Accuracy assessment of the joint CloudSat-CALIPSO global cloud amount based on the bootstrap confidence intervals

2021 ◽  
Author(s):  
Andrzej Kotarba ◽  
Mateusz Solecki
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Spatial Resolution ◽  
Confidence Level ◽  
Accuracy Assessment ◽  
Cloud Amount ◽  
Radiation Budget ◽  
Bootstrap Confidence Intervals ◽  
Fine Spatial Resolution ◽  
Interval Width

<p>Vertically-resolved cloud amount is essential for understanding the Earth’s radiation budget. Joint CloudSat-CALIPSO, lidar-radar cloud climatology remains the only dataset providing such information globally. However, a specific sampling scheme (pencil-like swath, 16-day revisit) introduces an uncertainty to CloudSat-CALIPSO cloud amounts. In the research we assess those uncertainties in terms of a bootstrap confidence intervals. Five years (2006-2011) of the 2B-GEOPROF-LIDAR (version P2_R05) cloud product was examined, accounting for  typical spatial resolutions of a global grids (1.0°, 2.5°, 5.0°, 10.0°), four confidence levels of confidence interval (0.85, 0.90, 0.95, 0.99), and three time scales of mean cloud amount (annual, seasonal, monthly). Results proved that cloud amount accuracy of 1%, or 5%, is not achievable with the dataset, assuming a 5-year mean cloud amount, high (>0.95) confidence level, and fine spatial resolution (1º–2.5º). The 1% requirement was only met by ~6.5% of atmospheric volumes at 1º and 2.5º, while more tolerant criterion (5%) was met by 22.5% volumes at 1º, or 48.9% at 2.5º resolution. In order to have at least 99% of volumes meeting an accuracy criterion, the criterion itself would have to be lowered to ~20% for 1º data, or to ~8% for 2.5º data. Study also quantified the relation between confidence interval width, and spatial resolution, confidence level, number of observations. Cloud regime (mean cloud amount, and standard deviation of cloud amount) was found the most important factor impacting the width of confidence interval. The research has been funded by the National Science Institute of Poland grant no. UMO-2017/25/B/ST10/01787. This research has been supported in part by PL-Grid Infrastructure (a computing resources).</p>

scholarly journals Uncertainty Assessment of the Vertically-Resolved Cloud Amount for Joint CloudSat–CALIPSO Radar–Lidar Observations

2021 ◽  
Vol 13 (4) ◽  
pp. 807
Author(s):  
Andrzej Z. Kotarba ◽  
Mateusz Solecki
Keyword(s):  
Confidence Interval ◽  
Spatial Resolution ◽  
Confidence Level ◽  
Cloud Amount ◽  
Satellite Observation ◽  
Uncertainty Assessment ◽  
Confidence Levels ◽  
Fine Spatial Resolution ◽  
Average Confidence ◽  
Accuracy Assessments

The joint CloudSat–Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) climatology remains the only dataset that provides a global, vertically-resolved cloud amount statistic. However, data are affected by uncertainty that is the result of a combination of infrequent sampling, and a very narrow, pencil-like swath. This study provides the first global assessment of these uncertainties, which are quantified using bootstrapped confidence intervals. Rather than focusing on a purely theoretical discussion, we investigate empirical data that span a five-year period between 2006 and 2011. We examine the 2B-Geometric Profiling (GEOPROF)-LIDAR cloud product, at typical spatial resolutions found in global grids (1.0°, 2.5°, 5.0°, and 10.0°), four confidence levels (0.85, 0.90, 0.95, and 0.99), and three time scales (annual, seasonal, and monthly). Our results demonstrate that it is impossible to estimate, for every location, a five-year mean cloud amount based on CloudSat–CALIPSO data, assuming an accuracy of 1% or 5%, a high confidence level (>0.95), and a fine spatial resolution (1°–2.5°). In fact, the 1% requirement was only met by ~6.5% of atmospheric volumes at 1° and 2.5°, while the more tolerant criterion (5%) was met by 22.5% volumes at 1°, or 48.9% at 2.5° resolution. In order for at least 99% of volumes to meet an accuracy criterion, the criterion itself would have to be lowered to ~20% for 1° data, or to ~8% for 2.5° data. Our study also showed that the average confidence interval: decreased four times when the spatial resolution increased from 1° to 10°; doubled when the confidence level increased from 0.85 to 0.99; and tripled when the number of data-months increased from one (monthly mean) to twelve (annual mean). The cloud regime arguably had the most impact on the width of the confidence interval (mean cloud amount and its standard deviation). Our findings suggest that existing uncertainties in the CloudSat–CALIPSO five-year climatology are primarily the result of climate-specific factors, rather than the sampling scheme. Results that are presented in the form of statistics or maps, as in this study, can help the scientific community to improve accuracy assessments (which are frequently omitted), when analyzing existing and future CloudSat–CALIPSO cloud climatologies.

scholarly journals Evaluation of Bootstrap Confidence Intervals Using a New Non-Normal Process Capability Index

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 484 ◽  
Author(s):  
Gadde Srinivasa Rao ◽  
Mohammed Albassam ◽  
Muhammad Aslam
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Process Capability ◽  
Real Data ◽  
Process Capability Index ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Confidence Intervals ◽  
Capability Index ◽  
Coverage Probabilities ◽  
Percentile Bootstrap

This paper assesses the bootstrap confidence intervals of a newly proposed process capability index (PCI) for Weibull distribution, using the logarithm of the analyzed data. These methods can be applied when the quality of interest has non-symmetrical distribution. Bootstrap confidence intervals, which consist of standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) confidence interval are constructed for the proposed method. A Monte Carlo simulation study is used to determine the efficiency of newly proposed index Cpkw over the existing method by addressing the coverage probabilities and average widths. The outcome shows that the BCPB confidence interval is recommended. The methodology of the proposed index has been explained by using the real data of breaking stress of carbon fibers.

BOOTSTRAP CONFIDENCE INTERVALS FOR STEADY-STATE AVAILABILITY

2004 ◽  
Vol 21 (03) ◽  
pp. 407-419 ◽  
Author(s):  
JAE-HAK LIM ◽  
SANG WOOK SHIN ◽  
DAE KYUNG KIM ◽  
DONG HO PARK
Keyword(s):  
Steady State ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Coverage Probability ◽  
Average Length ◽  
Repairable System ◽  
Bootstrap Confidence Interval ◽  
Bootstrap Confidence Intervals ◽  
Bootstrap Methods ◽  
Percentile Bootstrap

Steady-state availability, denoted by A, has been widely used as a measure to evaluate the reliability of a repairable system. In this paper, we develop new confidence intervals for steady-state availability based on four bootstrap methods; standard bootstrap confidence interval, percentile bootstrap confidence interval, bootstrap-t confidence interval, and bias-corrected and accelerated confidence interval. We also investigate the accuracy of these bootstrap confidence intervals by calculating the coverage probability and the average length of intervals.

scholarly journals ON THE NUMBER OF BOOTSTRAP REPETITIONS FOR BCa CONFIDENCE INTERVALS

2002 ◽  
Vol 18 (4) ◽  
pp. 962-984 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Moshe Buchinsky
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
High Probability ◽  
Random Variables ◽  
American Statistical Association ◽  
Bootstrap Confidence Interval ◽  
Statistical Association ◽  
Step Method ◽  
Bootstrap Confidence Intervals ◽  
The Ideal

This paper considers the problem of choosing the number of bootstrap repetitions B to use with the BCa bootstrap confidence intervals introduced by Efron (1987, Journal of the American Statistical Association 82, 171–200). Because the simulated random variables are ancillary, we seek a choice of B that yields a confidence interval that is close to the ideal bootstrap confidence interval for which B = ∞. We specify a three-step method of choosing B that ensures that the lower and upper lengths of the confidence interval deviate from those of the ideal bootstrap confidence interval by at most a small percentage with high probability.

Laplace Correction of Confusion Matrices to Produce Statistically Representative Confidence Intervals

2010 ◽  
Author(s):  
Craig R. Davison
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Confidence Intervals ◽  
Correction Factor ◽  
Confidence Level ◽  
Confusion Matrix ◽  
Diagnostic Algorithm ◽  
Total Sample ◽  
Total Sample Size ◽  
Size Number

During diagnostic algorithm development engine testing with implanted faults may be performed. The number of implanted faults is never large enough to truly capture the distribution in the confusion matrix. Misdiagnoses in particular are unlikely to be correctly represented. Misdiagnosis that could result in costly outcomes are frequently not captured in an implantation study, resulting in a deceptively reassuring zero value for the probability of it occurring. The Laplace correction can be applied to each element of the confusion matrix to improve the generated confidence interval. This also allows a confidence interval to be produced for zero value elements. Unfortunately, the choice of Laplace correction factor influences the size of the confidence interval, and without knowing the true distribution the best correction factor cannot be determined. The choice of correction factor depends on element probability, total sample size, number of faults and confidence level. The effect of the Laplace correction on the element probability is analytically examined to provide insight into the relative influence of the correction. This is followed by an examination of the influence of the element probability, total sample size, number of faults and confidence level on the required Laplace correction. This is achieved by sampling from known populations. A method of generating good confidence intervals on each element is proposed. This includes the production of a Laplace correction based on the sample size, number of faults and confidence level. This will allow consistent comparisons of Laplace corrected matrices rather than leaving the correction factor to each individual’s best engineering judgment.

Two-Condition Within-Participant Statistical Mediation Analysis: A Path-Analytic Framework

2019 ◽  
Author(s):  
Amanda Kay Montoya ◽  
Andrew F. Hayes
Keyword(s):  
Confidence Intervals ◽  
Indirect Effect ◽  
Mediation Analysis ◽  
Analytic Approach ◽  
Analytic Framework ◽  
Hypothesis Tests ◽  
Bootstrap Confidence Intervals ◽  
Complex Models ◽  
Path Analytic ◽  
Statistical Mediation Analysis

Researchers interested in testing mediation often use designs where participants are measured on a dependent variable Y and a mediator M in both of two different circumstances. The dominant approach to assessing mediation in such a design, proposed by Judd, Kenny, and McClelland (2001), relies on a series of hypothesis tests about components of the mediation model and is not based on an estimate of or formal inference about the indirect effect. In this paper we recast Judd et al.’s approach in the path-analytic framework that is now commonly used in between-participant mediation analysis. By so doing, it is apparent how to estimate the indirect effect of a within-participant manipulation on some outcome through a mediator as the product of paths of influence. This path analytic approach eliminates the need for discrete hypothesis tests about components of the model to support a claim of mediation, as Judd et al’s method requires, because it relies only on an inference about the product of paths— the indirect effect. We generalize methods of inference for the indirect effect widely used in between-participant designs to this within-participant version of mediation analysis, including bootstrap confidence intervals and Monte Carlo confidence intervals. Using this path analytic approach, we extend the method to models with multiple mediators operating in parallel and serially and discuss the comparison of indirect effects in these more complex models. We offer macros and code for SPSS, SAS, and Mplus that conduct these analyses.

Features of accumulation of amounts of measurement error

2017 ◽  
Vol 928 (10) ◽  
pp. 58-63 ◽  
Author(s):  
V.I. Salnikov
Keyword(s):  
Measurement Error ◽  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Level ◽  
Measurement Errors ◽  
Truncated Normal Distribution ◽  
Truncated Normal ◽  
The Law ◽  
Normal Law

The initial subject for study are consistent sums of the measurement errors. It is assumed that the latter are subject to the normal law, but with the limitation on the value of the marginal error Δpred = 2m. It is known that each amount ni corresponding to a confidence interval, which provides the value of the sum, is equal to zero. The paradox is that the probability of such an event is zero; therefore, it is impossible to determine the value ni of where the sum becomes zero. The article proposes to consider the event consisting in the fact that some amount of error will change value within 2m limits with a confidence level of 0,954. Within the group all the sums have a limit error. These tolerances are proposed to use for the discrepancies in geodesy instead of 2m*SQL(ni). The concept of “the law of the truncated normal distribution with Δpred = 2m” is suggested to be introduced.

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