Bayesian analysis of extreme events with threshold estimation

The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.

Anaerobic threshold estimation by statistical modelling.

Anaerobic threshold (AT) is usually estimated as a change point problem by visual analysis of the cardiorespiratory response to incremental dynamic exercise. In this study, two phase linear (TPL) models of the linear-linear and linear-quadratic type were used for the estimation of AT. The correlation coefficient between the classical and statistical approaches was 0.88, and 0.89 after outlier exclusion. The TPL models provide a simple method for estimating AT that can be easily implemented using a digital computer for the automatic pattern recognition of AT.

A comparison of fixed-step-size and Bayesian staircases for sensory threshold estimation

Fixed-step-size (FSS) and Bayesian staircases are widely used methods to estimate sensory thresholds in 2AFC tasks, although a direct comparison of both types of procedure under identical conditions has not previously been reported. A simulation study and an empirical test were conducted to compare the performance of optimized Bayesian staircases with that of four optimized variants of FSS staircase differing as to up-down rule. The ultimate goal was to determine whether FSS or Bayesian staircases are the best choice in experimental psychophysics. The comparison considered the properties of the estimates (i.e. bias and standard errors) in relation to their cost (i.e. the number of trials to completion). The simulation study showed that mean estimates of Bayesian and FSS staircases are dependable when sufficient trials are given and that, in both cases, the standard deviation (SD) of the estimates decreases with number of trials, although the SD of Bayesian estimates is always lower than that of FSS estimates (and thus, Bayesian staircases are more efficient). The empirical test did not support these conclusions, as (1) neither procedure rendered estimates converging on some value, (2) standard deviations did not follow the expected pattern of decrease with number of trials, and (3) both procedures appeared to be equally efficient. Potential factors explaining the discrepancies between simulation and empirical results are commented upon and, all things considered, a sensible recommendation is for psychophysicists to run no fewer than 18 and no more than 30 reversals of an FSS staircase implementing the 1-up/3-down rule.

Stopping rules in Bayesian adaptive threshold estimation

Threshold estimation with sequential procedures is justifiable on the surmise that the index used in the so-called dynamic stopping rule has diagnostic value for identifying when an accurate estimate has been obtained. The performance of five types of Bayesian sequential procedure was compared here to that of an analogous fixed-length procedure. Indices for use in sequential procedures were: (1) the width of the Bayesian probability interval, (2) the posterior standard deviation, (3) the absolute change, (4) the average change, and (5) the number of sign fluctuations. A simulation study was carried out to evaluate which index renders estimates with less bias and smaller standard error at lower cost (i.e. lower average number of trials to completion), in both yes–no and two-alternative forced-choice (2AFC) tasks. We also considered the effect of the form and parameters of the psychometric function and its similarity with themodel function assumed in the procedure. Our results show that sequential procedures do not outperform fixed-length procedures in yes–no tasks. However, in 2AFC tasks, sequential procedures not based on sign fluctuations all yield minimally better estimates than fixed-length procedures, although most of the improvement occurs with short runs that render undependable estimates and the differences vanish when the procedures run for a number of trials (around 70) that ensures dependability. Thus, none of the indices considered here (some of which are widespread) has the diagnostic value that would justify its use. In addition, difficulties of implementation make sequential procedures unfit as alternatives to fixed-length procedures.

Quantification of interpoint topographic correlations of threshold values in glaucomatous visual fields

Purpose: The authors sought to quantify neighboring and distant interpoint correlations of threshold values within the visual field in patients with glaucoma. Methods: Visual fields of patients with confirmed or suspected glaucoma were analyzed (n = 255). One eye per patient was included. Patients were examined using the 32 program of the Octopus 1-2-3. Linear regression analysis among each of the locations and the rest of the points of the visual field was performed, and the correlation coefficient was calculated. The degree of correlation was categorized as high (r > 0.66), moderate (0.66 = r > 0.33), or low (r = 0.33). The standard error of threshold estimation was calculated. Results: Most locations of the visual field had high and moderate correlations with neighboring points and with distant locations corresponding to the same nerve fiber bundle. Locations of the visual field had low correlations with those of the opposite hemifield, with the exception of locations temporal to the blind spot. The standard error of threshold estimation increased from 0.6 to 0.9 dB with an r reduction of 0.1. Conclusion: Locations of the visual field have highest interpoint correlation with neighboring points and with distant points in areas corresponding to the distribution of the retinal nerve fiber layer. The quantification of interpoint correlations may be useful in the design and interpretation of visual field tests in patients with glaucoma.

Sequential decision fusion of multibiometrics applied to text-dependent speaker verification for controlled errors

Reliability of the performance of biometric identity verification systems remains a significant challenge. Individual biometric samples of the same person (identity class) are not identical at each presentation and performance degradation arises from intra-class variability and inter-class similarity. These limitations lead to false accepts and false rejects that are dependent. It is therefore difficult to reduce the rate of one type of error without increasing the other. The focus of this dissertation is to investigate a method based on classifier fusion techniques to better control the trade-off between the verification errors using text-dependent speaker verification as the test platform. A sequential classifier fusion architecture that integrates multi-instance and multisample fusion schemes is proposed. This fusion method enables a controlled trade-off between false alarms and false rejects. For statistically independent classifier decisions, analytical expressions for each type of verification error are derived using base classifier performances. As this assumption may not be always valid, these expressions are modified to incorporate the correlation between statistically dependent decisions from clients and impostors. The architecture is empirically evaluated by applying the proposed architecture for text dependent speaker verification using the Hidden Markov Model based digit dependent speaker models in each stage with multiple attempts for each digit utterance. The trade-off between the verification errors is controlled using the parameters, number of decision stages (instances) and the number of attempts at each decision stage (samples), fine-tuned on evaluation/tune set. The statistical validation of the derived expressions for error estimates is evaluated on test data. The performance of the sequential method is further demonstrated to depend on the order of the combination of digits (instances) and the nature of repetitive attempts (samples). The false rejection and false acceptance rates for proposed fusion are estimated using the base classifier performances, the variance in correlation between classifier decisions and the sequence of classifiers with favourable dependence selected using the 'Sequential Error Ratio' criteria. The error rates are better estimated by incorporating user-dependent (such as speaker-dependent thresholds and speaker-specific digit combinations) and class-dependent (such as clientimpostor dependent favourable combinations and class-error based threshold estimation) information. The proposed architecture is desirable in most of the speaker verification applications such as remote authentication, telephone and internet shopping applications. The tuning of parameters - the number of instances and samples - serve both the security and user convenience requirements of speaker-specific verification. The architecture investigated here is applicable to verification using other biometric modalities such as handwriting, fingerprints and key strokes.

Racial and spatial interaction for neighborhood dynamics in Chicago

We look at at the empirical validity of Schelling’s models for racial residential segregation applied to the case of Chicago. Most of the empirical literature has focused exclusively the single neighborhood model, also known as the tipping point model and neglected a multineighborhood approach or a unified approach. The multi-neighborhood approach introduced spatial interaction across the neighborhoods, in particular we look at spatial interaction across neighborhoods sharing a border. An initial exploration of the data indicates that spatial contiguity might be relevant to properly analyse the so call tipping phenomena of predominately non-Hispanic white neighborhoods to predominantly minority neighborhoods within a decade. We introduce an econometric model that combines an approach to estimate tipping point using threshold effects and a spatial autoregressive model. The estimation results from the model disputes the existence of a tipping point, that is a discontinuous change in the rate of growth of the non-Hispanic white population due to a small increase in the minority share of the neighborhood. In addition we find that racial distance between the neighborhood of interest and it surrounding neighborhoods has an important effect on the dynamics of racial segregation in Chicago.

Properties of series feature aggregation schemes

Feature aggregation is a critical technique in content-based image retrieval (CBIR) that combines multiple feature distances to obtain image dissimilarity. Conventional parallel feature aggregation (PFA) schemes failed to effectively filter out the irrelevant images using individual visual features before ranking images in collection. Series feature aggregation (SFA) is a new scheme that aims to address this problem. This paper investigates three important properties of SFA that are significant for design of systems. They reveal the irrelevance of feature order and the convertibility of SFA and PFA as well as the superior performance of SFA. Furthermore, based on Gaussian kernel density estimator, the authors propose a new method to estimate the visual threshold, which is the key parameter of SFA. Experiments, conducted with IAPR TC-12 benchmark image collection (ImageCLEF2006) that contains over 20,000 photographic images and defined queries, have shown that SFA can outperform conventional PFA schemes.

Investigation of chromatic function in the normal and abnormal eye

This study examined the use of non-standard parameters to investigate the visual field, with particular reference to the detection of glaucomatous visual field loss. Evaluation of the new perimetric strategy for threshold estimation - FASTPAC, demonstrated a reduction in the examination time of normals compared to the standard strategy. Despite an increased within-test variability the FASTPAC strategy produced a similar mean sensitivity to the standard strategy, reducing the effects of patient fatigue. The new technique of Blue-Yellow perimetry was compared to White-White perimetry for the detection of glaucomatous field loss in OHT and POAG. Using a database of normal subjects, confidence limits for normality were constructed to account for the increased between-subject variability with increase in age and eccentricity and for the greater variability of the Blue-Yellow field compared to the White-White field. Effects of individual ocular media absorption had little effect on Blue-Yellow field variability. Total and pattern probability analysis revealed five of 27 OHTs to exhibit Blue-Yellow focal abnormalities; two of these patients subsequently developed White-White loss. Twelve of the 24 POAGs revealed wider and/or deeper Blue-Yellow loss compared with the White-White field. Blue-Yellow perimetry showed good sensitivity and specificity characteristics, however, lack of perimetric experience and the presence of cataract influenced the Blue-Yellow visual field and may confound the interpretation of Blue-Yellow visual field loss. Visual field indices demonstrated a moderate relationship to the structural parameters of the optic nerve head using scanning laser tomography. No abnormalities in Blue-Yellow or Red-Green colour CS was apparent for the OHT patients. A greater vulnerability of the SWS pathway in glaucoma was demonstrated using Blue-Yellow perimetry however predicting which patients may benefit from B-Y perimetric examination is difficult. Furthermore, cataract and the extent of the field loss may limit the extent to which the integrity of the SWS channels can be selectively examined.

Influence of threshold stress on the estimation of the Weibull statistics

The influence of threshold stress on the estimation of the Weibull statistics is discussed in terms of the Akaike information criterion. Numerical simulations show that, if sample data are limited in number and threshold stress is not too large, the two-parameter Weibull distribution is still a preferred choice. For example, the fit of strength data of glass and ceramics to the two- and three-parameter Weibull distributions is compared.

Estimation of the depth focus from wavefront measurements

It is possible to estimate the depth of focus (DOF) of the eye directly from wavefront measurements using various retinal image quality metrics (IQMs). In such methods, DOF is defined as the range of defocus error that degrades the retinal image quality calculated from IQMs to a certain level of the maximum value. Although different retinal image quality metrics are used, currently there have been two arbitrary threshold levels adopted, 50% and 80%. There has been limited study of the relationship between these threshold levels and the actual measured DOF. We measured the subjective DOF in a group of 17 normal subjects, and used through-focus augmented visual Strehl ratio based on optical transfer function (VSOTF) derived from their wavefront aberrations as the IQM. For each subject, a VSOTF threshold level was derived that would match the subjectively measured DOF. Significant correlation was found between the subject’s estimated threshold level and the HOA RMS (Pearson’s r=0.88, p<0.001). The linear correlation can be used to estimate the threshold level for each individual subject, subsequently leading to a method for estimating individual’s DOF from a single measurement of their wavefront aberrations.

Monotonous trend estimation using recursive prony analysis

This paper presents a solution to the problem of estimating the monotonous tendency of a slow-varying oscillating system. A recursive Prony Analysis (PA) scheme is developed which involves obtaining a dynamic model with parameters identified by implementing the forgetting factor recursive least square (FFRLS) method. A box threshold principle is proposed to separate the dominant components, which results in an accurate estimation of the trend of oscillating systems. Performance of the proposed PA is evaluated using real-time measurements when random noise and vibration effects are present. Moreover, the proposed method is used to estimate monotonous tendency of deck displacement to assist in a safe landing of an unmanned aerial vehicle (UAV). It is shown that the proposed method can estimate instantaneous mean deck satisfactorily, making it well suited for integration into ship-UAV approach and landing guidance systems.