Time Consistent Stopping for the Mean-Standard Deviation Problem---The Discrete Time Case

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

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PENGARUH PENDIDIKAN KESEHATAN REPRODUKSI PADA PEER GROUP (TEMAN SEBAYA) TERHADAP PENGETAHUAN DAN PERSEPSI REMAJA TENTANG PENDEWASAAN USIA PERKAWINAN DI SMA NEGERI 1 KECAMATAN NAMORAMBE KAB. DELI SERDANG 2018

COLOSTRUM : Jurnal Kebidanan ◽

10.36911/colostrum.v1i2.693 ◽

2020 ◽

Vol 1 (2) ◽

pp. 56-66

Author(s):

Irma Linda

Keyword(s):

Standard Deviation ◽

Health Education ◽

Reproductive Health ◽

Peer Group ◽

Peer Groups ◽

A Value ◽

Significant Difference ◽

Reproductive Health Education ◽

The Mean ◽

Adolescent Perceptions

Background: Early marriages are at high risk of marital failure, poor family quality, young pregnancies at risk of maternal death, and the risk of being mentally ill to foster marriage and be responsible parents. Objective: To determine the effect of reproductive health education on peer groups (peers) on the knowledge and perceptions of adolescents about marriage age maturity. Method: This research uses the Quasi experimental method with One group pre and post test design, conducted from May to September 2018. The statistical analysis used in this study is a paired T test with a confidence level of 95% (α = 0, 05). Results: There is an average difference in the mean value of adolescent knowledge between the first and second measurements is 0.50 with a standard deviation of 1.922. The mean difference in mean scores of adolescent perceptions between the first and second measurements was 4.42 with a standard deviation of 9.611. Conclusion: There is a significant difference between adolescent knowledge on the pretest and posttest measurements with a value of P = 0.002, and there is a significant difference between adolescent perceptions on the pretest and posttest measurements with a value of p = 0.001. Increasing the number of facilities and facilities related to reproductive health education by peer groups (peers) in adolescents is carried out on an ongoing basis at school, in collaboration with local health workers as prevention of risky pregnancy.

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Regularity and latency of units in ventral cochlear nucleus: implications for unit classification and generation of response properties

Journal of Neurophysiology ◽

10.1152/jn.1988.60.1.1 ◽

1988 ◽

Vol 60 (1) ◽

pp. 1-29 ◽

Cited By ~ 180

Author(s):

E. D. Young ◽

J. M. Robert ◽

W. P. Shofner

Keyword(s):

Standard Deviation ◽

Cochlear Nucleus ◽

Interspike Interval ◽

Rate Adaptation ◽

Stellate Cells ◽

Instantaneous Rate ◽

Ventral Cochlear Nucleus ◽

Bushy Cell ◽

Low Pass ◽

The Mean

1. The responses of neurons in the ventral cochlear nucleus (VCN) of decerebrate cats are described with regard to their regularity of discharge and latency. Regularity is measured by estimating the mean and standard deviation of interspike intervals as a function of time during responses to short tone bursts (25 ms). This method extends the usual interspike-interval analysis based on interval histograms by allowing the study of temporal changes in regularity during transient responses. The coefficient of variation (CV), equal to the ratio of standard deviation to mean interspike interval, is used as a measure of irregularity. Latency is measured as the mean and standard deviation of the latency of the first spike in response to short tone bursts, with 1.6-ms rise times. 2. The regularity and latency properties of the usual PST histogram response types are shown. Five major PST response type classes are used: chopper, primary-like, onset, onset-C, and unusual. The presence of a prepotential in a unit's action potentials is also noted; a prepotential implies that the unit is recorded from a bushy cell. 3. Units with chopper PST histograms give the most regular discharge. Three varieties of choppers are found. Chop-S units (regular choppers) have CVs less than 0.35 that are approximately constant during the response; chop-S units show no adaptation of instantaneous rate, as measured by the inverse of the mean interspike interval. Chop-T units have CVs greater than 0.35, show an increase in irregularity during the response and show substantial rate adaptation. Chop-U units have CVs greater than 0.35, show a decrease in irregularity during the response, and show a variety of rate adaptation behaviors, including negative adaptation (an increase in rate during a short-tone response). Irregular choppers (chop-T and chop-U units) rarely have CVs greater than 0.5. Choppers have the longest latencies of VCN units; all three groups have mean latencies at least 1 ms longer than the shortest auditory nerve (AN) fiber mean latencies. 4. Chopper units are recorded from stellate cells in VCN (35, 42). Our results for chopper units suggest a model for stellate cells in which a regularly firing action potential generator is driven by the summation of the AN inputs to the cell, where the summation is low-pass filtered by the membrane capacitance of the cell.(ABSTRACT TRUNCATED AT 400 WORDS)

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Blood Oxygenation Level Dependent Magnetic Resonance Imaging (MRI), Dynamic Contrast Enhanced MRI and Diffusion Weighted MRI for Benign and Malignant Breast Cancer Discrimination: A Preliminary Experience

Cancers ◽

10.3390/cancers13102421 ◽

2021 ◽

Vol 13 (10) ◽

pp. 2421

Author(s):

Roberta Fusco ◽

Vincenza Granata ◽

Mauro Mattace Raso ◽

Paolo Vallone ◽

Alessandro Pasquale De Rosa ◽

...

Keyword(s):

Standard Deviation ◽

Univariate Analysis ◽

Mean Value ◽

Blood Oxygenation ◽

Breast Lesions ◽

Dce Mri ◽

Malignant Lesions ◽

The Mean ◽

And Diffusion ◽

Skewness And Kurtosis

Purpose. To combine blood oxygenation level dependent magnetic resonance imaging (BOLD-MRI), dynamic contrast enhanced MRI (DCE-MRI), and diffusion weighted MRI (DW-MRI) in differentiation of benign and malignant breast lesions. Methods. Thirty-seven breast lesions (11 benign and 21 malignant lesions) pathologically proven were included in this retrospective preliminary study. Pharmaco-kinetic parameters including Ktrans, kep, ve, and vp were extracted by DCE-MRI; BOLD parameters were estimated by basal signal S0 and the relaxation rate R2*; and diffusion and perfusion parameters were derived by DW-MRI (pseudo-diffusion coefficient (Dp), perfusion fraction (fp), and tissue diffusivity (Dt)). The correlation coefficient, Wilcoxon-Mann-Whitney U-test, and receiver operating characteristic (ROC) analysis were calculated and area under the ROC curve (AUC) was obtained. Moreover, pattern recognition approaches (linear discrimination analysis and decision tree) with balancing technique and leave one out cross validation approach were considered. Results. R2* and D had a significant negative correlation (−0.57). The mean value, standard deviation, Skewness and Kurtosis values of R2* did not show a statistical significance between benign and malignant lesions (p > 0.05) confirmed by the ‘poor’ diagnostic value of ROC analysis. For DW-MRI derived parameters, the univariate analysis, standard deviation of D, Skewness and Kurtosis values of D* had a significant result to discriminate benign and malignant lesions and the best result at the univariate analysis in the discrimination of benign and malignant lesions was obtained by the Skewness of D* with an AUC of 82.9% (p-value = 0.02). Significant results for the mean value of Ktrans, mean value, standard deviation value and Skewness of kep, mean value, Skewness and Kurtosis of ve were obtained and the best AUC among DCE-MRI extracted parameters was reached by the mean value of kep and was equal to 80.0%. The best diagnostic performance in the discrimination of benign and malignant lesions was obtained at the multivariate analysis considering the DCE-MRI parameters alone with an AUC = 0.91 when the balancing technique was considered. Conclusions. Our results suggest that the combined use of DCE-MRI, DW-MRI and/or BOLD-MRI does not provide a dramatic improvement compared to the use of DCE-MRI features alone, in the classification of breast lesions. However, an interesting result was the negative correlation between R2* and D.

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On the absorption probabilities and mean time for absorption for discrete Markov chains

Monte Carlo Methods and Applications ◽

10.1515/mcma-2021-2084 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Nikolaos Halidias

Keyword(s):

Markov Chain ◽

Random Walk ◽

Markov Chains ◽

Generating Function ◽

Discrete Time ◽

Probability Generating Function ◽

The Mean ◽

Mean Time ◽

Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

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Quantification of Measurement and Model Effects in Monopile Foundation Scour Protection Experiments

Journal of Marine Science and Engineering ◽

10.3390/jmse9060585 ◽

2021 ◽

Vol 9 (6) ◽

pp. 585

Author(s):

Minghao Wu ◽

Leen De Vos ◽

Carlos Emilio Arboleda Chavez ◽

Vasiliki Stratigaki ◽

Maximilian Streicher ◽

...

Keyword(s):

Standard Deviation ◽

Flow Field ◽

Three Dimensional ◽

Small Scale ◽

Maximum Wave Height ◽

Chaotic Flow ◽

The Mean ◽

Scour Protection ◽

Damage Number ◽

Measurement Effects

The present work introduces an analysis of the measurement and model effects that exist in monopile scour protection experiments with repeated small scale tests. The damage erosion is calculated using the three dimensional global damage number S3D and subarea damage number S3D,i. Results show that the standard deviation of the global damage number σ(S3D)=0.257 and is approximately 20% of the mean S3D, and the standard deviation of the subarea damage number σ(S3D,i)=0.42 which can be up to 33% of the mean S3D. The irreproducible maximum wave height, chaotic flow field and non-repeatable armour layer construction are regarded as the main reasons for the occurrence of strong model effects. The measurement effects are limited to σ(S3D)=0.039 and σ(S3D,i)=0.083, which are minor compared to the model effects.

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Random additions in urns of integers

Journal of Applied Probability ◽

10.1017/jpr.2020.90 ◽

2021 ◽

Vol 58 (2) ◽

pp. 335-346

Author(s):

Mackenzie Simper

Keyword(s):

Finite Group ◽

Random Process ◽

Uniform Distribution ◽

Discrete Time ◽

Random Variable ◽

Urn Model ◽

Infinite Type ◽

The Mean ◽

A Finite Group ◽

Proof Of Convergence

AbstractConsider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn labels. This model was introduced by Siegmund and Yakir (2005) Ann. Prob.33, 2036 for labels taking values in a finite group, in which case the distribution defined by the urn converges to the uniform distribution on the group. For the urn of integers, the main result of this paper is an exponential limit law. The mean of the exponential is a random variable with distribution depending on the starting configuration. This is a novel urn model which combines multi-drawing and an infinite type of balls. The proof of convergence uses the contraction method for recursive distributional equations.

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