Sequential analysis by cooperative reactions on copolymers. III. Second-order Markovian chains with arbitrary protection

1977 ◽  
Vol 67 (6) ◽  
pp. 2509 ◽  
Author(s):  
J. J. González ◽  
P. C. Hemmer
Keyword(s):  
Sequential Analysis ◽  
Second Order ◽  
Markovian Chains

scholarly journals On Near Optimality of One-sample Update for Joint Detection and Estimation

2017 ◽  
Author(s):  
Yang Cao ◽  
Liyan Xie ◽  
Yao Xie ◽  
Huan Xu
Keyword(s):  
Sequential Analysis ◽  
Fundamental Problem ◽  
Hypothesis Test ◽  
Real Data ◽  
Second Order ◽  
Change Point Detection ◽  
Likelihood Ratios ◽  
Mirror Descent ◽  
Distribution Parameters ◽  
Regret Bound

Sequential hypothesis test and change-point detection when the distribution parameters are unknown is a fundamental problem in statistics and machine learning. We show that for such problems, detection procedures based on sequential likelihood ratios with simple one-sample update estimates such as online mirror descent are nearly second-order optimal. This means that the upper bound for the algorithm performance meets the lower bound asymptotically up to a log-log factor in the false-alarm rate when it tends to zero. This is a blessing, since although the generalized likelihood ratio (GLR) statistics are optimal theoretically, but they cannot be computed recursively, and their exact computation usually requires infinite memory of historical data. We prove the nearly second-order optimality by making a connection between sequential analysis and online convex optimization and leveraging the logarithmic regret bound property of online mirror descent algorithm. Numerical and real data examples validate our theory.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Second order interference in two photon absorption

1996 ◽  
Vol 43 (9) ◽  
pp. 1765-1771 ◽  
Author(s):  
M. W. HAMILTON and D. S. ELLIOTT
Keyword(s):  
Second Order ◽  
Photon Absorption ◽  
Two Photon Absorption ◽  
Two Photon

Die faktorielle Struktur des Partnerschaftsfragebogens

2012 ◽  
Vol 41 (2) ◽  
pp. 109-113 ◽  
Author(s):  
Sören Kliem ◽  
Christoph Kröger ◽  
Yve Stöbel-Richter ◽  
Kurt Hahlweg ◽  
Elmar Brähler
Keyword(s):  
Maximum Likelihood ◽  
Second Order ◽  
Bundesrepublik Deutschland

Zusammenfassung. Theoretischer Hintergrund: Der Partnerschaftsfragebogen (PFB) wird im deutschen Sprachraum zur Erfassung der Partnerschafts- und Ehequalität bevorzugt eingesetzt. Fragestellung: Neben der Überprüfung der Eindimensionalität der PFB-Subskalen (Streitverhalten, Zärtlichkeit, Gemeinsamkeit/Kommunikation) wird in der vorliegenden Arbeit überprüft, ob das Zusammenfassen der PFB-Subskalen zu einem Generalfaktor „Partnerschaftsqualität” angemessen ist. Methoden: Es wurden Daten einer Bevölkerungsstichprobe für die Bundesrepublik Deutschland genutzt (N = 1.289). Aufgrund der Abweichung von einer multivariaten Normalverteilung wurden konfirmatorische Faktorenanalysen mittels Maximum-Likelihood-Methode mit robusten Standardfehlern und einem mittelwertsadjustierten Chi2-Wert (Satorra-Bentler-scaled-χ2) durchgeführt. Ergebnisse: Es ergaben sich sowohl für die Eindimensionalität der PFB-Subskalen als auch für die Second-Order-Faktorenanalyse sehr gute Modellanapassungen. Schlussfolgerungen: Die Subsumierung der PFB-Items zu Skalenwerten sowie der PFB-Subskalen zu einem Gesamtwert kann als angemessen eingestuft werden.

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