The filtering equations revisited

The problem of nonlinear filtering has engendered a surprising number of mathematical techniques for its treatment. A notable example is the change-of--probability-measure method originally introduced by Kallianpur and Striebel to derive the filtering equations and the Bayes-like formula that bears their names. More recent work, however, has generally preferred other methods. In this paper, we reconsider the change-of-measure approach to the derivation of the filtering equations and show that many of the technical conditions present in previous work can be relaxed. The filtering equations are established for general Markov signal processes that can be described by a martingale-problem formulation. Two specific applications are treated

Isolated HbA1c identifies a different subgroup of individuals with type 2 diabetes compared to fasting or post-challenge glucose in Asian Indians: The CARRS and MASALA studies.

AIMS: Guidelines recommend hemoglobin A1c (HbA1c) as a diagnostic test for type 2 diabetes, but its accuracy may differ in certain ethnic groups. METHODS: The prevalence of type 2 diabetes by HbA1c, fasting glucose, and 2 h glucose was compared in 3016 participants from Chennai and Delhi, India from the CARRS-2 Study to 757 Indians in the U.S. from the MASALA Study. Type 2 diabetes was defined as fasting glucose ≥ 7.0 mmol/L, 2-h glucose ≥ 11.1 mmol/L, or HbA1c ≥ 6.5%. Isolated HbA1c diabetes was defined as HbA1c ≥ 6.5% with fasting glucose < 7.0 mmol/L and 2 h glucose < 11.1 mmol/L. RESULTS: The age, sex, and BMI adjusted prevalence of diabetes by isolated HbA1c was 2.9% (95% CI: 2.2-4.0), 3.1% (95% CI: 2.3-4.1), and 0.8% (95% CI: 0.4-1.8) in CARRS-Chennai, CARRS-Delhi, and MASALA, respectively. The proportion of diabetes diagnosed by isolated HbA1c was 19.4%, 26.8%, and 10.8% in CARRS-Chennai, CARRS-Delhi, and MASALA respectively. In CARRS-2, individuals with type 2 diabetes by isolated HbA1c milder cardio-metabolic risk than those diagnosed by fasting or 2-h measures. CONCLUSIONS: In Asian Indians, the use of HbA1c for type 2 diabetes diagnosis could result in a higher prevalence. HbA1c may identify a subset of individuals with milder glucose intolerance

HMM based scenario generation for an investment optimisation problem

This is the post-print version of the article. The official published version can be accessed from the link below - Copyright @ 2012 Springer-Verlag.The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, important features of the time series, like extreme behaviour or volatility clustering cannot be captured. We propose an approach by which the parameters of the GBM are able to switch between regimes, more precisely they are governed by a hidden Markov chain. Thus, we model the financial time series via a hidden Markov model (HMM) with a GBM in each state. Using this approach, we generate scenarios for a financial portfolio optimisation problem in which the portfolio CVaR is minimised. Numerical results are presented.This study was funded by NET ACE at OptiRisk Systems

Canalization effect in the coagulation cascade and the interindividual variability of oral anticoagulant response. a simulation Study

<p>Abstract</p> <p>Background</p> <p>Increasing the predictability and reducing the rate of side effects of oral anticoagulant treatment (OAT) requires further clarification of the cause of about 50% of the interindividual variability of OAT response that is currently unaccounted for. We explore numerically the hypothesis that the effect of the interindividual expression variability of coagulation proteins, which does not usually result in a variability of the coagulation times in untreated subjects, is unmasked by OAT.</p> <p>Results</p> <p>We developed a stochastic variant of the Hockin-Mann model of the tissue factor coagulation pathway, using literature data for the variability of coagulation protein levels in the blood of normal subjects. We simulated <it>in vitro </it>coagulation and estimated the Prothrombin Time and the INR across a model population. In a model of untreated subjects a "canalization effect" can be observed in that a coefficient of variation of up to 33% of each protein level results in a simulated INR of 1 with a clinically irrelevant dispersion of 0.12. When the mean and the standard deviation of vitamin-K dependent protein levels were reduced by 80%, corresponding to the usual Warfarin treatment intensity, the simulated INR was 2.98 ± 0.48, a clinically relevant dispersion, corresponding to a reduction of the canalization effect.</p> <p>Then we combined the Hockin-Mann stochastic model with our previously published model of population response to Warfarin, that takes into account the genetical and the phenotypical variability of Warfarin pharmacokinetics and pharmacodynamics. We used the combined model to evaluate the coagulation protein variability effect on the variability of the Warfarin dose required to reach an INR target of 2.5. The dose variance when removing the coagulation protein variability was 30% lower. The dose was mostly related to the pretreatment levels of factors VII, X, and the tissue factor pathway inhibitor (TFPI).</p> <p>Conclusions</p> <p>It may be worth exploring in experimental studies whether the pretreatment levels of coagulation proteins, in particular VII, X and TFPI, are predictors of the individual warfarin dose, even though, maybe due to a canalization-type effect, their effect on the INR variance in untreated subjects appears low.</p

Robustness and Generalization

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel approach, different from the complexity or stability arguments, to study generalization of learning algorithms. We further show that a weak notion of robustness is both sufficient and necessary for generalizability, which implies that robustness is a fundamental property for learning algorithms to work

Association of coagulation-related and inflammation-related genes and factor VIIc levels with stroke: the Cardiovascular Health Study: Coagulation and inflammation genes and stroke

Thrombosis and inflammation are critical in stroke etiology, but associations of coagulation and inflammation gene variants with stroke, and particularly factor VII levels are inconclusive

Inflammatory and Coagulation Biomarkers and Mortality in Patients with HIV Infection

Analyzing biomarker data from participants in a previous randomized controlled trial of continuous versus interrupted HIV treatment (the SMART trial), James Neaton and colleagues find that mortality was related to IL-6 and fibrin D-dimers