Average Number Of Observations Research Articles

The role of social resources and trajectories of functional health following stroke

Stroke is a major cause of disability in old age. Research has revealed that social resources available after the onset of stroke can mitigate functional prognosis. However, most studies have conceptualized resources as static rather than dynamic and have not measured changes in social resources from the pre-to post-stroke periods. To better understand the recovery process following stroke, we examined how social resources available before its onset and changes from pre-to post-stroke were associated with trajectories of functional health following stroke. Data were derived from an up to 19-year longitudinal study of a nationally representative sample of Japanese adults aged 60 years and older. We identified 389 people who experienced self- or proxy-reported first stroke during follow-up (age at stroke onset: M = 75.9, SD = 6.8; 49.1% women). The average number of observations was 4.6 (SD = 1.6, range 2–7). Functional health was measured with self- or proxy-reported basic and instrumental activities of daily living. Social resources were indexed as residential status, contact with own non-coresident children, social participation, and perceived support. Analyses were adjusted for age at stroke onset, sex, education, health condition, and cognitive function. A multiphase growth model indicated that individuals who participated more frequently in social groups prior to stroke exhibited less functional deterioration post-stroke than those who participated less frequently. Whereas contact frequency with non-coresident children typically declined following stroke, the analysis further revealed that individuals who maintained contact frequency from pre-to post-stroke showed less steep functional decline over time in the post-stroke period despite minor individual differences. We found that social resources before stroke onset and changes in the resources following stroke may play a protective role against adverse prognoses. Inclusive communities may help older adults remain independent even after serious health events.

An improved variable parameter mean square error control chart

In order to improve the efficiency of the mean square error control chart in detecting small to moderate shifts, an improved variable parameter mean square error (VPt MSE) control chart is proposed, which uses three different sampling intervals, two different sample sizes and two different control limits. Markov chain method is used to calculate the average time to signal and average number of observations to signal. The performance of the adaptive chart was compared with the variable sample size and sampling interval (VSSI), the improved variable sample size and sampling interval (VSSIt), the variable parameter (VP), the exponentially weighted moving average (EWMA), and the variable sampling interval exponentially weighted moving average (VSI EWMA) mean square error control chart. Numerical results show that the VPt MSE chart surpasses the other charts in detecting small to moderate shifts. At the same time, we also improve the VPt MSE chart, which greatly improves the statistical performance. An example is provided to illustrate the implementation of the VPt MSE chart.

Data quantity is more important than its spatial bias for predictive species distribution modelling.

Biological records are often the data of choice for training predictive species distribution models (SDMs), but spatial sampling bias is pervasive in biological records data at multiple spatial scales and is thought to impair the performance of SDMs. We simulated presences and absences of virtual species as well as the process of recording these species to evaluate the effect on species distribution model prediction performance of (1) spatial bias in training data, (2) sample size (the average number of observations per species), and (3) the choice of species distribution modelling method. Our approach is novel in quantifying and applying real-world spatial sampling biases to simulated data. Spatial bias in training data decreased species distribution model prediction performance, but sample size and the choice of modelling method were more important than spatial bias in determining the prediction performance of species distribution models.

Bayesian Methods for Multiple Change-Point Detection With Reduced Communication

In many modern applications, large-scale sensor networks are used to perform statistical inference tasks. In this article, we propose Bayesian methods for multiple change-point detection using a sensor network in which a fusion center (FC) can receive a data stream from each sensor. Due to communication limitations, the FC monitors only a subset of the sensors at each time slot. Since the number of change points can be high, we adopt the false discovery rate (FDR) criterion for controlling the rate of false alarms, while aiming to minimize the average detection delay (ADD) and the average number of observations (ANO) communicated until discovery. We propose two Bayesian detection procedures that handle the communication limitations by monitoring the subset of the sensors with the highest posterior probabilities of change points having occurred. This monitoring policy aims to minimize the delay between the occurrence of each change point and its declaration using the corresponding posterior probabilities. One of the proposed procedures is more conservative than the second one in terms of having lower FDR at the expense of higher ADD. It is analytically shown that both procedures control the FDR under a specified tolerated level and are also scalable in the sense that they attain ADD and ANO that do not increase asymptotically with the number of sensors. In addition, it is demonstrated that the proposed detection procedures are useful for trading off between reduced ADD and reduced ANO. Numerical simulations are conducted for validating the analytical results and for demonstrating the properties of the proposed procedures.

Comparative Statistical Analysis of Selected Control Charts for Highly Capable Processes

When a high-quality process is to be controlled by 100% inspection and yes-no decision is employed, several types of charts come into account, e.g. CCC, CCC-r or geometric CUSUM (CCC-CUSUM). The aim of the paper is to examine performance of these charts so that a suitable one can be chosen for a given process. The charts are compared according to the quickness with which the upward shift in the fraction of nonconforming items is detected. The average number of observations to signal (ANOS) instead of the usual average run length (ARL) is determined. While ANOS for CCC or CCC-r charts can be easily calculated based on a geometric or a negative binomial distribution, its computation is quite diffi cult in the case of CCC-CUSUM chart. The corrected diffusion (CD) approximation was used to determine ANOS and the results were verifi ed by Monte Carlo simulation. Zero-state and steady-state (both fi xed-shift and random-shift model) analyses were performed to take different scenarios of the process shift occurrence into account. CCC-3 or CCC-2 and CCC-CUSUM charts were compared. The order r for CCC-r chart was chosen as an optimal value for the given process based on the semi-economic model suggested in Brodecka (2013). Our study revealed that for in-control p0 equal to 0.0002 the CCC-CUSUM chart performs best especially for shifts around the pre-specifi ed out-of-control fraction nonconforming. The CCC-r chart may be comparable or even better in detecting larger shifts. The results of the comparative study were utilized for the choice of the most suitable and best performing control chart to control the high-yield process producing ERG (Exhaust Gas Recirculation) sensors. Comparisons of CCC-r and CCC-CUSUM charts can be found elsewhere in literature, but conclusions seem to be rather inconsistent. To our best knowledge no study dealing with such small in-control fraction nonconforming together with the low risk of false alarm has been published yet. The choice of CUSUM’s parameters and consequent values of ANOS can help practitioners who need to control high-quality processes.

DYNAMICS OF SNOW STORAGES IN FORESTS AND FIELDS OF RUSSIAN PLAINS UNDER CLIMATE CHANGES

In 1966-2010, snow surveys were simultaneously performed in forests and fields on the Russian plain territory. This made it possible to analyze characteristics of snow storages on fields and in forests as well as a dynamics of them under the present-day climate changes. Data of 81 weather stations located on the territory were used. According to data of these stations for the period 2001–2010 we obtained the following estimates for the maximal snow storage values, on average: for 20 stations located on the European territory of Russia to the north of 60° N –167 mmin forests and 162 on fields; for 44 stations to the south of 60° N – 118 and116 mm, respectively; for 10 stations in the south of West Siberia – 125 and107 mm; and for 7 stations in the East Siberia – 64 and70 mm. As one can see the last region is characterized by the opposite relation between forest and field conditions. Comparison of these values with similar data for the period 1966-2000 demonstrated that maximal snow storages decreased in forests by 7% but in fields they increased by 2%. The ratio of the maximum snow storage in the forest to their value in the field (i.e. a coefficient of snow reserve) for the periods 1981–1990, 1991–2000, and 2001–2010 are 1.15; 1.11 and 1.03, respectively. One of the reasons for the equalization of snow storage in forest and field may be changes of intensity and duration of snowstorms. In the calendar winters of 2001-2010, the average number of observations at weather stations with wind speeds over 10 m/s decreased relative to 1966-2010: in the European part of Russia by factor of 8.9 times, and in Western and Eastern Siberia – by 2.0 and 1.9 times, respectively. In the European part ofRussia, the number of observation periods when wind speed from 6 to 10 m/s was observed decreased by 1.9 times.

D-Guaranteed Discrimination of Statistical Hypotheses: a Review of Results and Unsolved Problems

We compare two sequential d-guaranteed tests and an optimal d-guaranteed test based on a fixed number of observations with respect to the average number of observations within the most accepted practical applications of Bayesian probabilistic models. We consider the sequential “first skipping” test, the sequential locally efficient test based on the score statistic, and the test based on a fixed number of observations that minimizes the necessary sample size. We study various characteristics of these tests connected with the number of observations within three probabilistic models, namely, the normal (ϑ, σ 2) distribution of the observed random variable and the normal a priori distribution of ϑ with fixed σ 2; the exponential distribution with the intensity parameter ϑ and the a priori gamma distribution of ϑ; and the Bernoulli sampling with the success probability ϑ and the a priori beta distribution of ϑ. We discuss the connection of the d-posterior approach with the compound decision problem as applied to the analysis of data provided by microchips (when the false discovery rate, or FDR, for short, is treated as the d-risk of the first kind). We present the vast data on characteristics of the mentioned tests obtained by the method of mathematical modeling in several tables. We discuss unsolved problems of the d-guaranteed discrimination of hypotheses with the minimal number of observations and approaches to their solution.

Information inequalities for characteristics of group-sequential test with groups of observations of random size

We consider a group-sequential test for testing a simple hypothesis against a composite one-sided alternative, which defines the following sequential statistical procedure: At each stage a random number of independent identically distributed observations (a group of observations) is observed and, based on the collected data, the decision to accept or to reject the hypothesis or to continue the observation is made. For the tests with finite number of observations, we prove the existence of the derivative of the power function and establish the information-type inequalities relating that derivative to other characteristics of the test: the average number of observations and the type I error.

Performance comparison for the CRL control charts with estimated parameters for high-quality processes

The conforming run length (CRL) control charts based on Bernoulli data have been shown to be effective when monitoring the proportion nonconforming rate, especially for high-quality processes. Considering the usage simplicity in practice, the count of conforming chart, RL2 chart and the geometric cumulative sum (CUSUM) chart are subject matter of this paper. When implementing the CRL control charts, the in-control proportion nonconforming rate is seldom known and accurate estimation is needed. Thus, we investigate the effects of parameter estimation on the CRL control charts using the average number of observations to signal and the standard deviation of the average number of observations to signal with a Bayes estimator. The SDANOS values of the CRL control charts show that practitioners should rarely expect in-control performance close to that obtained under the assumption when the process parameters are known. By comparing in-control performance of the CRL control charts, the geometric CUSUM chart is most sensitive to the parameter estimation.

Comparing the Performance of Approaches for Testing the Homogeneity of Variance Assumption in One-Factor ANOVA Models.

Various tests to check the homogeneity of variance assumption have been proposed in the literature, yet there is no consensus as to their robustness when the assumption of normality does not hold. This simulation study evaluated the performance of 14 tests for the homogeneity of variance assumption in one-way ANOVA models in terms of Type I error control and statistical power. Seven factors were manipulated: number of groups, average number of observations per group, pattern of sample sizes in groups, pattern of population variances, maximum variance ratio, population distribution shape, and nominal alpha level for the test of variances. Overall, the Ramsey conditional, O'Brien, Brown-Forsythe, Bootstrap Brown-Forsythe, and Levene with squared deviations tests maintained adequate Type I error control, performing better than the others across all the conditions. The power for each of these five tests was acceptable and the power differences were subtle. Guidelines for selecting a valid test for assessing the tenability of this critical assumption are provided based on average cell size.

Understanding Winter Precipitation Impacts on Automated Gauge Observations within a Real-Time System

Abstract Precipitation gauge observations are routinely classified as ground truth and are utilized in the verification and calibration of radar-derived quantitative precipitation estimation (QPE). This study quantifies the challenges of utilizing automated hourly gauge networks to measure winter precipitation within the real-time Multi-Radar Multi-Sensor (MRMS) system from 1 October 2013 to 1 April 2014. Gauge observations were compared against gridded radar-derived QPE over the entire MRMS domain. Gauges that reported no precipitation were classified as potentially stuck in the MRMS system if collocated hourly QPE values indicated nonzero precipitation. The average number of potentially stuck gauge observations per hour doubled in environments defined by below-freezing surface wet-bulb temperatures, while the average number of observations when both the gauge and QPE reported precipitation decreased by 77%. Periods of significant winter precipitation impacts resulted in over a thousand stuck gauge observations, or over 10%–18% of all gauge observations across the MRMS domain, per hour. Partial winter impacts were observed prior to the gauges becoming stuck. Simultaneous postevent thaw and precipitation resulted in unreliable gauge values, which can introduce inaccurate bias correction factors when calibrating radar-derived QPE. The authors then describe a methodology to quality control (QC) gauge observations compromised by winter precipitation based on these results. A comparison of two gauge instrumentation types within the National Weather Service (NWS) Automated Surface Observing System (ASOS) network highlights the need for improved gauge instrumentation for more accurate liquid-equivalent values of winter precipitation.

A modified variable sample size and sampling interval controlchart

In this article, a modified version of variable sample size and sampling interval chart using three sampling intervals and two sample sizes, called the VSSIt control chart, is proposed to overcome the weakness of the standard Shewhart (SS) control chart in detecting small and moderate shifts. In order to evaluate the performance of the proposed scheme, average time to signal (ATS), average number of observations to signal (ANOS), and average number of samples to signal (ANSS) are used. Using this control chart can reduce the ATS value around 68, 27, 7, and 1.83 time unit (sampling interval of the SS chart) in detecting shift of size 0.25, 0.5, 0.75, and 1 standard deviation, respectively. The performance of the constructed adaptive chart is compared with various adaptive charts such as variable sample size (VSS), variable sampling interval (VSI), variable sample size and sampling interval (VSSI), and special variable sample size and sampling interval (SVSSI) \( \overline{x} \) control chart. It is shown that the proposed chart always outperforms SS, VSI, VSS, and VSSI schemes. It also can detect shift of size 0.25 standard deviation quicker than SVSSI scheme. Finally, the optimal parameters of the proposed chart are recommended.

CREATION OF LARGE CATALOGUES BY USING OF VIRTUAL OBSERVATORIES

We developed an application program to search images in the registers and databases of Virtual Observatories and to download them to local computer. The program has the ability to process XML file in VO Table format to generate links to images, as well as to work directly with the astronomical servers. To improve the efficiency for downloading of large number of images, we used multi-threaded mode. The program runs under the Windows operating system. Using the program in 2014 year, we found and downloaded more than 145 thousand of images of open clusters, having total volume of about 300 GB. Total download time was about 7 days. To process the downloaded images, we created and configured a complex of 10 virtual machines on two PCs for parallel image processing by using Astrometrica program. Total processing time was about 14 days. An application program was also created to analyse the obtained results, which were used to create four catalogues of stellar coordinates at the average epoch of 1953 to 1998. The total number of stars in the catalogues is more than 35 million. The standard error is 0.04 to 0.07, and the average number of observations is 4 to 6. The catalogs are used to improve proper motions of stars in and around of open clusters.

Distributions of stopping times in some sequential estimation procedures

A class of sequential estimation procedures is considered in the case when relevant data may become available only at random times. The exact distributions of the optimal stopping time and the number of observations at the moment of stopping are derived in some sequential procedures. The results obtained in an explicit form are applied to derive the expected time of observing the process, the average number of observations and the expected loss of sequential estimation procedures based on delayed observations. The use of the results is illustrated in a special model of normally distributed observations and the Weibull distributed lifetimes. The probabilistic characteristics are also derived for an adaptive sequential procedures and the behavior of the adaptive procedure is compared with the corresponding optimal sequential procedure.

Optimal Variable Sample Size and Sampling Interval MSE Chart Based on Improved Square Root Transformation

In the field of statistical process control (SPC), control charts for attributes are widely used to detect the out-of-control condition by checking the number of nondefective units or nondefective in a sample. In this article, we use the average time to signal (ATS) and the average number of observations to signal (ANOS) to evaluate the performance of the optimal variable sample size and sampling interval (VSSI) improved square root transformation (ISRT) mean square error (MSE) (VSSI_ ISRT_ MSE) control chart for attribute data. In addition, this control chart will be used to monitor: (1) the difference between the process mean and the target value, and (2) the process variance shifts. We found that the optimal VSSI_ ISRT_ MSE chart performs better than the specific VSSI, the optimal variable sampling interval (VSI), and the fixed parameters (FP) ISRT_MSE charts. An example is given to illustrate this new proposed approach.

The Design of GLR Control Charts for Monitoring the Process Mean and Variance

This paper investigates generalized likelihood ratio (GLR) control charts for the problem of monitoring the mean and variance of a normally distributed process variable when the objective is to effectively detect both small and large shifts in these parameters. It is shown that the GLR charts are generally as effective at detecting a wide range of shift sizes as other options, such as the traditional practice of using a combination of a control chart for the mean and a control chart for the variance. Using a combination of control charts requires that multiple control-chart design parameters be specified. Although multiple design parameters allow for the charts to be tuned to be more sensitive to certain shifts that may be of particular interest, they complicate the process of designing these charts. The GLR chart for detecting a change in the mean or an increase in the variance does not have any control-chart parameters that need to be specified other than the control limit. The GLR chart for the case in which decreases in the variance are also of interest has one design parameter in addition to the control limit. Tables of control limits corresponding to specified values of the in-control average number of observations to signal are provided, so it is very easy to design the GLR chart for use in applications.

SURVEILLANCE OF DIABETES PREVALENCE RATE THROUGH THE DEVELOPMENT OF A MARKOV-BASED CONTROL CHART

In the field of statistical process control (SPC), usually two issues are addressed; the variables and the attribute quality characteristics control charting. Focusing on discrete data generated from a process to be monitored, attributes control charts would be useful. The discrete data could be classified into two categories; the independent and auto-correlated data. Regarding the independence in the sequence of discrete data, the typical Shewhart-based control charts, such as p-chart and np-chart would be effective enough to monitor the related process. But considering auto-correlation in the sequence of the data, such control charts would not workanymore. In this paper, considering the auto-correlated sequence of X1, X2,…, Xt,… as the sequence of zeros or ones, we have developed a control chart based on a two-state Markov model. This control chart is compared with the previously developed charts in terms of the average number of observations (ANOS) measure. In addition, a case study related to the diabetic people is investigated to demonstrate the applicability and high performance of the developed chart.

A Binomial GLR Control Chart for Monitoring a Proportion

This paper considers a control chart for monitoring a process proportion based on a generalized likelihood ratio (GLR) statistic. The objective is to effectively detect a wide range of shift sizes. The GLR statistic is obtained from a moving window of past sample statistics that follow a binomial distribution. The Phase II performance of this chart is evaluated using the steady state average number of observations to signal (SSANOS) for detecting sustained increases in the proportion. Comparisons of the binomial GLR chart to the Shewhart np-chart, the individual binomial cumulative sum (CUSUM) chart, and combinations of multiple binomial CUSUM charts show that the overall performance of the binomial GLR chart is at least as good as these other options. Moreover, unlike the other charts, the binomial GLR chart has an advantage that it does not require users to specify multiple charting parameters that may be difficult to obtain, and this makes it easier for the GLR chart to be designed for practical applications.

Data-Efficient Quickest Change Detection with On–Off Observation Control

In this article we extend Shiryaev's quickest change detection formulation by also accounting for the cost of observations used before the change point. The observation cost is captured through the average number of observations used in the detection process before the change occurs. The objective is to select an on–off observation control policy that decides whether or not to take a given observation, along with the stopping time at which the change is declared, to minimize the average detection delay, subject to constraints on both the probability of false alarm and the observation cost. By considering a Lagrangian relaxation of the constraint problem and using dynamic programming arguments, we obtain an a posteriori probability-based two-threshold algorithm that is a generalized version of the classical Shiryaev algorithm. We provide an asymptotic analysis of the two-threshold algorithm and show that the algorithm is asymptotically optimal—that is, the performance of the two-threshold algorithm approaches that of the Shiryaev algorithm—for a fixed observation cost, as the probability of false alarm goes to zero. We also show, using simulations, that the two-threshold algorithm has good observation cost-delay trade-off curves and provides significant reduction in observation cost compared to the naïve approach of fractional sampling, where samples are skipped randomly. Our analysis reveals that, for practical choices of constraints, the two thresholds can be set independent of each other: one based on the constraint of false alarm and another based on the observation cost constraint alone.

Type-Based Detection with a Fusion Center Performing the Sequential Test in Wireless Sensor Networks

In this paper, we propose a sequential type-based detection scheme for wireless sensor networks in the case of spatially and temporally identically and independently distributed observations. First, we investigate the optimal sequential detection rule of the proposed scheme, and then with the motivation of reducing the computational complexity of the optimal detection rule, we consider an approximation scheme and derive a suboptimal detection rule. We also compare the performances of the type-based sequential detection scheme with those of the non-sequential type-based detection scheme in terms of both average number of observations and total energy consumption, and determine the region of individual node power where the proposed scheme outperforms the non-sequential scheme. In addition, we show that the approximated detection rule provides the similar results as the optimal detection rule with a significant reduction of the computational complexity, which makes the approximated detection rule useful for real-time applications.