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The goal of this paper is to compare the accuracy of two approximate confidence interval estimators for the Bernoulli parameter p. The approximate confidence intervals are based on the normal and Poisson approximations to the binomial distribution. Charts are given to indicate which approximation is appropriate for certain sample sizes and point estimators.
Canada's boreal forests, which occupy approximately 30% of boreal forests world wide, play an important role in the global carbon budget. However, there is lit tle quantitative information available regarding the spatiotemporal changes in the drought-induced tree mortality of Canada's boreal forests overall and their associ ated impacts on biomass carbon dynamics. Here, we develop spatiotemporally ex plicit estimates of drought-induced tree mortality and corresponding biomass carbon sink capacity changes in Canada's boreal forests from 1970 to 2020. We show that the average annual tree mortality rate is approximately 2.7%. Approximately 43% of Canada's boreal forests have experienced significantly increasing tree mortality trends (71% of which are located in the western region of the country), and these trends have accelerated since 2002. This increase in tree mortality has resulted in sig nificant biomass carbon losses at an approximate rate of 1.51±0.29 MgC ha -1 year -1 (95% confidence interval) with an approximate total loss of 0.46±0.09 PgC year -1 (95% confidence interval). Under the drought condition increases predicted for this century, the capacity of Canada's boreal forests to act as a carbon sink will be further reduced, potentially leading to a significant positive climate feedback effect
Described here are the results of comparison between lidar and conventional contact measurements of the vertical temperature profile of the atmosphere. The lidar measurements are based on the method of temperature dependence of pure rotational Raman scattering of nitrogen and oxygen molecules. The presented results show that, as a whole, the motion of the lidar and conventional profiles coincide in the confidence intervals. Still there are districts in which the differences lay out of the confidence intervals. In analysis and estimation of the coincidence and the distinction in moving the profiles, we must take into account the differences between the methods for measuring the temperature profiles by lidar and contact methods, i.e. the next additional factors. The tied balloon meter gives the momentary values of the temperature in particular points of the profile, as these momentary values are the results of consequent, but not simultaneous measurements. In the case of free flying balloon, the time of measuring the lower several hundred meters is little because of high vertical velocity (about 300 m/min). This leads to an indefinite increase of the measuring error. The complete space coincidence between the lidar's and conventional profiles isn't possible. The contribution of the factors mentioned above about the error of comparison could increase because of nonstable layers in the planetary boundary layer of the atmosphere as well as by the influence of the mountains and the city situated nearby.
Two of the primary parametric costing tools used to estimate the development and production cost of future spacecraft hardware are PRICE TruePlanning by PRICE Systems, and System Estimation and Evaluation of Resources-Hardware (SEER-H) by Galorath. These are standard tools used by NASA and industry to estimate the cost of new aerospace hardware. This study is an independent verification of the accuracy of these tools and was originally published in 2018. The purpose of this presentation is to circulate the findings of that study among the NASA cost community. Both PRICE Systems and Galorath have completed internal validation studies of their parametric cost estimating tools; however, they only provided the results of the studies and did not detail the exact methods used to perform the validation. In the present study, cost estimators used PRICE TruePlanning and SEER-H to estimate the cost of twelve different past NASA science missions. The estimators were prevented from knowing the actual cost of the missions in an effort to minimize cognitive biases. In the present study, SEER-H had an average error of 23%, median error of -0.3%, with a standard deviation of 43%. PRICE had an average error of 52%, median error of 50%, and standard deviation of 45%. Nine of the twelve mission's actual costs fell within the 80% confidence interval of SEER's probabilistic estimates; however, none of the missions fell within PRICE’s confidence intervals. There were several factors independent of PRICE and SEER-H which may have affected the accuracy of the results in the present study including: uncertainty in the technical data used for the estimates, the methods used to estimate uncertainty in spacecraft component mass and numbers of prototypes, and the experience of the estimators.
Background: Models can help guide colorectal cancer screening policy. Although models are carefully calibrated and validated, there is less scrutiny of assumptions about test performance. Methods: We examined the validity of the CRC-SPIN model and colonoscopy sensitivity assumptions. Standard sensitivity assumptions, consistent with published decision analyses, assume sensitivity equal to 0.75 for diminutive adenomas (<6 mm), 0.85 for small adenomas (6–10 mm), 0.95 for large adenomas (≥10 mm), and 0.95 for preclinical cancer. We also selected adenoma sensitivity that resulted in more accurate predictions. Targets were drawn from the Wheat Bran Fiber study. In the study, we examined how well the model predicted outcomes measured over a three-year follow-up period, including the number of adenomas detected, the size of the largest adenoma detected, and incident colorectal cancer. Results: Using standard sensitivity assumptions, the model predicted adenoma prevalence that was too low (42.5% versus 48.9% observed, with 95% confidence interval 45.3%–50.7%) and detection of too few large adenomas (5.1% versus 14.% observed, with 95% confidence interval 11.8%–17.4%). Predictions were close to targets when we set sensitivities to 0.20 for diminutive adenomas, 0.60 for small adenomas, 0.80 for 10- to 20-mm adenomas, and 0.98 for adenomas 20 mm and larger. Conclusions: Colonoscopy may be less accurate than currently assumed, especially for diminutive adenomas. Alternatively, the CRC-SPIN model may not accurately simulate onset and progression of adenomas in higher-risk populations. Impact: Misspecification of either colonoscopy sensitivity or disease progression in high-risk populations may affect the predicted effectiveness of colorectal cancer screening. When possible, decision analyses used to inform policy should address these uncertainties.
The very low error probability obtained with long error-correcting codes results in a very small number of observed errors in simulation studies of practical size and renders the usual confidence interval techniques inapplicable to the observed error probability. A natural extension of the notion of a 'confidence interval' is made and applied to such determinations of error probability by simulation. An example is included to show the surprisingly great significance of as few as two decoding errors in a very large number of decoding trials.
The paper will address Theme 7: Multi-sensor opportunities for VEGETATION. We present analysis of a long-term vegetation record derived from three moderate resolution sensors: AVHRR, VEGETATION, and MODIS. While empirically based manipulation can ensure agreement between the three data sets, there is a need to validate the series. This paper uses atmospherically corrected ETM+ data available over the EOS Land Validation Core Sites as an independent data set with which to compare the time series. We use ETM+ data from 15 globally distributed sites, 7 of which contain repeat coverage in time. These high-resolution data are compared to the values of each sensor by spatially aggregating the ETM+ to each specific sensors' spatial coverage. The aggregated ETM+ value provides a point estimate for a specific site on a specific date. The standard deviation of that point estimate is used to construct a confidence interval for that point estimate. The values from each moderate resolution sensor are then evaluated with respect to that confident interval. Result show that AVHRR, VEGETATION, and MODIS data can be combined to assess temporal uncertainties and address data continuity issues and that the atmospherically corrected ETM+ data provide an independent source with which to compare that record. The final product is a consistent time series climate record that links historical observations to current and future measurements.
Available are independent observations (continuous data) that are believed to be a random sample. Desired are distribution-free confidence intervals and significance tests for the population median. However, there is the possibility that either the smallest or the largest observation is an outlier. Then, use of a procedure for rejection of an outlying observation might seem appropriate. Such a procedure would consider that two alternative situations are possible and would select one of them. Either (1) the n observations are truly a random sample, or (2) an outlier exists and its removal leaves a random sample of size n-1. For either situation, confidence intervals and tests are desired for the median of the population yielding the random sample. Unfortunately, satisfactory rejection procedures of a distribution-free nature do not seem to be available. Moreover, all rejection procedures impose undesirable conditional effects on the observations, and also, can select the wrong one of the two above situations. It is found that two-sided intervals and tests based on two symmetrically located order statistics (not the largest and smallest) of the n observations have this property.
Wetlands have long been drained for human use, thereby strongly affecting greenhouse gas fluxes, flood control, nutrient cycling and biodiversity. Nevertheless, the global extent of natural wetland loss remains remarkably uncertain. Here, we reconstruct the spatial distribution and timing of wetland loss through conversion to seven human land uses between 1700 and 2020, by combining national and subnational records of drainage and conversion with land-use maps and simulated wetland extents. We estimate that 3.4 million km 2 (confidence interval 2.9–3.8) of inland wetlands have been lost since 1700, primarily for conversion to croplands. This net loss of 21% (confidence interval 16–23%) of global wetland area is lower than that suggested previously by extrapolations of data disproportionately from high-loss regions. Wetland loss has been concentrated in Europe, the United States and China, and rapidly expanded during the mid-twentieth century. Our reconstruction elucidates the timing and land-use drivers of global wetland losses, providing an improved historical baseline to guide assessment of wetland loss impact on Earth system processes, conservation planning to protect remaining wetlands and prioritization of sites for wetland restoration.
Stochastic robustness, a simple technique used to estimate the robustness of linear, time-invariant systems, is applied to a twin-jet transport aircraft control system. Concepts behind stochastic stability robustness are extended to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications and measures specific to aircraft handling qualities are introduced. Confidence intervals for both individual stochastic robustness measures and for comparing two measures are presented. The application of stochastic performance robustness, the use of confidence intervals, and tradeoffs between performance objectives are demonstrated by means of the twin-jet aircraft example.
An overview of common approaches used to assess a dose response for radiation therapy–associated endpoints is presented, using lung toxicity data sets analyzed as a part of the High Dose per Fraction, Hypofractionated Treatment Effects in the Clinic effort as an example. Each component presented (eg, data-driven analysis, dose-response analysis, and calculating uncertainties on model prediction) is addressed using established approaches. Specifically, the maximum likelihood method was used to calculate best parameter values of the commonly used logistic model, the profile-likelihood to calculate confidence intervals on model parameters, and the likelihood ratio to determine whether the observed data fit is statistically significant. The bootstrap method was used to calculate confidence intervals for model predictions. Correlated behavior of model parameters and implication for interpreting dose response are discussed.
Methods for calculating return values of extreme precipitation and their uncertainty are compared using daily precipitation rates over the Western U.S. and Southwestern Canada from a large ensemble of climate model simulations. The roles of return-value estimation procedures and sample size in uncertainty are evaluated for various return periods. We compare two different generalized extreme value (GEV) parameter estimation techniques, namely L-moments and maximum likelihood (MLE), as well as empirical techniques. Even for very large datasets, confidence intervals calculated using GEV techniques are narrower than those calculated using empirical methods. Furthermore, the more efficient L-moments parameter estimation techniques result in narrower confidence intervals than MLE parameter estimation techniques at small sample sizes, but similar best estimates. It should be noted that we do not claim that either parameter fitting technique is better calibrated than the other to estimate long period return values. While a non-stationary MLE methodology is readily available to estimate GEV parameters, it is not for the L-moments method. Comparison of uncertainty quantification methods are found to yield significantly different estimates for small sample sizes but converge to similar results as sample size increases. Finally, practical recommendations about the length and size of climate model ensemble simulations and the choice of statistical methods to robustly estimate long period return values of extreme daily precipitation statistics and quantify their uncertainty.
This paper presents results of uncertainty and sensitivity analyses conducted to assess the relative merits of three duct propagation codes. Results from this study are intended to support identification of a "working envelope" within which to use the various approaches underlying these propagation codes. This investigation considers a segmented liner configuration that models the NASA Langley Grazing Incidence Tube, for which a large set of measured data was available. For the uncertainty analysis, the selected input parameters (source sound pressure level, average Mach number, liner impedance, exit impedance, static pressure and static temperature) are randomly varied over a range of values. Uncertainty limits (95% confidence levels) are computed for the predicted values from each code, and are compared with the corresponding 95% confidence intervals in the measured data. Generally, the mean values of the predicted attenuation are observed to track the mean values of the measured attenuation quite well and predicted confidence intervals tend to be larger in the presence of mean flow. A two-level, six factor sensitivity study is also conducted in which the six inputs are varied one at a time to assess their effect on the predicted attenuation. As expected, the results demonstrate the liner resistance and reactance to be the most important input parameters. They also indicate the exit impedance is a significant contributor to uncertainty in the predicted attenuation.
It is important to understand the risk of serious hypobaric decompression sickness (DCS) in order to develop procedures and treatment responses to mitigate the risk. Since it is not ethical to conduct prospective tests about serious DCS with humans, the necessary information was gathered from 73 published reports. We hypothesize that a 4-hr 100% oxygen (O2) prebreathe results in a very low risk of serious DCS, and test this through analysis. We evaluated 258 tests containing information from 79,366 exposures in attitude chambers. Serious DCS was documented in 918 men during the tests. Serious DCS are signs and symptoms broadly classified as Type II DCS. A risk function analysis with maximum likelihood optimization was performed to identify significant explanatory variables, and to create a predictive model for the probability of serious DCS [P(serious DCS)]. Useful variables were Tissue Ratio, the planned time spent at altitude (T(sub alt)), and whether or not repetitive exercise was performed at altitude. Tissue Ratio is P1N2/P2, where P1N2 is calculated nitrogen (N2) pressure in a compartment with a 180-min half-time for N2 pressure just before ascent, and P2 is ambient pressure after ascent. A prebreathe and decompression profile Shuttle astronauts use for extravehicular activity (EVA) includes a 4-hr prebreathe with 100% O2, an ascent to P2 = 4.3 lb per sq. in. absolute, and a T(sub alt) = 6 hr. The P(serious DCS) is: 0.0014 (0.00096 - 0.00196, 95% confidence interval) with exercise and 0.00025 (0.00016 - 0.00035) without exercise. Given 100 Shuttle EVAs to date and no report of serious DCS, the true risk is less than 0.03 with 95% confidence (Binomial Theorem). It is problematic to estimate the risk of serious DCS since it appears infrequently, even if the estimate is based on thousands of altitude chamber exposures. The true risk to astronauts may lie between the extremes of the confidence intervals (0.00016 - 0.00196) since the contribution of other factors, particularly exercise, to the risk of serious DCS during EVA is unknown. A simple model that only accounts for four important variables in retrospective data is still helpful to increase our understanding about the risk of serious DCS.
We present a frequentist analysis of clustering measurements from Data Release 1 of the Dark Energy Spectroscopic Instrument (DESI) using the standard profile likelihood method. While Bayesian inferences for effective field theory models of galaxy clustering can be highly sensitive to prior choices for extended cosmological models, frequentist inferences are not susceptible to such effects. We compare frequentist and Bayesian constraints for the parameter set {σ 8 , H 0 , Ω m , w 0 , w a } using the full-shape power spectrum multipoles, post-reconstruction baryon acoustic oscillation (BAO) measurements, and external datasets from the CMB and type Ia supernovae measurements. The frequentist confidence intervals are significantly shifted relative to the Bayesian credible intervals for the w 0 w a CDM model, unless supernovae data are included. When DESI full-shape and BAO data are fit jointly, we obtain the following 1σ frequentist confidence intervals for ΛCDM (w 0 w a CDM): σ 8 = 0.863 +0.048 -0.040 , H 0 = 68.96 +0.81 -0.80 km s -1 Mpc -1 , Ω m = 0.3034 ± 0.0110 (σ 8 = 0.782 +0.060 -0.036 , H 0 = 63.7 +4.2 -2.0 km s -1 Mpc -1 , Ω m = 0.378 +0.024 -0.047 , w 0 = -0.16 +0.10 -0.50 , w a = -3.0 +1.7 ), corresponding to 0.8σ, 0.3σ, 0.7σ (2.1σ, 4.1σ, 6.5σ, 6.3σ, 6.6σ) shifts between the maximum likelihood estimate and the Bayesian posterior mean for ΛCDM (w 0 w a CDM) respectively.
A procedure for estimating uncertainties in the aerodynamic-heating and thermal protection system (TPS) thermal-performance methodologies developed for the Shuttle Orbiter is presented. This procedure is used in predicting uncertainty bands around expected or nominal TPS thermal responses for the Orbiter during entry. Individual flowfield and TPS parameters that make major contributions to these uncertainty bands are identified and, by statistical considerations, combined in a manner suitable for making engineering estimates of the TPS thermal confidence intervals and temperature margins relative to design limits. Thus, for a fixed TPS design, entry trajectories for future Orbiter missions can be shaped subject to both the thermal-margin and confidence-interval requirements. This procedure is illustrated by assessing the thermal margins offered by selected areas of the existing Orbiter TPS design for an entry trajectory typifying early flight test missions.
The expressions for the maximum likelihood functions are given when the failure data are censored at a given point or at multiple points, or when the data come in groups. Different models applicable to failure data are presented with their characteristics. A graphical method of distinguishing different models by using cumulative hazard fucnction is discussed. For the failure data on controllers the model is determined by cumulative hazard function and chi-square goodness of fit. Using the Weibull Model the maximum likelihood estimators of the shape parameter and the failure rate parameter are obtained. The confidence intervals, meantime between failures, and B1 are determined. Similarly, for the data on Space Shuttle Main Engine (SSME) blade failures the maximum likelihood estimators are obtained for the Weibull parameters. The variances, confidence intervals, meantime between failures, and reliability are determined. The analysis is performed under assumption of grouped data as well as randomly placed data.
The accurate determination of upper ocean apparent optical properties (AOP's) is essential for the vicarious calibration of the sea-viewing wide field-of-view sensor (SeaWiFS) instrument and the validation of the derived data products. To evaluate the role that data analysis methods have upon values of derived AOP's, the first Data Analysis Round-Robin (DARR-94) workshop was sponsored by the SeaWiFS Project during 21-23 July, 1994. The focus of this intercomparison study was the estimation of the downwelling irradiance spectrum just beneath the sea surface, E(sub d)(0(sup -), lambda); the upwelling nadir radiance just beneath the sea surface, L(sub u)(0(sup -), lambda); and the vertical profile of the diffuse attenuation coefficient spectrum, K(sub d)(z, lambda). In the results reported here, different methodologies from four research groups were applied to an identical set of 10 spectroradiometry casts in order to evaluate the degree to which data analysis methods influence AOP estimation, and whether any general improvements can be made. The overall results of DARR-94 are presented in Chapter 1 and the individual methods of the four groups are presented in Chapters 2-5. The DARR-94 results do not show a clear winner among data analysis methods evaluated. It is apparent, however, that some degree of outlier rejection is required in order to accurately estimate L(sub u)(0(sup -), lambda) or E(sub d)(0(sup -), lambda). Furthermore, the calculation, evaluation and exploitation of confidence intervals for the AOP determinations needs to be explored. That is, the SeaWiFS calibration and validation problem should be recast in statistical terms where the in situ AOP values are statistical estimates with known confidence intervals.