Managing uncertainty in complex stochastic models: design and emulation of a Rabies model

In this paper we present a novel method for emulating a stochastic, or random output, computer model and show its application to a complex rabies model. The method is evaluated both in terms of accuracy and computational efficiency on synthetic data and the rabies model. We address the issue of experimental design and provide empirical evidence on the effectiveness of utilizing replicate model evaluations compared to a space-filling design. We employ the Mahalanobis error measure to validate the heteroscedastic Gaussian process based emulator predictions for both the mean and (co)variance. The emulator allows efficient screening to identify important model inputs and better understanding of the complex behaviour of the rabies model.

A projected process kriging algorithm for sensor networks with heterogeneous error characteristics

Large monitoring networks are becoming increasingly common and can generate large datasets from thousands to millions of observations in size, often with high temporal resolution. Processing large datasets using traditional geostatistical methods is prohibitively slow and in real world applications different types of sensor can be found across a monitoring network. Heterogeneities in the error characteristics of different sensors, both in terms of distribution and magnitude, presents problems for generating coherent maps. An assumption in traditional geostatistics is that observations are made directly of the underlying process being studied and that the observations are contaminated with Gaussian errors. Under this assumption, sub–optimal predictions will be obtained if the error characteristics of the sensor are effectively non–Gaussian. One method, model based geostatistics, assumes that a Gaussian process prior is imposed over the (latent) process being studied and that the sensor model forms part of the likelihood term. One problem with this type of approach is that the corresponding posterior distribution will be non–Gaussian and computationally demanding as Monte Carlo methods have to be used. An extension of a sequential, approximate Bayesian inference method enables observations with arbitrary likelihoods to be treated, in a projected process kriging framework which is less computationally intensive. The approach is illustrated using a simulated dataset with a range of sensor models and error characteristics.

Bayesian error bars for regression

Regression problems are concerned with predicting the values of one or more continuous quantities, given the values of a number of input variables. For virtually every application of regression, however, it is also important to have an indication of the uncertainty in the predictions. Such uncertainties are expressed in terms of the error bars, which specify the standard deviation of the distribution of predictions about the mean. Accurate estimate of error bars is of practical importance especially when safety and reliability is an issue. The Bayesian view of regression leads naturally to two contributions to the error bars. The first arises from the intrinsic noise on the target data, while the second comes from the uncertainty in the values of the model parameters which manifests itself in the finite width of the posterior distribution over the space of these parameters. The Hessian matrix which involves the second derivatives of the error function with respect to the weights is needed for implementing the Bayesian formalism in general and estimating the error bars in particular. A study of different methods for evaluating this matrix is given with special emphasis on the outer product approximation method. The contribution of the uncertainty in model parameters to the error bars is a finite data size effect, which becomes negligible as the number of data points in the training set increases. A study of this contribution is given in relation to the distribution of data in input space. It is shown that the addition of data points to the training set can only reduce the local magnitude of the error bars or leave it unchanged. Using the asymptotic limit of an infinite data set, it is shown that the error bars have an approximate relation to the density of data in input space.

Intelligent execution monitoring and error analysis in planning involving processes

An intelligent agent, operating in an external world which cannot be fully described in its internal world model, must be able to monitor the success of a previously generated plan and to respond to any errors which may have occurred. The process of error analysis requires the ability to reason in an expert fashion about time and about processes occurring in the world. Reasoning about time is needed to deal with causality. Reasoning about processes is needed since the direct effects of a plan action can be completely specified when the plan is generated, but the indirect effects cannot. For example, the action `open tap' leads with certainty to `tap open', whereas whether there will be a fluid flow and how long it might last is more difficult to predict. The majority of existing planning systems cannot handle these kinds of reasoning, thus limiting their usefulness. This thesis argues that both kinds of reasoning require a complex internal representation of the world. The use of Qualitative Process Theory and an interval-based representation of time are proposed as a representation scheme for such a world model. The planning system which was constructed has been tested on a set of realistic planning scenarios. It is shown that even simple planning problems, such as making a cup of coffee, require extensive reasoning if they are to be carried out successfully. The final Chapter concludes that the planning system described does allow the correct solution of planning problems involving complex side effects, which planners up to now have been unable to solve.

Discriminative training of the hidden vector state model for semantic parsing

In this paper, we discuss how discriminative training can be applied to the hidden vector state (HVS) model in different task domains. The HVS model is a discrete hidden Markov model (HMM) in which each HMM state represents the state of a push-down automaton with a finite stack size. In previous applications, maximum-likelihood estimation (MLE) is used to derive the parameters of the HVS model. However, MLE makes a number of assumptions and unfortunately some of these assumptions do not hold. Discriminative training, without making such assumptions, can improve the performance of the HVS model by discriminating the correct hypothesis from the competing hypotheses. Experiments have been conducted in two domains: the travel domain for the semantic parsing task using the DARPA Communicator data and the Air Travel Information Services (ATIS) data and the bioinformatics domain for the information extraction task using the GENIA corpus. The results demonstrate modest improvements of the performance of the HVS model using discriminative training. In the travel domain, discriminative training of the HVS model gives a relative error reduction rate of 31 percent in F-measure when compared with MLE on the DARPA Communicator data and 9 percent on the ATIS data. In the bioinformatics domain, a relative error reduction rate of 4 percent in F-measure is achieved on the GENIA corpus.

Estimating the SCAN*PRO model of store sales: HB, FM or just OLS?

In this paper we investigate whether consideration of store-level heterogeneity in marketing mix effects improves the accuracy of the marketing mix elasticities, fit, and forecasting accuracy of the widely-applied SCAN*PRO model of store sales. Models with continuous and discrete representations of heterogeneity, estimated using hierarchical Bayes (HB) and finite mixture (FM) techniques, respectively, are empirically compared to the original model, which does not account for store-level heterogeneity in marketing mix effects, and is estimated using ordinary least squares (OLS). The empirical comparisons are conducted in two contexts: Dutch store-level scanner data for the shampoo product category, and an extensive simulation experiment. The simulation investigates how between- and within-segment variance in marketing mix effects, error variance, the number of weeks of data, and the number of stores impact the accuracy of marketing mix elasticities, model fit, and forecasting accuracy. Contrary to expectations, accommodating store-level heterogeneity does not improve the accuracy of marketing mix elasticities relative to the homogeneous SCAN*PRO model, suggesting that little may be lost by employing the original homogeneous SCAN*PRO model estimated using ordinary least squares. Improvements in fit and forecasting accuracy are also fairly modest. We pursue an explanation for this result since research in other contexts has shown clear advantages from assuming some type of heterogeneity in market response models. In an Afterthought section, we comment on the controversial nature of our result, distinguishing factors inherent to household-level data and associated models vs. general store-level data and associated models vs. the unique SCAN*PRO model specification.

An aspect-oriented and model-driven approach for managing dynamic variability

Constructing and executing distributed systems that can adapt to their operating context in order to sustain provided services and the service qualities are complex tasks. Managing adaptation of multiple, interacting services is particularly difficult since these services tend to be distributed across the system, interdependent and sometimes tangled with other services. Furthermore, the exponential growth of the number of potential system configurations derived from the variabilities of each service need to be handled. Current practices of writing low-level reconfiguration scripts as part of the system code to handle run time adaptation are both error prone and time consuming and make adaptive systems difficult to validate and evolve. In this paper, we propose to combine model driven and aspect oriented techniques to better cope with the complexities of adaptive systems construction and execution, and to handle the problem of exponential growth of the number of possible configurations. Combining these techniques allows us to use high level domain abstractions, simplify the representation of variants and limit the problem pertaining to the combinatorial explosion of possible configurations. In our approach we also use models at runtime to generate the adaptation logic by comparing the current configuration of the system to a composed model representing the configuration we want to reach. © 2008 Springer-Verlag Berlin Heidelberg.

A fuzzy decision tree-based duration model for Standard Yorùbá text-to-speech synthesis

In this paper, we present syllable-based duration modelling in the context of a prosody model for Standard Yorùbá (SY) text-to-speech (TTS) synthesis applications. Our prosody model is conceptualised around a modular holistic framework. This framework is implemented using the Relational Tree (R-Tree) techniques. An important feature of our R-Tree framework is its flexibility in that it facilitates the independent implementation of the different dimensions of prosody, i.e. duration, intonation, and intensity, using different techniques and their subsequent integration. We applied the Fuzzy Decision Tree (FDT) technique to model the duration dimension. In order to evaluate the effectiveness of FDT in duration modelling, we have also developed a Classification And Regression Tree (CART) based duration model using the same speech data. Each of these models was integrated into our R-Tree based prosody model. We performed both quantitative (i.e. Root Mean Square Error (RMSE) and Correlation (Corr)) and qualitative (i.e. intelligibility and naturalness) evaluations on the two duration models. The results show that CART models the training data more accurately than FDT. The FDT model, however, shows a better ability to extrapolate from the training data since it achieved a better accuracy for the test data set. Our qualitative evaluation results show that our FDT model produces synthesised speech that is perceived to be more natural than our CART model. In addition, we also observed that the expressiveness of FDT is much better than that of CART. That is because the representation in FDT is not restricted to a set of piece-wise or discrete constant approximation. We, therefore, conclude that the FDT approach is a practical approach for duration modelling in SY TTS applications. © 2006 Elsevier Ltd. All rights reserved.

Non-Gaussian error probability in optical soliton transmission

We find the probability distribution of the fluctuating parameters of a soliton propagating through a medium with additive noise. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagation within the framework of noisy nonlinear Schrödinger equation. We then consider model modifications due to in-line (filtering, amplitude and phase modulation) control. It is examined how control elements change the error probability in optical soliton transmission. Even though a weak noise is considered, we are interested here in probabilities of error-causing large fluctuations which are beyond perturbation theory. We describe in detail a new phenomenon of soliton collapse that occurs under the combined action of noise, filtering and amplitude modulation. © 2004 Elsevier B.V. All rights reserved.

Mathematical Model and Simulation of a Pneumatic Apparatus for In-Drilling Alignment of an Inertial Navigation Unit during Horizontal Well Drilling

Conventional methods in horizontal drilling processes incorporate magnetic surveying techniques for determining the position and orientation of the bottom-hole assembly (BHA). Such means result in an increased weight of the drilling assembly, higher cost due to the use of non-magnetic collars necessary for the shielding of the magnetometers, and significant errors in the position of the drilling bit. A fiber-optic gyroscope (FOG) based inertial navigation system (INS) has been proposed as an alternative to magnetometer -based downhole surveying. The utilizing of a tactical-grade FOG based surveying system in the harsh downhole environment has been shown to be theoretically feasible, yielding a significant BHA position error reduction (less than 100m over a 2-h experiment). To limit the growing errors of the INS, an in-drilling alignment (IDA) method for the INS has been proposed. This article aims at describing a simple, pneumatics-based design of the IDA apparatus and its implementation downhole. A mathematical model of the setup is developed and tested with Bloodshed Dev-C++. The simulations demonstrate a simple, low cost and feasible IDA apparatus.

Laser-induced breakdown spectroscopy quantitative analysis method via adaptive analytical line selection and relevance vector machine regression model

Abstract A new LIBS quantitative analysis method based on analytical line adaptive selection and Relevance Vector Machine (RVM) regression model is proposed. First, a scheme of adaptively selecting analytical line is put forward in order to overcome the drawback of high dependency on a priori knowledge. The candidate analytical lines are automatically selected based on the built-in characteristics of spectral lines, such as spectral intensity, wavelength and width at half height. The analytical lines which will be used as input variables of regression model are determined adaptively according to the samples for both training and testing. Second, an LIBS quantitative analysis method based on RVM is presented. The intensities of analytical lines and the elemental concentrations of certified standard samples are used to train the RVM regression model. The predicted elemental concentration analysis results will be given with a form of confidence interval of probabilistic distribution, which is helpful for evaluating the uncertainness contained in the measured spectra. Chromium concentration analysis experiments of 23 certified standard high-alloy steel samples have been carried out. The multiple correlation coefficient of the prediction was up to 98.85%, and the average relative error of the prediction was 4.01%. The experiment results showed that the proposed LIBS quantitative analysis method achieved better prediction accuracy and better modeling robustness compared with the methods based on partial least squares regression, artificial neural network and standard support vector machine.

A Bayesian Spatial Mixture Model for FMRI Analysis

We develop, implement and study a new Bayesian spatial mixture model (BSMM). The proposed BSMM allows for spatial structure in the binary activation indicators through a latent thresholded Gaussian Markov random field. We develop a Gibbs (MCMC) sampler to perform posterior inference on the model parameters, which then allows us to assess the posterior probabilities of activation for each voxel. One purpose of this article is to compare the HJ model and the BSMM in terms of receiver operating characteristics (ROC) curves. Also we consider the accuracy of the spatial mixture model and the BSMM for estimation of the size of the activation region in terms of bias, variance and mean squared error. We perform a simulation study to examine the aforementioned characteristics under a variety of configurations of spatial mixture model and BSMM both as the size of the region changes and as the magnitude of activation changes.

2D-3D registration of CT vertebra volume to fluoroscopy projection:a calibration model assessment

This study extends a previous research concerning intervertebral motion registration by means of 2D dynamic fluoroscopy to obtain a more comprehensive 3D description of vertebral kinematics. The problem of estimating the 3D rigid pose of a CT volume of a vertebra from its 2D X-ray fluoroscopy projection is addressed. 2D-3D registration is obtained maximising a measure of similarity between Digitally Reconstructed Radiographs (obtained from the CT volume) and real fluoroscopic projection. X-ray energy correction was performed. To assess the method a calibration model was realised a sheep dry vertebra was rigidly fixed to a frame of reference including metallic markers. Accurate measurement of 3D orientation was obtained via single-camera calibration of the markers and held as true 3D vertebra position; then, vertebra 3D pose was estimated and results compared. Error analysis revealed accuracy of the order of 0.1 degree for the rotation angles of about 1mm for displacements parallel to the fluoroscopic plane, and of order of 10mm for the orthogonal displacement. © 2010 P. Bifulco et al.

A laser induced breakdown spectroscopy quantitative analysis method based on the robust least squares support vector machine regression model

Data fluctuation in multiple measurements of Laser Induced Breakdown Spectroscopy (LIBS) greatly affects the accuracy of quantitative analysis. A new LIBS quantitative analysis method based on the Robust Least Squares Support Vector Machine (RLS-SVM) regression model is proposed. The usual way to enhance the analysis accuracy is to improve the quality and consistency of the emission signal, such as by averaging the spectral signals or spectrum standardization over a number of laser shots. The proposed method focuses more on how to enhance the robustness of the quantitative analysis regression model. The proposed RLS-SVM regression model originates from the Weighted Least Squares Support Vector Machine (WLS-SVM) but has an improved segmented weighting function and residual error calculation according to the statistical distribution of measured spectral data. Through the improved segmented weighting function, the information on the spectral data in the normal distribution will be retained in the regression model while the information on the outliers will be restrained or removed. Copper elemental concentration analysis experiments of 16 certified standard brass samples were carried out. The average value of relative standard deviation obtained from the RLS-SVM model was 3.06% and the root mean square error was 1.537%. The experimental results showed that the proposed method achieved better prediction accuracy and better modeling robustness compared with the quantitative analysis methods based on Partial Least Squares (PLS) regression, standard Support Vector Machine (SVM) and WLS-SVM. It was also demonstrated that the improved weighting function had better comprehensive performance in model robustness and convergence speed, compared with the four known weighting functions.

A Note on Bayesian Estimation for the Negative-Binomial Model

2000 Mathematics Subject Classification: 62F15.