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.

Association Between Results of a Gene Expression Signature Assay and Recurrence-Free Interval in Patients With Stage II Colon Cancer in Cancer and Leukemia Group B 9581 (Alliance)

PURPOSE: Conventional staging methods are inadequate to identify patients with stage II colon cancer (CC) who are at high risk of recurrence after surgery with curative intent. ColDx is a gene expression, microarray-based assay shown to be independently prognostic for recurrence-free interval (RFI) and overall survival in CC. The objective of this study was to further validate ColDx using formalin-fixed, paraffin-embedded specimens collected as part of the Alliance phase III trial, C9581.

PATIENTS AND METHODS: C9581 evaluated edrecolomab versus observation in patients with stage II CC and reported no survival benefit. Under an initial case-cohort sampling design, a randomly selected subcohort (RS) comprised 514 patients from 901 eligible patients with available tissue. Forty-nine additional patients with recurrence events were included in the analysis. Final analysis comprised 393 patients: 360 RS (58 events) and 33 non-RS events. Risk status was determined for each patient by ColDx. The Self-Prentice method was used to test the association between the resulting ColDx risk score and RFI adjusting for standard prognostic variables.

RESULTS: Fifty-five percent of patients (216 of 393) were classified as high risk. After adjustment for prognostic variables that included mismatch repair (MMR) deficiency, ColDx high-risk patients exhibited significantly worse RFI (multivariable hazard ratio, 2.13; 95% CI, 1.3 to 3.5; P < .01). Age and MMR status were marginally significant. RFI at 5 years for patients classified as high risk was 82% (95% CI, 79% to 85%), compared with 91% (95% CI, 89% to 93%) for patients classified as low risk.

CONCLUSION: ColDx is associated with RFI in the C9581 subsample in the presence of other prognostic factors, including MMR deficiency. ColDx could be incorporated with the traditional clinical markers of risk to refine patient prognosis.

Radiation-induced bystander and adaptive responses in cell and tissue models.

The use of microbeam approaches has been a major advance in probing the relevance of bystander and adaptive responses in cell and tissue models. Our own studies at the Gray Cancer Institute have used both a charged particle microbeam, producing protons and helium ions and a soft X-ray microprobe, delivering focused carbon-K, aluminium-K and titanium-K soft X-rays. Using these techniques we have been able to build up a comprehensive picture of the underlying differences between bystander responses and direct effects in cell and tissue-like models. What is now clear is that bystander dose-response relationships, the underlying mechanisms of action and the targets involved are not the same as those observed for direct irradiation of DNA in the nucleus. Our recent studies have shown bystander responses even when radiation is deposited away from the nucleus in cytoplasmic targets. Also the interaction between bystander and adaptive responses may be a complex one related to dose, number of cells targeted and time interval.

Developing an integrated hydrograph separation and lumped modelling approach to quantifying hydrological pathways in Irish river catchments

An appreciation of the quantity of streamflow derived from the main hydrological pathways involved in transporting diffuse contaminants is critical when addressing a wide range of water resource management issues. In order to assess hydrological pathway contributions to streams, it is necessary to provide feasible upper and lower bounds for flows in each pathway. An important first step in this process is to provide reliable estimates of the slower responding groundwater pathways and subsequently the quicker overland and interflow pathways. This paper investigates the effectiveness of a multi-faceted approach applying different hydrograph separation techniques, supplemented by lumped hydrological modelling, for calculating the Baseflow Index (BFI), for the development of an integrated approach to hydrograph separation. A semi-distributed, lumped and deterministic rainfall runoff model known as NAM has been applied to ten catchments (ranging from 5 to 699 km2). While this modelling approach is useful as a validation method, NAM itself is also an important tool for investigation. These separation techniques provide a large variation in BFI, a difference of 0.741 predicted for BFI in a catchment with the less reliable fixed and sliding interval methods and local minima turning point methods included. This variation is reduced to 0.167 with these methods omitted. The Boughton and Eckhardt algorithms, while quite subjective in their use, provide quick and easily implemented approaches for obtaining physically realistic hydrograph separations. It is observed that while the different separation techniques give varying BFI values for each of the catchments, a recharge coefficient approach developed in Ireland, when applied in conjunction with the Master recession Curve Tabulation method, predict estimates in agreement with those obtained using the NAM model, and these estimates are also consistent with the study catchments’ geology. These two separation methods, in conjunction with the NAM model, were selected to form an integrated approach to assessing BFI in catchments.

Incidence and natural history of proliferative sickle cell retinopathy:Observations from a cohort study

Objective: To describe the incidence, prevalence, and natural history of proliferative sickle cell retinopathy (PSR). Design: Prospective longitudinal study over 20 years. Participants: Newborn screening of 100000 consecutive deliveries from 1973 to 1981 identified 315 children with homozygous sickle cell (SS) disease and 201 with SS-hemoglobin C (SC) disease. By the age of 5 years, 307 SS patients and 166 SC patients were alive and living in Jamaica and were recruited for this ophthalmic study. Methods: Description of retinal vascular changes on annual angiography and angioscopy. Main Outcome Measures: Incidence and prevalence of PSR and its behavior on follow-up. Progression of PSR was investigated using the number of eyes affected (none, one, both) and the interval until PSR onset. Results: At last review in January 2000, PSR had developed in 59 patients (14 SS, 45 SC), unilaterally in 36 patients and bilaterally in 23. Incidence increased with age in both genotypes, with crude annual incidence rates of 0.5 cases (95% confidence interval [CI], 0.3-0.8) per 100 SS subjects and 2.5 cases (95% CI, 1.9-3.3) per 100 SC subjects. Prevalence was greater in SC disease, and by the ages of 24 to 26 years, PSR had occurred in 43% subjects with SC disease and in 14% subjects with SS disease. Patients with unilateral PSR had a 16% (11% SS, 17% SC) probability of regressing to no PSR and a 14% (16% SS, 13% SC) probability of progressing to bilateral PSR. Those with bilateral PSR had an 8% (8% SS, 8% SC) probability of regressing to unilateral PSR and a 1% (0 SS, 2% SC) probability of regressing to a PSR-free state. Irretrievable visual loss occurred in only 1 of 82 PSR-affected eyes, and 1 required detachment surgery and recovered normal visual acuity. Conclusions: Longitudinal observations over 20 years in a cohort of patients followed from birth confirms a greater incidence and severity of PSR in SC disease, and shows that spontaneous regression occurred in 32% of PSR-affected eyes. Permanent visual loss was uncommon in subjects observed up to the age of 26 years. © 2005 by the American Academy of Ophthalmology.

What is a reasonable time from decision to delivery by Caesarean section? Evidence from 533 deliveries.

Objective To determine how long it takes from the decision to achieve delivery by non-elective caesarean section (DDI), the influence on this interval, and the impact on neonatal condition at birth. Design Twelve months prospective data collection on all non-elective caesarean sections. Methods Prospective collection of data relating to all caesarean sections in 1996 in a major teaching hospital obstetric unit was conducted, without the knowledge of the other clinicians providing clinical care. Details of the indication for section, the day and time of the decision and the interval till delivery were recorded as well as the seniority of the surgeon, and condition of the baby at birth. Results The mean time from decision-to-delivery for 100 emergency intrapartum caesarean sections was 42.9 minutes for fetal distress and 71.1 minutes for 230 without fetal distress (P<0.0001). For 22 'crash' sections the mean time from decision-to-delivery was 27.4 minutes; for 13 urgent antepartum deliveries for fetal reasons it was 124.7 minutes and for 21 with maternal reasons it was 97.4 minutes. The seniority of the surgeon managing the patient did not appear to influence the interval, nor did the time of day or day of the week when the delivery occurred. Intrapartum sections were quicker the more advanced the labour, and general anaesthesia was associated with shorter intervals than regional anaesthesia for emergency caesarean section for fetal distress (P<0.001). Babies born within one hour of the decision tended to be more acidaemic than those born later, irrespective of the indication for delivery. Babies tended to be in better condition when a time from decision-to-delivery was not recorded than those for whom the information had been recorded. Conclusion Fewer than 40% intrapartum deliveries by caesarean section for fetal distress were achieved within 30 minutes of the decision, despite that being the unit standard. There was, however, no evidence to indicate that overall an interval up to 120 minutes was detrimental to the neonate unless the delivery was a 'crash' caesarean section. These data thus do not provide evidence to sustain the recommendation of a standard of 30 minutes for intrapartum delivery by caesarean section.

Sliding window two-thermocouple sensor characterization for variable flow environments

A two-thermocouple sensor characterization method for use in variable flow applications is proposed. Previous offline methods for constant velocity flow are extended using sliding data windows and polynomials to accommodate variable velocity. Analysis of Monte-Carlo simulation studies confirms that the unbiased and consistent parameter estimator outperforms alternatives in the literature and has the added advantage of not requiring a priori knowledge of the time constant ratio of thermocouples. Experimental results from a test rig are also presented. © 2008 The Institute of Measurement and Control.

Wide Matching - An Approach to Improving Noise Robustness for Speech Enhancement

It is shown that under certain conditions it is possible to obtain a good speech estimate from noise without requiring noise estimation. We study an implementation of the theory, namely wide matching, for speech enhancement. The new approach performs sentence-wide joint speech segment estimation subject to maximum recognizability to gain noise robustness. Experiments have been conducted to evaluate the new approach with variable noises and SNRs from -5 dB to noise free. It is shown that the new approach, without any estimation of the noise, significantly outperformed conventional methods in the low SNR conditions while retaining comparable performance in the high SNR conditions. It is further suggested that the wide matching and deep learning approaches can be combined towards a highly robust and accurate speech estimator.

Partially Ordered Preferences in Decision Trees: Computing Strategies with Imprecision in Probabilities

Partially ordered preferences generally lead to choices that do not abide by standard expected utility guidelines; often such preferences are revealed by imprecision in probability values. We investigate five criteria for strategy selection in decision trees with imprecision in probabilities: “extensive” Γ-maximin and Γ-maximax, interval dominance, maximality and E-admissibility. We present algorithms that generate strategies for all these criteria; our main contribution is an algorithm for Eadmissibility that runs over admissible strategies rather than over sets of probability distributions.

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.