Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

A model for radiation-induced bystander effects, with allowance for spatial position and the effects of cell turnover

Bystander effects, whereby cells that are not directly exposed to ionizing radiation exhibit adverse biological effects, have been observed in a number of experimental systems. A novel stochastic model of the radiation-induced bystander effect is developed that takes account of spatial location, cell killing and repopulation. The ionizing radiation dose- and time-responses of this model are explored, and it is shown to exhibit pronounced downward curvature in the high dose-rate region, similar to that observed in many experimental systems, reviewed in the paper. It is also shown to predict the augmentation of effect after fractionated delivery of dose that has been observed in certain experimental systems. It is shown that the generally intractable solution of the full stochastic system can be considerably simplified by assumption of pairwise conditional dependence that varies exponentially over time. (C) 2004 Elsevier Ltd. All rights reserved.

Hui and Walter's latent-class model extended to estimate diagnostic test properties from surveillance data: a latent model for latent data

Diagnostic test sensitivity and specificity are probabilistic estimates with far reaching implications for disease control, management and genetic studies. In the absence of 'gold standard' tests, traditional Bayesian latent class models may be used to assess diagnostic test accuracies through the comparison of two or more tests performed on the same groups of individuals. The aim of this study was to extend such models to estimate diagnostic test parameters and true cohort-specific prevalence, using disease surveillance data. The traditional Hui-Walter latent class methodology was extended to allow for features seen in such data, including (i) unrecorded data (i.e. data for a second test available only on a subset of the sampled population) and (ii) cohort-specific sensitivities and specificities. The model was applied with and without the modelling of conditional dependence between tests. The utility of the extended model was demonstrated through application to bovine tuberculosis surveillance data from Northern and the Republic of Ireland. Simulation coupled with re-sampling techniques, demonstrated that the extended model has good predictive power to estimate the diagnostic parameters and true herd-level prevalence from surveillance data. Our methodology can aid in the interpretation of disease surveillance data, and the results can potentially refine disease control strategies.

Bayesian Estimation for Performance Measures of Two Diagnostic Tests in the Presence of Verification Bias

Sensitivity and specificity are measures that allow us to evaluate the performance of a diagnostic test. In practice, it is common to have situations where a proportion of selected individuals cannot have the real state of the disease verified, since the verification could be an invasive procedure, as occurs with biopsy. This happens, as a special case, in the diagnosis of prostate cancer, or in any other situation related to risks, that is, not practicable, nor ethical, or in situations with high cost. For this case, it is common to use diagnostic tests based only on the information of verified individuals. This procedure can lead to biased results or workup bias. In this paper, we introduce a Bayesian approach to estimate the sensitivity and the specificity for two diagnostic tests considering verified and unverified individuals, a result that generalizes the usual situation based on only one diagnostic test.

A General Latent Class Model for Performance Evaluation of Diagnostic Tests in the Absence of a Gold Standard: An Application to Chagas Disease

We propose a new general Bayesian latent class model for evaluation of the performance of multiple diagnostic tests in situations in which no gold standard test exists based on a computationally intensive approach. The modeling represents an interesting and suitable alternative to models with complex structures that involve the general case of several conditionally independent diagnostic tests, covariates, and strata with different disease prevalences. The technique of stratifying the population according to different disease prevalence rates does not add further marked complexity to the modeling, but it makes the model more flexible and interpretable. To illustrate the general model proposed, we evaluate the performance of six diagnostic screening tests for Chagas disease considering some epidemiological variables. Serology at the time of donation (negative, positive, inconclusive) was considered as a factor of stratification in the model. The general model with stratification of the population performed better in comparison with its concurrents without stratification. The group formed by the testing laboratory Biomanguinhos FIOCRUZ-kit (c-ELISA and rec-ELISA) is the best option in the confirmation process by presenting false-negative rate of 0.0002% from the serial scheme. We are 100% sure that the donor is healthy when these two tests have negative results and he is chagasic when they have positive results.

Mining tissue microarray data to uncover combinations of biomarker expression patterns that improve intermediate staging and grading of clear cell renal cell cancer

PURPOSE: Tumor stage and nuclear grade are the most important prognostic parameters of clear cell renal cell carcinoma (ccRCC). The progression risk of ccRCC remains difficult to predict particularly for tumors with organ-confined stage and intermediate differentiation grade. Elucidating molecular pathways deregulated in ccRCC may point to novel prognostic parameters that facilitate planning of therapeutic approaches. EXPERIMENTAL DESIGN: Using tissue microarrays, expression patterns of 15 different proteins were evaluated in over 800 ccRCC patients to analyze pathways reported to be physiologically controlled by the tumor suppressors von Hippel-Lindau protein and phosphatase and tensin homologue (PTEN). Tumor staging and grading were improved by performing variable selection using Cox regression and a recursive bootstrap elimination scheme. RESULTS: Patients with pT2 and pT3 tumors that were p27 and CAIX positive had a better outcome than those with all remaining marker combinations. A prolonged survival among patients with intermediate grade (grade 2) correlated with both nuclear p27 and cytoplasmic PTEN expression, as well as with inactive, nonphosphorylated ribosomal protein S6. By applying graphical log-linear modeling for over 700 ccRCC for which the molecular parameters were available, only a weak conditional dependence existed between the expression of p27, PTEN, CAIX, and p-S6, suggesting that the dysregulation of several independent pathways are crucial for tumor progression. CONCLUSIONS: The use of recursive bootstrap elimination, as well as graphical log-linear modeling for comprehensive tissue microarray (TMA) data analysis allows the unraveling of complex molecular contexts and may improve predictive evaluations for patients with advanced renal cancer.

Multi-dimensional classification with super-classes

The multi-dimensional classification problem is a generalisation of the recently-popularised task of multi-label classification, where each data instance is associated with multiple class variables. There has been relatively little research carried out specific to multi-dimensional classification and, although one of the core goals is similar (modelling dependencies among classes), there are important differences; namely a higher number of possible classifications. In this paper we present method for multi-dimensional classification, drawing from the most relevant multi-label research, and combining it with important novel developments. Using a fast method to model the conditional dependence between class variables, we form super-class partitions and use them to build multi-dimensional learners, learning each super-class as an ordinary class, and thus explicitly modelling class dependencies. Additionally, we present a mechanism to deal with the many class values inherent to super-classes, and thus make learning efficient. To investigate the effectiveness of this approach we carry out an empirical evaluation on a range of multi-dimensional datasets, under different evaluation metrics, and in comparison with high-performing existing multi-dimensional approaches from the literature. Analysis of results shows that our approach offers important performance gains over competing methods, while also exhibiting tractable running time.

Fusión de redes Bayesianas Gaussianas

Las redes Bayesianas constituyen un modelo ampliamente utilizado para la representación de relaciones de dependencia condicional en datos multivariantes. Su aprendizaje a partir de un conjunto de datos o expertos ha sido estudiado profundamente desde su concepción. Sin embargo, en determinados escenarios se demanda la obtención de un modelo común asociado a particiones de datos o conjuntos de expertos. En este caso, se trata el problema de fusión o agregación de modelos. Los trabajos y resultados en agregación de redes Bayesianas son de naturaleza variada, aunque escasos en comparación con aquellos de aprendizaje. En este documento, se proponen dos métodos para la agregación de redes Gaussianas, definidas como aquellas redes Bayesianas que modelan una distribución Gaussiana multivariante. Los métodos presentados son efectivos, precisos y producen redes con menor cantidad de parámetros en comparación con los modelos obtenidos individualmente. Además, constituyen un enfoque novedoso al incorporar nociones exploradas tradicionalmente por separado en el estado del arte. Futuras aplicaciones en entornos escalables hacen dichos métodos especialmente atractivos, dada su simplicidad y la ganancia en compacidad de la representación obtenida.---ABSTRACT---Bayesian networks are a widely used model for the representation of conditional dependence relationships among variables in multivariate data. The task of learning them from a data set or experts has been deeply studied since their conception. However, situations emerge where there is a need of obtaining a consensuated model from several data partitions or a set of experts. This situation is referred to as model fusion or aggregation. Results about Bayesian network aggregation, although rich in variety, have been scarce when compared to the learning task. In this context, two methods are proposed for the aggregation of Gaussian Bayesian networks, that is, Bayesian networks whose underlying modelled distribution is a multivariate Gaussian. Both methods are effective, precise and produce networks with fewer parameters in comparison with the models obtained by individual learning. They constitute a novel approach given that they incorporate notions traditionally explored separately in the state of the art. Future applications in scalable computer environments make such models specially attractive, given their simplicity and the gaining in sparsity of the produced model.

An investigation of the impact of various geographical scales for the specification of spatial dependence

Ecological studies are based on characteristics of groups of individuals, which are common in various disciplines including epidemiology. It is of great interest for epidemiologists to study the geographical variation of a disease by accounting for the positive spatial dependence between neighbouring areas. However, the choice of scale of the spatial correlation requires much attention. In view of a lack of studies in this area, this study aims to investigate the impact of differing definitions of geographical scales using a multilevel model. We propose a new approach -- the grid-based partitions and compare it with the popular census region approach. Unexplained geographical variation is accounted for via area-specific unstructured random effects and spatially structured random effects specified as an intrinsic conditional autoregressive process. Using grid-based modelling of random effects in contrast to the census region approach, we illustrate conditions where improvements are observed in the estimation of the linear predictor, random effects, parameters, and the identification of the distribution of residual risk and the aggregate risk in a study region. The study has found that grid-based modelling is a valuable approach for spatially sparse data while the SLA-based and grid-based approaches perform equally well for spatially dense data.

Gaussian Process Vine Copulas for Multivariate Dependence

Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, it is common to assume that each of these conditional bivariate copulas is independent from its conditioning variables. In this paper, we relax this assumption by discovering the latent functions that specify the shape of a conditional copula given its conditioning variables We learn these functions by following a Bayesian approach based on sparse Gaussian processes with expectation propagation for scalable, approximate inference. Experiments on real-world datasets show that, when modeling all conditional dependencies, we obtain better estimates of the underlying copula of the data.

Exploitation of symbolic information in interprocedural dependence analysis

The requirement for a very accurate dependence analysis to underpin software tools to aid the generation of efficient parallel implementations of scalar code is argued. The current status of dependence analysis is shown to be inadequate for the generation of efficient parallel code, causing too many conservative assumptions to be made. This paper summarises the limitations of conventional dependence analysis techniques, and then describes a series of extensions which enable the production of a much more accurate dependence graph. The extensions include analysis of symbolic variables, the development of a symbolic inequality disproof algorithm and its exploitation in a symbolic Banerjee inequality test; the use of inference engine proofs; the exploitation of exact dependence and dependence pre-domination attributes; interprocedural array analysis; conditional variable definition tracing; integer array tracing and division calculations. Analysis case studies on typical numerical code is shown to reduce the total dependencies estimated from conventional analysis by up to 50%. The techniques described in this paper have been embedded within a suite of tools, CAPTools, which combines analysis with user knowledge to produce efficient parallel implementations of numerical mesh based codes.

Sequencing and its consequences:Path dependence and the relationships between genetics and medicalization

Both advocacy for and critiques of the Human Genome Project assume a self-sustaining relationship between genetics and. medicalization. However, this assumption ignores the ways in which the meanings of genetic research are conditional on its position in sequences of events. Based, on analyses of three conditions for which at least one putative gene or genetic marker has been identified, this article argues that critical junctures in the institutional stabilization of phenotypes and the mechanisms that sustain such classifications over time configure the practices and meanings of genetic research. Path dependence is critical to understanding the lack of consistent fit between genetics and medlcalization.

Conditional male dimorphism and alternative reproductive tactics in a Neotropical arachnid (Opiliones)

In arthropods, most cases of morphological dimorphism within males are the result of a conditional evolutionarily stable strategy (ESS) with status-dependent tactics. In conditionally male-dimorphic species, the status` distributions of male morphs often overlap, and the environmentally cued threshold model (ET) states that the degree of overlap depends on the genetic variation in the distribution of the switchpoints that determine which morph is expressed in each value of status. Here we describe male dimorphism and alternative mating behaviors in the harvestman Serracutisoma proximum. Majors express elongated second legs and use them in territorial fights; minors possess short second legs and do not fight, but rather sneak into majors` territories and copulate with egg-guarding females. The static allometry of second legs reveals that major phenotype expression depends on body size (status), and that the switchpoint underlying the dimorphism presents a large amount of genetic variation in the population, which probably results from weak selective pressure on this trait. With a mark-recapture study, we show that major phenotype expression does not result in survival costs, which is consistent with our hypothesis that there is weak selection on the switchpoint. Finally, we demonstrate that switchpoint is independent of status distribution. In conclusion, our data support the ET model prediction that the genetic correlation between status and switchpoint is low, allowing the status distribution to evolve or to fluctuate seasonally, without any effect on the position of the mean switchpoint.

Parametric conditional frailty models for recurrent cardiovascular events in the lipid study

Background Analysis of recurrent event data is frequently needed in clinical and epidemiological studies. An important issue in such analysis is how to account for the dependence of the events in an individual and any unobserved heterogeneity of the event propensity across individuals.Methods We applied a number of conditional frailty and nonfrailty models in an analysis involving recurrent myocardial infarction events in the Long-Term Intervention with Pravastatin in Ischaemic Disease study. A multiple variable risk prediction model was developed for both males and females. Results A Weibull model with a gamma frailty term fitted the data better than other frailty models for each gender. Among nonfrailty models the stratified survival model fitted the data best for each gender. The relative risk estimated by the elapsed time model was close to that estimated by the gap time model. We found that a cholesterol-lowering drug, pravastatin (the intervention being tested in the trial) had significant protective effect against the occurrence of myocardial infarction in men (HR¼0.71, 95% CI0.60–0.83). However, the treatment effect was not significant in women due to smaller sample size (HR¼0.75, 95% CI 0.51–1.10). There were no significant interactions between the treatment effect and each recurrent MI event (p¼0.24 for men and p¼0.55 for women). The risk of developing an MI event for a male who had an MI event during follow-up was about 3.4 (95% CI 2.6–4.4) times the risk compared with those who did not have an MI event. The corresponding relative risk for a female was about 7.8 (95% CI 4.4–13.6). Limitations The number of female patients was relatively small compared with their male counterparts, which may result in low statistical power to find real differences in the effect of treatment and other potential risk factors.Conclusions The conditional frailty model suggested that after accounting for all the risk factors in the model, there was still unmeasured heterogeneity of the risk for myocardial infarction, indicating the effect of subject-specific risk factors. These risk prediction models can be used to classify cardiovascular disease patients into different risk categories and may be useful for the most effective targeting of preventive therapies for cardiovascular disease.