examples of some of the new challenges that maintain the importance of improving forecasting in this domain. This thesis aims to address questions in retail forecasting that are closely linked with relevant problems faced in the industry. As such, the problems have been identified through a combination of reviewing the academic literature, discussion, and engagement with practitioners. This thesis starts by considering the situation where demand series are influenced by multiple seasonal and calendar effects. This is a challenge which is widespread due to high frequency sampling and decision making in retailing. We develop a new model to accommodate flexibility in modelling complex seasonal patterns, which also aids with mitigating the effect of short demand histories on forecasting performance. The new model is embedded in an innovations state-space formulation and it is demonstrated empirically using wholesale food data to provide competitive forecasting accuracy to established benchmarks. Next, the dual problems of SKU-level model parameter estimation and forecasting are considered. For retailers experiencing frequent promotional activities, this is a principal issue. The parameter estimates provide insights about the elasticity of different factors on demand for the SKU, and therefore inform marketing planning. Accurate forecasts, for both promotional and baseline periods, support other functions such as replenishment and inventory management. First, a geometric parameter inheritance procedure is proposed, which uses aggregate information within a product hierarchy to improve parameter estimates under certain assumptions. At brand level, it is typically easier to better estimate elasticity effects, making this strategy preferable. Second, a debiasing approximation is derived for the forecasting procedure, which is demonstrated to reduce bias, whilst remaining competitive in terms of forecast accuracy, as shown in a simulation study. The debiasing approximation is then evaluated with an inventory simulation study, which examines the conditions under which improvements in inventory performance can be gained. The conclusions give useful insights for inventory managers, and demonstrate that bias is a significant factor in inventory performance.

A general (possibly nonminimum phase and/or asymmetric noncausal) two-dimensional (2-D) moving average (MA) model driven by a zero-mean i.i.d. 2-D sequence is considered. The input sequence is not observed. The signal observations may be noisy. We consider the problems of model order determination and model parameter estimation using the higher order (third- or fourth-order, for example) cumulants of the 2-D signal. Second-order statistics of the data can consistently identify only a smaller class of MA models. The proposed approaches are illustrated via computer simulations.

A general (possibly nonminimum phase and/or asymmetric noncausal) two dimensional (2-D) moving average (MA) model driven by a zero-mean i.i.d. 2-D sequence is considered. The input sequence is not observed. The signal observations may be noisy. We consider the problems of model order determination and model parameter estimation using the higher-order (third- or fourth-order, for example) cumulants of the 2-D signal. Second-order statistics of the data can consistently identify only a smaller class of MA models. Consistency of the proposed approaches is established and a simulation example is presented.

Inverse higher-order statistics of non-Gaussian, stationary random processes are introduced in this paper, as an extension of their 2nd- order counterparts, known as inverse correlations. Their use in system identification, and specifically in model order determination and parameter estimation problems, is investigated. Estimation procedures are proposed for obtaining sample estimates of inverse statistics and the corresponding (poly)spectra. The algorithms derived are illustrated by simulation examples, involving inverse 2nd- and 3rd-order statistics.

Parameter Estimation that Improves Validity of Model for a Certain Model Use

MRS of hyperpolarized (13) C-labeled compounds represents a promising technique for in vivo metabolic studies. However, robust quantification and metabolic modeling are still important areas of investigation. In particular, time and spatial resolution constraints may lead to the analysis of MRS signals with low signal-to-noise ratio (SNR). The relationship between SNR and the precision of quantitative analysis for the evaluation of the in vivo kinetic behavior of metabolites is unknown. In this article, this topic is addressed by Monte Carlo simulations, covering the problem of MRS signal model parameter estimation, with strong emphasis on the peak amplitude and kinetic model parameters. The results of Monte Carlo simulation were confirmed by in vivo experiments on medium-sized animals injected with hyperpolarized [1-(13) C]pyruvate. The results of this study may be useful for the establishment of experimental planning and for the optimization of kinetic model estimation as a function of the SNR value.

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.

Fast and robust parameter estimation for statistical partial volume models in brain MRI.

This paper considers the estimation problem of traffic state in freeway networks in light of the unknown input filtering (UIF) framework. The freeway traffic flow is modeled as a dynamic stochastic nonlinear system and is based on a recently developed speed-extended cell-transmission model of freeway traffic. Since the environmental conditions on a freeway may change over time, model parameters estimation is also considered. It is shown that the dual state and parameter estimation problem can be solved by applying the UIF to a nonlinear system with unknown inputs. Recently, a nonlinear version of the extended recursive three-step filter, named as the NERTSF, was employed to solve the problem. However, a numerical approximation method is used to calculate the model partial derivatives. To relax that restriction, in this paper a derivative-free versions of the NERTSF is further proposed to solve the addressed estimation problem of the freeway traffic flow.

We consider the problem of parameter estimation and energy minimization for a region-based semantic segmentation model. The model divides the pixels of an image into non-overlapping connected regions, each of which is to a semantic class. In the context of energy minimization, the main problem we face is the large number of putative pixel-to-region assignments. We address this problem by designing an accurate linear programming based approach for selecting the best set of regions from a large dictionary. The dictionary is constructed by merging and intersecting segments obtained from multiple bottom-up over-segmentations. The linear program is solved efficiently using dual decomposition. In the context of parameter estimation, the main problem we face is the lack of fully supervised data. We address this issue by developing a principled framework for parameter estimation using diverse data. More precisely, we propose a latent structural support vector machine formulation, where the latent variables model any missing information in the human annotation. Of particular interest to us are three types of annotations: (i) images segmented using generic foreground or background classes; (ii) images with bounding boxes specified for objects; and (iii) images labeled to indicate the presence of a class. Using large, publicly available datasets we show that our methods are able to significantly improve the accuracy of the region-based model.

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.