Embedding submartingales in wiener processes with drift, with applications to sequential analysis

1969 ◽  
Vol 6 (03) ◽  
pp. 612-632 ◽  
Author(s):  
W. J. Hall

Summary Skorokhod (1961) demonstrated how the study of martingale sequences (and zero-mean random walks) can be reduced to the study of the Wiener process (without drift) at a sequence of random stopping times. We show how the study of certain submartingale sequences, including certain random walks with drift and log likelihood ratio sequences, can be reduced to the study of the Wiener process with drift at a sequence of stopping times (Theorem 4.1). Applications to absorption problems are given. Specifically, we present new derivations of a number of the basic approximations and inequalities of classical sequential analysis, and some variations on them — including an improvement on Wald's lower bound for the expected sample size function (Corollary 7.5).

1969 ◽  
Vol 6 (3) ◽  
pp. 612-632 ◽  
Author(s):  
W. J. Hall

SummarySkorokhod (1961) demonstrated how the study of martingale sequences (and zero-mean random walks) can be reduced to the study of the Wiener process (without drift) at a sequence of random stopping times. We show how the study of certain submartingale sequences, including certain random walks with drift and log likelihood ratio sequences, can be reduced to the study of the Wiener process with drift at a sequence of stopping times (Theorem 4.1). Applications to absorption problems are given. Specifically, we present new derivations of a number of the basic approximations and inequalities of classical sequential analysis, and some variations on them — including an improvement on Wald's lower bound for the expected sample size function (Corollary 7.5).


2007 ◽  
Vol 07 (01) ◽  
pp. 75-89
Author(s):  
ZHIHUI YANG

Symmetric random walks can be arranged to converge to a Wiener process in the area of normal deviation. However, random walks and Wiener processes have, in general, different asymptotics of the large deviation probabilities. The action functionals for random-walks and Wiener processes are compared in this paper. The correction term is calculated. Exit problem and stochastic resonance for random-walk-type perturbation are also considered and compared with the white-noise-type perturbation.


2017 ◽  
Vol 10 (2) ◽  
pp. 64
Author(s):  
Serpil Ucar ◽  
Ceyhun Yukselir

This research was conducted to investigate how frequently Turkish advanced learners of English use the logical connector ‘thus’ in their academic prose and to investigate whether it was overused, underused or misused semantically in comparison to English native speakers. The data were collected from three corpora; Corpus of Contemporary American English and 20 scientific articles of native speakers as control corpora, and 20 scientific articles of Turkish advanced EFL learners. The raw frequencies, frequencies per million words, frequencies per text and log-likelihood ratio were measured so as to compare varieties across the three corpora. The findings revealed that Turkish learners of English showed underuse in the use of the connector ‘thus’ in their academic prose compared to native speakers. Additionally, they did not demonstrate misuse in the use of the connector ‘thus’. Nevertheless, non-native learners of English tended to use this connector in a resultative role (cause-effect relation) more frequently whereas native speakers used it in appositional and summative roles more as well as its resultative role. Furthermore, the most frequent occurrences of ‘thus’ have been in academic genre.


2021 ◽  
Vol 4 (Supplement_1) ◽  
pp. 210-212
Author(s):  
R Trasolini ◽  
S Wong ◽  
B Salh

Abstract Background Fecal calprotectin is a non-invasive test of colonic inflammation used for monitoring inflammatory bowel disease activity and for risk stratifying non-specific colonic symptoms. Calprotectin is a leukocyte specific enzyme. A similar test, leukocyte esterase is used to detect leukocytes in urine and is widely available as a low-cost point-of-care test strip. We hypothesize that an unmodified version of the urine test strip would be highly accurate in predicting a positive fecal calprotectin test in a real world sample of patients. Aims To explore a low cost, rapid alternative to the fecal calprotectin test Methods All inpatient and outpatient stool samples tested for calprotectin by the Vancouver General Hospital laboratory from February 2020 to November 2020 were included prospectively. Samples were simultaneously tested for fecal leukocyte esterase using an unmodified Roche Cobas Chemstrip urinalysis test strip by central lab personnel. An identical aliquot was sent to LifeLabs for calprotectin as per standard protocol. All samples were suspended in buffer using established laboratory protocols prior to testing. Fecal leukocyte esterase results were reported as 0–4+ based on visual interpretation, calprotectin results were reported as mcg/g of stool. REB review and approval was obtained prior to data collection. Sensitivity, Specificity and AUROC were calculated using Microsoft Excel and JROCFIT. Results 26 samples were collected. Using a fecal calprotectin greater than 120 mcg/g as a gold standard an AUROC of 0.89 (SE= .06) was calculated. A leukocyte esterase reading of 2+ or greater had the best test characteristics based on ROC curve analysis. Using this cutoff, 21/26 samples were concordant, giving an accuracy of 80.8%, sensitivity of 90.9% and specificity of 73.3%. Positive likelihood ratio was 8.07 and negative likelihood ratio was 0.29. Assuming an AUROC of 0.8, the sample size N=26 is 90% powered (β=0.9) to predict the true AUROC within 0.1 with a type I error rate of .05 (α<.05). Conclusions This study suggests application of a prepared stool sample to a urinalysis test strip gives a result highly predictive of a positive fecal calprotectin test. Further results are being collected prospectively to improve the robustness of these preliminary data. Secondary outcomes including comparison to endoscopy and biopsy results where available are planned if an adequate sample size can be accrued. Future studies justifying independent clinical use of leukocyte esterase would require a common gold standard comparator such as endoscopy. Fecal calprotectin testing is not universally insured and is not available as a rapid test strip. Use of fecal leukocyte esterase may reduce costs and shorten time to results if proven to be independently reliable. Funding Agencies None


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