A direct approach to a Bayesian sequential test for a normal mean

AbstractWe consider a fractional Brownian motion with linear drift such that its unknown drift coefficient has a prior normal distribution and construct a sequential test for the hypothesis that the drift is positive versus the alternative that it is negative. We show that the problem of constructing the test reduces to an optimal stopping problem for a standard Brownian motion obtained by a transformation of the fractional Brownian motion. The solution is described as the first exit time from some set, and it is shown that its boundaries satisfy a certain integral equation, which is solved numerically.

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Designing microwave effect experiment based on Bayesian sequential test method

High Power Laser and Particle Beams ◽

10.3788/hplpb20132502.0411 ◽

2013 ◽

Vol 25 (2) ◽

pp. 411-414

Author(s):

韩峰 Han Feng ◽

陆希成 Lu Xicheng ◽

刘钰 Liu Yu ◽

杨志强 Yang Zhiqiang ◽

王建国 Wang Jianguo

Keyword(s):

Test Method ◽

Sequential Test ◽

Microwave Effect ◽

Effect Experiment ◽

Bayesian Sequential Test

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A one-sided confidence set hidden under a two-sided sequential test of a normal mean

Statistics & Probability Letters ◽

10.1016/s0167-7152(98)00234-x ◽

1999 ◽

Vol 41 (4) ◽

pp. 435-438 ◽

Cited By ~ 1

Author(s):

Wei Liu

Keyword(s):

Sequential Test ◽

Confidence Set ◽

Normal Mean

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Information and estimation in image processing

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125142 ◽

1987 ◽

Vol 45 ◽

pp. 14-17

Author(s):

B. Roy Frieden

Keyword(s):

Image Processing ◽

Optical System ◽

Large Amplitude ◽

Communication Theory ◽

Image Data ◽

Direct Approach ◽

Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

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Direct Approach for Jugular Paraganglioma by Enlarged Mastoidectomy and Hypotympanotomy without Middle Ear Obliteration

Journal of Neurological Surgery Part B Skull Base ◽

10.1055/s-0036-1592632 ◽

2016 ◽

Vol 77 (S 02) ◽

Author(s):

Kazimierz Niemczyk ◽

Robert Bartoszewicz ◽

Krzysztof Morawski ◽

Izabela Popieluch

Keyword(s):

Middle Ear ◽

Direct Approach

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Very Low Activated Factor VII and Reduced Factor VII Antigen in Familial Abetalipoproteinaemia

Thrombosis and Haemostasis ◽

10.1055/s-0037-1615179 ◽

1998 ◽

Vol 80 (08) ◽

pp. 233-238 ◽

Cited By ~ 8

Author(s):

K. A. Mitropoulos ◽

M. N. Nanjee ◽

D. J. Howarth ◽

J. C. Martin ◽

M. P. Esnouf ◽

...

Keyword(s):

Plasma Concentrations ◽

Positive Association ◽

Factor Ix ◽

Factor Vii ◽

Unesterified Fatty Acid ◽

Factor Xii ◽

Factor X ◽

Factor Xi ◽

Activated Factor Vii ◽

Normal Mean

SummaryAbetalipoproteinaemia is a rare disorder of apolipoprotein B metabolism associated with extremely low plasma concentrations of triglyce-ride. To discover whether the general positive association between factor VII and triglyceride levels extends to this condition, 5 patients were compared with 18 controls. All patients had a triglyceride below 100 μmol/l. Plasma unesterified fatty acid concentration was normal. Although factor IX activity was only slightly reduced (mean 88% standard) and factor IX antigen was normal, mean activated factor VII in patients was strikingly reduced to 34% of that in controls, a level similar to that found in haemophilia B. The patients’ mean factor VII activity and factor VII antigen were also significantly reduced to 54% and 63% of those in controls, respectively. Mean factor XI activity and tissue factor pathway inhibitor activity were reduced in patients to 70% and 75% of control values respectively, while factor XII, factor XI antigen, factor X, prothrombin and protein C were normal.

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