Representation errors and retrievals in linear and nonlinear data assimilation

This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.

Asset liability modelling and pension schemes: the application of robust optimization to USS

This paper uses a novel numerical optimization technique - robust optimization - that is well suited to solving the asset-liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximise the Sharpe ratio. We disaggregate pension liabilities into three components - active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme’s projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes-Stein, and Black-Litterman models as well as the actual USS investment decisions. Over a 144 month out-of-sample period robust optimization is superior to the four benchmarks across 20 performance criteria, and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.

A Variance-Minimizing Filter for Large-Scale Applications

A truly variance-minimizing filter is introduced and its per for mance is demonstrated with the Korteweg– DeV ries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four - dimensional variational data assimilation (4DV AR)-like methods relying on per fect model dynamics have dif- ficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When obser vations are available, the so-called importance resampling algorithm is applied. From Bayes’ s theorem it follows that each ensemble member receives a new weight dependent on its ‘ ‘distance’ ’ t o the obser vations. Because the weights are strongly var ying, a resampling of the ensemble is necessar y. This resampling is done such that members with high weights are duplicated according to their weights, while low-weight members are largely ignored. In passing, it is noted that data assimilation is not an inverse problem by nature, although it can be for mulated that way . Also, it is shown that the posterior variance can be larger than the prior if the usual Gaussian framework is set aside. However , i n the examples presented here, the entropy of the probability densities is decreasing. The application to the ocean area around South Africa, gover ned by strongly nonlinear dynamics, shows that the method is working satisfactorily . The strong and weak points of the method are discussed and possible improvements are proposed.

An Ensemble Smoother with Error Estimates

A smoother introduced earlier by van Leeuwen and Evensen is applied to a problem in which real obser vations are used in an area with strongly nonlinear dynamics. The derivation is new , but it resembles an earlier derivation by van Leeuwen and Evensen. Again a Bayesian view is taken in which the prior probability density of the model and the probability density of the obser vations are combined to for m a posterior density . The mean and the covariance of this density give the variance-minimizing model evolution and its errors. The assumption is made that the prior probability density is a Gaussian, leading to a linear update equation. Critical evaluation shows when the assumption is justified. This also sheds light on why Kalman filters, in which the same ap- proximation is made, work for nonlinear models. By reference to the derivation, the impact of model and obser vational biases on the equations is discussed, and it is shown that Bayes’ s for mulation can still be used. A practical advantage of the ensemble smoother is that no adjoint equations have to be integrated and that error estimates are easily obtained. The present application shows that for process studies a smoother will give superior results compared to a filter , not only owing to the smooth transitions at obser vation points, but also because the origin of features can be followed back in time. Also its preference over a strong-constraint method is highlighted. Further more, it is argued that the proposed smoother is more efficient than gradient descent methods or than the representer method when error estimates are taken into account

An LDA and probability-based classifier for the diagnosis of Alzheimer's Disease from structural MRI

In this paper a custom classification algorithm based on linear discriminant analysis and probability-based weights is implemented and applied to the hippocampus measurements of structural magnetic resonance images from healthy subjects and Alzheimer’s Disease sufferers; and then attempts to diagnose them as accurately as possible. The classifier works by classifying each measurement of a hippocampal volume as healthy controlsized or Alzheimer’s Disease-sized, these new features are then weighted and used to classify the subject as a healthy control or suffering from Alzheimer’s Disease. The preliminary results obtained reach an accuracy of 85.8% and this is a similar accuracy to state-of-the-art methods such as a Naive Bayes classifier and a Support Vector Machine. An advantage of the method proposed in this paper over the aforementioned state of the art classifiers is the descriptive ability of the classifications it produces. The descriptive model can be of great help to aid a doctor in the diagnosis of Alzheimer’s Disease, or even further the understand of how Alzheimer’s Disease affects the hippocampus.

Bayesian model comparison with un-normalised likelihoods

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalizing constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes’ factors for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates.

Essays on robust portfolio selection and pension finance

This thesis examines three different, but related problems in the broad area of portfolio management for long-term institutional investors, and focuses mainly on the case of pension funds. The first idea (Chapter 3) is the application of a novel numerical technique – robust optimization – to a real-world pension scheme (the Universities Superannuation Scheme, USS) for first time. The corresponding empirical results are supported by many robustness checks and several benchmarks such as the Bayes-Stein and Black-Litterman models that are also applied for first time in a pension ALM framework, the Sharpe and Tint model and the actual USS asset allocations. The second idea presented in Chapter 4 is the investigation of whether the selection of the portfolio construction strategy matters in the SRI industry, an issue of great importance for long term investors. This study applies a variety of optimal and naïve portfolio diversification techniques to the same SRI-screened universe, and gives some answers to the question of which portfolio strategies tend to create superior SRI portfolios. Finally, the third idea (Chapter 5) compares the performance of a real-world pension scheme (USS) before and after the recent major changes in the pension rules under different dynamic asset allocation strategies and the fixed-mix portfolio approach and quantifies the redistributive effects between various stakeholders. Although this study deals with a specific pension scheme, the methodology can be applied by other major pension schemes in countries such as the UK and USA that have changed their rules.

The hidden diversity of Coleodactylus amazonicus (Sphaerodactylinae, Gekkota) revealed by molecular data

Coleodactylus amazonicus, a small leaf-litter diurnal gecko widely distributed in Amazon Basin has been, considered a single species with no significant morphological differences between populations along its range. A recent molecular study, however, detected large genetic differences between populations of central Amazonia and those in the easternmost part of the Amazon Basin, suggesting the presence of taxonomically unrecognised diversity. In this study, DNA sequences of three mitochondrial (165, cytb, and ND4) and two nuclear genes (RAG-1, c-mos) were used to investigate whether the species currently identified as C. amazonicus contains morphologically cryptic species lineages. The present phylogenetic analysis reveals further genetic subdivision including at least five potential species lineages, restricted to northeastern (lineage A), southeastern (lineage B), central-northern (lineage E) and central-southern (lineages C and D) parts of Amazon Basin. All clades are characterized by exclusive groups of alleles for both nuclear genes and highly divergent mitochondrial haplotype clades, with corrected pairwise net sequence divergence between sister lineages ranging from 9.1% to 20.7% for the entire mtDNA dataset. Results of this study suggest that the real diversity of ""C. amazonicus"" has been underestimated due to its apparent cryptic diversification. (C) 2009 Elsevier Inc. All rights reserved.

Bayesian network classifiers: Beyond classification accuracy

This work proposes and discusses an approach for inducing Bayesian classifiers aimed at balancing the tradeoff between the precise probability estimates produced by time consuming unrestricted Bayesian networks and the computational efficiency of Naive Bayes (NB) classifiers. The proposed approach is based on the fundamental principles of the Heuristic Search Bayesian network learning. The Markov Blanket concept, as well as a proposed ""approximate Markov Blanket"" are used to reduce the number of nodes that form the Bayesian network to be induced from data. Consequently, the usually high computational cost of the heuristic search learning algorithms can be lessened, while Bayesian network structures better than NB can be achieved. The resulting algorithms, called DMBC (Dynamic Markov Blanket Classifier) and A-DMBC (Approximate DMBC), are empirically assessed in twelve domains that illustrate scenarios of particular interest. The obtained results are compared with NB and Tree Augmented Network (TAN) classifiers, and confinn that both proposed algorithms can provide good classification accuracies and better probability estimates than NB and TAN, while being more computationally efficient than the widely used K2 Algorithm.

On the influence of imputation in classification: practical issues

The substitution of missing values, also called imputation, is an important data preparation task for many domains. Ideally, the substitution of missing values should not insert biases into the dataset. This aspect has been usually assessed by some measures of the prediction capability of imputation methods. Such measures assume the simulation of missing entries for some attributes whose values are actually known. These artificially missing values are imputed and then compared with the original values. Although this evaluation is useful, it does not allow the influence of imputed values in the ultimate modelling task (e.g. in classification) to be inferred. We argue that imputation cannot be properly evaluated apart from the modelling task. Thus, alternative approaches are needed. This article elaborates on the influence of imputed values in classification. In particular, a practical procedure for estimating the inserted bias is described. As an additional contribution, we have used such a procedure to empirically illustrate the performance of three imputation methods (majority, naive Bayes and Bayesian networks) in three datasets. Three classifiers (decision tree, naive Bayes and nearest neighbours) have been used as modelling tools in our experiments. The achieved results illustrate a variety of situations that can take place in the data preparation practice.

Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported. (C) 2011 Elsevier B.V. All rights reserved.

A robust Bayesian approach to null intercept measurement error model with application to dental data

Measurement error models often arise in epidemiological and clinical research. Usually, in this set up it is assumed that the latent variable has a normal distribution. However, the normality assumption may not be always correct. Skew-normal/independent distribution is a class of asymmetric thick-tailed distributions which includes the Skew-normal distribution as a special case. In this paper, we explore the use of skew-normal/independent distribution as a robust alternative to null intercept measurement error model under a Bayesian paradigm. We assume that the random errors and the unobserved value of the covariate (latent variable) follows jointly a skew-normal/independent distribution, providing an appealing robust alternative to the routine use of symmetric normal distribution in this type of model. Specific distributions examined include univariate and multivariate versions of the skew-normal distribution, the skew-t distributions, the skew-slash distributions and the skew contaminated normal distributions. The methods developed is illustrated using a real data set from a dental clinical trial. (C) 2008 Elsevier B.V. All rights reserved.

Simultaneous prediction of symptom severity and cause in data from a test battery for Parkinson patients, using machine learning methods

The main purpose of this thesis project is to prediction of symptom severity and cause in data from test battery of the Parkinson’s disease patient, which is based on data mining. The collection of the data is from test battery on a hand in computer. We use the Chi-Square method and check which variables are important and which are not important. Then we apply different data mining techniques on our normalize data and check which technique or method gives good results.The implementation of this thesis is in WEKA. We normalize our data and then apply different methods on this data. The methods which we used are Naïve Bayes, CART and KNN. We draw the Bland Altman and Spearman’s Correlation for checking the final results and prediction of data. The Bland Altman tells how the percentage of our confident level in this data is correct and Spearman’s Correlation tells us our relationship is strong. On the basis of results and analysis we see all three methods give nearly same results. But if we see our CART (J48 Decision Tree) it gives good result of under predicted and over predicted values that’s lies between -2 to +2. The correlation between the Actual and Predicted values is 0,794in CART. Cause gives the better percentage classification result then disability because it can use two classes.

Speech Assessment for the Classification of Hypokinetic Dysthria in Parkinson Disease

The aim of this thesis is to investigate computerized voice assessment methods to classify between the normal and Dysarthric speech signals. In this proposed system, computerized assessment methods equipped with signal processing and artificial intelligence techniques have been introduced. The sentences used for the measurement of inter-stress intervals (ISI) were read by each subject. These sentences were computed for comparisons between normal and impaired voice. Band pass filter has been used for the preprocessing of speech samples. Speech segmentation is performed using signal energy and spectral centroid to separate voiced and unvoiced areas in speech signal. Acoustic features are extracted from the LPC model and speech segments from each audio signal to find the anomalies. The speech features which have been assessed for classification are Energy Entropy, Zero crossing rate (ZCR), Spectral-Centroid, Mean Fundamental-Frequency (Meanf0), Jitter (RAP), Jitter (PPQ), and Shimmer (APQ). Naïve Bayes (NB) has been used for speech classification. For speech test-1 and test-2, 72% and 80% accuracies of classification between healthy and impaired speech samples have been achieved respectively using the NB. For speech test-3, 64% correct classification is achieved using the NB. The results direct the possibility of speech impairment classification in PD patients based on the clinical rating scale.