Nonparametric Modeling Approach Research Articles

Using a Nonparametric Multilevel Latent Markov Model to Evaluate Diagnostics for Trachoma

In disease control or elimination programs, diagnostics are essential for assessing the impact of interventions, refining treatment strategies, and minimizing the waste of scarce resources. Although high-performance tests are desirable, increased accuracy is frequently accompanied by a requirement for more elaborate infrastructure, which is often not feasible in the developing world. These challenges are pertinent to mapping, impact monitoring, and surveillance in trachoma elimination programs. To help inform rational design of diagnostics for trachoma elimination, we outline a nonparametric multilevel latent Markov modeling approach and apply it to 2 longitudinal cohort studies of trachoma-endemic communities in Tanzania (2000–2002) and The Gambia (2001–2002) to provide simultaneous inferences about the true population prevalence of Chlamydia trachomatis infection and disease and the sensitivity, specificity, and predictive values of 3 diagnostic tests for C. trachomatis infection. Estimates were obtained by using data collected before and after mass azithromycin administration. Such estimates are particularly important for trachoma because of the absence of a true “gold standard” diagnostic test for C. trachomatis. Estimated transition probabilities provide useful insights into key epidemiologic questions about the persistence of disease and the clearance of infection as well as the required frequency of surveillance in the postelimination setting.

Nonlinear and nonparametric modeling approaches for probabilistic forecasting of the US gross national product

Numerous time series models are available for forecasting economic output. Autoregressive models were initially applied to US gross national product (GNP), and have been extended to nonlinear structures, such as the self-exciting threshold autoregressive (SETAR) and Markov-switching autoregressive (MS-AR) models. We show that while these nonlinear models fit the in-sample data better than linear models, the out- of-sample forecast performance of extremely simple methods, such as the unconditional mean is competi- tive compared with both previously published linear and nonlinear models for GNP time series. Motivated by Occams razor and the forecasting competitiveness of the unconditional mean, we seek parsimonious models which are based on simple assumptions, incorporate few parameters, and can generate accurate forecasts. We propose nonlinear and nonparametric models based on nearest neighbor and kernel regression by forming a state-space of time delayed GNP observations. The rationale of the proposed methodology lies in identification of local regions of state-space known as nearest neighbor sub-spaces, whereby we utilize future trajectories of the neighboring states and weight them using a double kernel estimator to generate density forecasts. The models proposed in this work incorporate only one or two parameters, and the model estima- tion framework relies on optimizing the performance of in-sample density forecasts. The proposed modeling approach does not require prior assumptions regarding the form of the error distribution, and can provide transition between regimes of growth and contraction. We compare the forecasts from proposed models with classical time series models for GNP and a range of benchmarks, and validate our results on two post-war GNP time series using different performance scores, such as the root mean squared error (RMSE), mean abso- lute error (MAE), and the continuous ranked probability score (CRPS). We find that proposed models consist- ently outperformed previously published models for point and density forecasts of GNP at varying horizons.

Nonparametric regression analysis of multivariate longitudinal data

Multivariate longitudinal data are common in medical, industrial, and social science research. However, statistical analysis of such data in the current literature is restricted to linear or parametric modeling, which may well be inap- propriate in applications. On the other hand, all existing nonparametric methods for analyzing longitudinal data are for univariate cases only. When longitudinal data are multivariate, nonparametric modeling becomes challenging, as one needs to properly handle the association among the observed data across different time points and across different components of the multivariate response. Motivated by data from the National Hearth Lung and Blood Institute, this paper proposes a nonparametric modeling approach for analyzing multivariate longitudinal data. Our method is based on multivariate local polynomial smoothing. Both theoretical and numerical results show that it is useful in various settings.

Bayesian Semiparametric Multivariate GARCH Modeling

This paper proposes a Bayesian nonparametric modeling approach for the return distribution in multivariate GARCH models. In contrast to the parametric literature, the return distribution can display general forms of asymmetry and thick tails. An infinite mixture of multivariate normals is given a flexible Dirichlet process prior. The GARCH functional form enters into each of the components of this mixture. We discuss conjugate methods that allow for scale mixtures and nonconjugate methods, which provide mixing over both the location and scale of the normal components. MCMC methods are introduced for posterior simulation and computation of the predictive density. Bayes factors and density forecasts with comparisons to GARCH models with Student-t innovations demonstrate the gains from our flexible modeling approach.

Stochastic Modeling of Structural Uncertainty/Variability from Ground Vibration Modal Test Data

Abstract : The focus of this investigation is on the formulation and validation of a methodology for the estimation of a stochastic linear modal model of a structure from measurements of a few of its natural frequencies and mode shapes on a few nominally identical samples of the structure. The basis for the modal model is composed of the modes of an approximate representation of the structure, e.g., a nonupdated or preliminary finite element model. Furthermore, the variability or uncertainty in the structure is assumed to originate from stiffness properties (e.g., Young's modulus, boundary conditions, attachment conditions) so that the mass matrix of the uncertain linear modal model is identity but the corresponding stiffness matrix is random. The nonparametric stochastic modeling approach is adopted here for the representation of this latter matrix; thus, the quantities to be estimated are the mean stiffness matrix and the uncertainty level. This effort is accomplished using the maximum likelihood framework using both natural frequencies and mode shapes data. The successful application of this approach to data from the Air Force.

Collateralized Commodity Obligations: Rating and Risk Assessment

In this article we address risk characteristics and rating of Collateralized Commodity Obligations (CCO), which are recently devised structured products similar to the Collateralized Debt Obligation (CDO). Commodities as an asset class have been in the spotlight of investors’ attention for the last decade. CCOs, which are fixed income instruments, provide fixed income investors an exposure to commodity markets. The underlying assets of a CCO are Commodity Trigger Swaps (CTS), similar to a Credit Default Swap, but instead of a default, a “trigger” occurs when a commodity price reaches a certain pre-set level. Rating agencies have used their CDO evaluators to rate CCOs; however, particular characteristics of commodity prices and an abundance of historical price data for commodities render such an approach questionable. Recently, S&P has withdrawn their ratings for CCOs, which may be linked to some concerns regarding their rating approach. We examine the historical performance of CCOs and propose two novel approaches to their rating. The first is a flexible multivariate parametric model for commodity prices: a mean-reversion model with correlated trends. The second approach is close in spirit to the historical simulation method for risk management and is based on the block bootstrap technique. We apply both approaches to an example of a CCO and compare the results to the ratings provided by the rating agencies. We find that: * Simulated ratings are sensitive to the model assumptions. * The default probabilities resulting from the agencies’ ratings underestimate both historically observed and bootstrap-simulated default probabilities. * The non-parametric approach most closely matches the historically observed probabilities of default. The results demonstrate the benefit of a data-driven, non-parametric modelling approach to rating CCOs.

Bayesian nonparametric analysis of neuronal intensity rates

We propose a flexible hierarchical Bayesian nonparametric modeling approach to compare the spiking patterns of neurons recorded under multiple experimental conditions. In particular, we showcase the application of our statistical methodology using neurons recorded from the supplementary eye field region of the brains of two macaque monkeys trained to make delayed eye movements to three different types of targets. The proposed Bayesian methodology can be used to perform either a global analysis, allowing for the construction of posterior comparative intervals over the entire experimental time window, or a pointwise analysis for comparing the spiking patterns locally, in a predetermined portion of the experimental time window. By developing our nonparametric Bayesian model we are able to analyze neuronal data from three or more conditions while avoiding the computational expenses typically associated with more traditional analysis of physiological data.

Modeling moulin distribution on Sermeq Avannarleq glacier using ASTER and WorldView imagery and fuzzy set theory

A fuzzy set overlay model is used to analyze the distribution of moulins (vertical meltwater conduits) on Sermeq Avannarleq (“Dead Glacier”) in West Greenland in 1985 and 2008–09. Input data is derived from a historical topographic map based on airborne visible imagery and more recent WorldView-1 panchromatic imagery, as well as an Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) digital elevation model (DEM). A non-parametric best-fit model approach using a Monte Carlo simulation is used to derive the membership functions for moulin location based on three independent variables – elevation, slope and aspect – and to test for the robustness of the model. We determine that there is a topographic setting independent of time that favors the development of moulins in this region. Using the membership functions, and an optimal alpha cut derived for 1985, we could correctly predict the locations of ~ 88% of the moulins in 2008–09. The model accounts for increased surface melt in 2008–09 in comparison to 1985. Our results demonstrate the potential of a fuzzy set based approach to improve models of ice sheet hydrology in Western Greenland, by providing more reliable spatial distributions of entry points of meltwater into the ice based on remotely sensed datasets of the ice surface, which are readily available.

Modeling hysteretic nonlinear behavior of bridge aerodynamics via cellular automata nested neural network

A new approach to model aerodynamic nonlinearities in the time domain utilizing an artificial neural network (ANN) framework with embedded cellular automata (CA) scheme has been developed. This nonparametric modeling approach has shown good promise in capturing the hysteretic nonlinear behavior of aerodynamic systems in terms of hidden neurons involving higher-order terms. Concurrent training of a set of higher-order neural networks facilitates a unified approach for modeling the combined analysis of flutter and buffeting of cable-supported bridges. Accordingly the influence of buffeting response on the self-excited forces can be captured, including the contribution of damping and coupling effects on the buffeting response. White noise is intentionally introduced to the input data to enhance the robustness of the trained neural network embedded with optimal typology of CA. The effectiveness of this approach and its applications are discussed by way of modeling the aerodynamic behavior of a single-box girder cross-section bridge deck (2-D) under turbulent wind conditions. This approach can be extended to a full-bridge (3-D) model that also takes into account the correlation of aerodynamic forces along the bridge axis. This novel application of data-driven modeling has shown a remarkable potential for applications to bridge aerodynamics and other related areas.

Nonparametric Stochastic Modeling of Uncertainty in Rotordynamics—Part I: Formulation

A systematic and rational approach is presented for the consideration of uncertainty in rotordynamics systems, i.e., in rotor mass and gyroscopic matrices, stiffness matrix, and bearing coefficients. The approach is based on the nonparametric stochastic modeling technique, which permits the consideration of both data and modeling uncertainty. The former is induced by a lack of exact knowledge of properties such as density, Young’s modulus, etc. The latter occurs in the generation of the computational model from the physical structure as some of its features are invariably ignored, e.g., small anisotropies, or approximately represented, e.g., detailed meshing of gears. The nonparametric stochastic modeling approach, which is briefly reviewed first, introduces uncertainty in reduced order models through the randomization of their system matrices (e.g., stiffness, mass, and damping matrices of nonrotating structural dynamic systems). Here, this methodology is extended to permit the consideration of uncertainty in symmetric and asymmetric rotor dynamic systems. More specifically, uncertainties on the rotor stiffness (stiffness matrix) and/or mass properties (mass and gyroscopic matrices) are first introduced that maintain the symmetry of the rotor. The generalization of these concepts to uncertainty in the bearing coefficients is achieved next. Finally, the consideration of uncertainty in asymmetric rotors is described in detail.

End-member modelling of isothermal remanent magnetization (IRM) acquisition curves: a novel approach to diagnose remagnetization

SUMMARY To identify remagnetization is essential for palaeomagnetic studies and their geodynamic implications. The traditional approach is often based on directional analysis of palaeomagnetic data and field tests, which may be inconclusive if the apparent polar wander path (APWP) is poorly constrained or if the remagnetization predates folding. In several cases, rock magnetic work, particularly, the measurement of hysteresis loops allows identification of the so-called ‘remagnetized’ and ‘non-remagnetized’ trends. However, for weakly magnetic samples, this approach can be equivocal. Here, to improve the diagnosis of remagnetization, we investigated 192 isothermal remanent magnetization (IRM) acquisition curves (up to 700 mT) of remagnetized and non-remagnetized limestones from the Organy` a Basin, northern Spain. Also, 96 IRM acquisition curves from non-remagnetized marls were studied as a cross-check for the non-remagnetized limestones. A non-parametric end-member modelling approach is used to analyse the IRM acquisition curve data sets. First, remagnetized and non-remagnetized groups were treated separately. Two or three end-members were found to adequately describe the data variability: one end-member represents the high-coercivity contribution, whereas the low-coercivity part can be described by either one end-member or two reasonably similar endmembers. In the remagnetized limestones, the low-coercivity end-members tend to saturate at higher field values than in the non-remagnetized limestones. When the entire data set was processed together, a three-end-member model was judged optimal. This model consists of a high-coercivity end-member, a low-coercivity end-member that saturates at ∼300–400 mT and a low-coercivity end-member that approximately saturates at 700 mT. Higher contributions of the latter end-member appear to occur dominantly in the remagnetized limestones, whereas the reverse is true for the non-remagnetized limestones, so they plot in clearly distinguishable areas. Meanwhile, the IRM curves from non-remagnetized marls show a behaviour similar to that of the non-remagnetized end-member in the limestones. Therefore, this new approach can be a very useful tool to diagnose remagnetization in weakly magnetic limestones and marls. We recommend applying it to other areas of potentially remagnetized low-intensity sediments.

Growth rates and age at adult size of loggerhead sea turtles (<em>Caretta caretta</em>) in the Mediterranean Sea, estimated through capture-mark-recapture records

Growth rates of the juvenile phase of loggerhead turtles (Caretta caretta) were estimated for the first time in the Mediterranean Sea from capture-mark-recapture records. Thirty-eight turtles were released from Italian coasts and re-encountered after 1.0-10.9 years in the period 1986-2007. Their mean CCL (curved carapace length) ranged from 32.5 to 82.0 cm and they showed variable growth rates, ranging from 0 to 5.97 cm/yr (mean: 2.5). The association between annual growth rate and three covariates (mean year, mean size and time interval) was investigated through a non-parametric modelling approach. Only mean size showed a clear effect on growth rate, described by a monotonic declining curve. Variability indicates that factors not included in the model, probably individual-related ones, have an important effect on growth rates. Based on the monotonic decreasing growth function which indicates no growth spurt, a von Bertalanffy growth function was used to estimate the time required by turtles to grow within the observed size range. The results indicate that turtles would take 16-28 years to reach 66.5-84.7 cm CCL, the average nesting female sizes observed at the most important Mediterranean nesting sites, which can be considered an approximation of the size at maturity.

A semiparametric model for the systematic factors of portfolio credit risk premia

The aim of this paper is to investigate the empirical relationship between daily fluctuations in the risk premium for holding a large diversified credit portfolio, which we approximate by a benchmark credit index, and some tradeable market factors which capture systematic risk. The analysis is based on an adaptive nonparametric modelling approach which allows for the data-driven estimation of the nonlinear dynamic relationship between portfolio credit risk premia and their hypothetical components. Our main finding is that the empirical weights of the systematic factors display sudden jumps during market crises and a less intense time-dependent behaviour during normal market conditions. In addition, we find that during market crises the directions of the empirical relationships are often inconsistent with ordinary economic intuition, as they are influenced by the specific circumstances of financial markets distress.

Exchange rate forecasting using a combined parametric and nonparametric self-organising modelling approach

Financial prediction has attracted a lot of interest due to the financial implications that the accurate prediction of financial markets can have. A variety of data driven modelling approaches have been applied but their performance has produced mixed results. In this study we apply both parametric (neural networks with active neurons) and nonparametric (analog complexing) self-organising modelling methods for the daily prediction of the exchange rate market. We also propose a combined approach where the parametric and nonparametric self-organising methods are combined sequentially, exploiting the advantages of the individual methods with the aim of improving their performance. The combined method is found to produce promising results and to outperform the individual methods when tested with two exchange rates: the American Dollar and the Deutche Mark against the British Pound.

AN ARCHITECTURE FOR UNDERSTANDING INTENT USING A NOVEL HIDDEN MARKOV FORMULATION

Understanding intent is an important aspect of communication among people and is an essential component of the human cognitive system. This capability is particularly relevant to situations that involve collaboration among multiple agents or detection of situations that can pose a particular threat. In this paper, we propose an approach that allows a physical robot to detect the intent of others based on experience acquired through its own sensory–motor capabilities, then use this experience while taking the perspective of the agent whose intent should be recognized. Our method uses a novel formulation of hidden Markov models (HMMs) designed to model a robot's experience and interaction with the world when performing various actions. The robot's capability to observe and analyze the current scene employs a novel vision-based technique for target detection and tracking, using a nonparametric recursive modeling approach. We validate this architecture with a physically embedded robot, detecting the intent of several people performing various activities.

Modeling Disease Incidence Data with Spatial and Spatio Temporal Dirichlet Process Mixtures

Disease incidence or mortality data are typically available as rates or counts for specified regions, collected over time. We propose Bayesian nonparametric spatial modeling approaches to analyze such data. We develop a hierarchical specification using spatial random effects modeled with a Dirichlet process prior. The Dirichlet process is centered around a multivariate normal distribution. This latter distribution arises from a log-Gaussian process model that provides a latent incidence rate surface, followed by block averaging to the areal units determined by the regions in the study. With regard to the resulting posterior predictive inference, the modeling approach is shown to be equivalent to an approach based on block averaging of a spatial Dirichlet process to obtain a prior probability model for the finite dimensional distribution of the spatial random effects. We introduce a dynamic formulation for the spatial random effects to extend the model to spatio-temporal settings. Posterior inference is implemented through Gibbs sampling. We illustrate the methodology with simulated data as well as with a data set on lung cancer incidences for all 88 counties in the state of Ohio over an observation period of 21 years.

Safety Aspects of a Cyanamide Reaction: Inherent Safe Design through Kinetic Modelling and Adiabatic Testing

The synthesis of an active pharmaceutical ingredient involves the use of the highly unstable compound cyanamide. At temperatures above ambient, cyanamide starts to decompose slowly, so that proper safety testing is needed to facilitate safe use in chemical production. To determine the decomposition behaviour of cyanamide, we used the nonparametric kinetic modelling approach as provided in the Advanced Kinetics and Technology Solutions software package. The model was constructed on the basis of five different DSC runs, each with a different heating rate, and its validity was checked through a comparison of the predicted adiabatic runaway profile with the results of actual adiabatic experiments in the Phi-Tec calorimeter. The simulations and the experiments showed that the consequences of a runaway reaction could be very serious. Since very high concentrations of the starting materials were used in the original recipe for this reaction, the severity of a possible runaway reaction could be decreased consider...

Causal effects in longitudinal studies: Definition and maximum likelihood estimation

Recently, a nonparametric marginal structural model (NPMSM) approach to Causal Inference has been proposed [Neugebauer, R., van der Laan, M., 2006. Nonparametric causal effects based on marginal structural models. J. Statist. Plann. Inference (in press), 〈 www http://www.sciencedirect.com/science/journal/03783758 〉 .] as an appealing practical alternative to the original parametric MSM (PMSM) approach introduced by Robins [Robins, J., 1998a. Marginal structural models. In: 1997 Proceedings of the American Statistical Association, American Statistical Association, Alexandria, VA, pp. 1–10]. The new MSM-based causal inference methodology generalizes the concept of causal effects: the proposed nonparametric causal effects are interpreted as summary measures of the causal effects defined with PMSMs. In addition, causal inference with NPMSM does not rely on the assumed correct specification of a parametric MSM but instead defines causal effects based on a user-specified working causal model which can be willingly misspecified. The NPMSM approach was developed for studies with point treatment data or with longitudinal data where the outcome is not time-dependent (typically collected at the end of data collection). In this paper, we generalize this approach to longitudinal studies where the outcome is time-dependent, i.e. collected throughout the span of the studies, and address the subsequent estimation inconsistency which could easily arise from a hasty generalization of the algorithm for maximum likelihood estimation. More generally, we provide an overview of the multiple causal effect representations which have been developed based on MSMs in longitudinal studies.

Predictive control of a gas–liquid separation plant based on a Gaussian process model

Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of non-linear dynamic systems. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or to its complexity, by indicating the higher variance around the predicted mean. Gaussian process models contain noticeably less coefficients to be optimised. This paper demonstrates feasibility of application and realisation of a control algorithm based on a Gaussian process model. The extra information provided by the Gaussian process model is used in predictive control, where optimisation of the control signal takes the variance information into account. The feasibility of Gaussian process model usage for predictive control in industrial practice is demonstrated via the control of a gas–liquid separation plant.

Dynamic systems identification with Gaussian processes

This paper describes the identification of nonlinear dynamic systems with a Gaussian process (GP) prior model. This model is an example of the use of a probabilistic non-parametric modelling approach. GPs are flexible models capable of modelling complex nonlinear systems. Also, an attractive feature of this model is that the variance associated with the model response is readily obtained, and it can be used to highlight areas of the input space where prediction quality is poor, owing to the lack of data or complexity (high variance). We illustrate the GP modelling technique on a simulated example of a nonlinear system.