In the early 1960s, Shiryaev obtained the structure of Bayesian stopping rules for detecting abrupt changes in independent and identically distributed sequences as well as in a constant drift of the Brownian motion. Since then, the methodology of optimal change-point detection has concentrated on the search for stopping rules that achieve the best balance of the mean detection delay and the rate of false alarms or minimize the mean delay under a fixed false alarm probability. In this respect, analysis of the performance of the Shiryaev procedure has been an open problem. Recently, Tartakovsky and Veeravalli (2005) investigated asymptotic performance of the Shiryaev Bayesian change detection procedure, the Page procedure, and the Shiryaev-Roberts procedure when the false alarm probability goes to zero for general discrete-time models. In this article, we investigate the asymptotic performance of Shiryaev and Shiryaev-Roberts procedures for general continuous-time stochastic models for a small false alarm probability and small cost of detection delay. We show that the Shiryaev procedure has asymptotic optimality properties under mild conditions, while the Shiryaev-Roberts procedure may or may not be asymptotically optimal depending on the type of the prior distribution. The presented asymptotic Bayesian detection theory substantially generalizes previous work in the field of change-point detection for continuous-time processes.

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Sequential procedures are developed for simultaneous testing of multiple hypotheses in sequential experiments. Proposed stopping rules and decision rules achieve strong control of both family-wise error rates I and II. The optimal procedure is sought that minimizes the expected sample size under these constraints. Bonferroni methods for multiple comparisons are extended to sequential setting and are shown to attain an approximately 50% reduction in the expected sample size compared with the earlier approaches. Asymptotically optimal procedures are derived under Pitman alternative.

Gulf War Illness (GWI) is a multisymptom disorder including widespread chronic pain, fatigue and gastrointestinal problems. The objective of this study was to examine the low glutamate diet as a treatment for GWI. Forty veterans with GWI were recruited from across the US. Outcomes included symptom score, myalgic score, tender point count, dolorimetry and the Chalder Fatigue Scale. Subjects were randomized to the low glutamate diet or a wait-listed control group, with symptom score being compared after one month. Subjects then went onto a double-blind, placebo-controlled crossover challenge with monosodium glutamate (MSG)/placebo to test for return of symptoms. Symptom score was compared between diet intervention and wait-listed controls with an independent t-test and effect size was calculated with Cohen’s d. Change scores were analyzed with Wilcoxon Signed Rank tests. Crossover challenge results were analyzed with General Linear Models and cluster analysis. The diet intervention group reported significantly less symptoms (p = 0.0009) than wait-listed controls, with a very large effect size, d = 1.16. Significant improvements in average dolorimetry (p = 0.0006), symptom score, tender point number, myalgic score and the Chalder Fatigue Scale (all p < 0.0001) were observed after the 1-month diet. Challenge with MSG/placebo resulted in significant variability in individual response. These results suggest that the low glutamate diet can effectively reduce overall symptoms, pain and fatigue in GWI, but differential results upon challenge suggest that other aspects of the diet, or underlying differences within the population, may be driving these changes. Future research is needed to identify potential nutrient effects, biomarkers, and underlying metabolic differences between responders and non-responders.