Showing papers on "Coverage probability published in 2018"

Likelihood-based meta-analysis with few studies: Empirical and simulation studies

Abstract: Standard random-effects meta-analysis methods perform poorly when applied to few studies only. Such settings however are commonly encountered in practice. It is unclear, whether or to what extent small-sample-size behaviour can be improved by more sophisticated modeling. We consider several likelihood-based inference methods. Confidence intervals are based on normal or Student-t approximations. We extract an empirical data set of 40 meta-analyses from recent reviews published by the German Institute for Quality and Efficiency in Health Care (IQWiG). Methods are then compared empirically as well as in a simulation study, considering odds-ratio and risk ratio effect sizes. Empirically, a majority of the identified meta-analyses include only 2 studies. In the simulation study, coverage probability is, in the presence of heterogeneity and few studies, below the nominal level for all frequentist methods based on normal approximation, in particular when sizes in meta-analyses are not balanced, but improve when confidence intervals are adjusted. Bayesian methods result in better coverage than the frequentist methods with normal approximation in all scenarios. Credible intervals are empirically and in the simulation study wider than unadjusted confidence intervals, but considerably narrower than adjusted ones. Confidence intervals based on the generalized linear mixed models are in general, slightly narrower than those from other frequentist methods. Certain methods turned out impractical due to frequent numerical problems. In the presence of between-study heterogeneity, especially with unbalanced study sizes, caution is needed in applying meta-analytical methods to few studies, as either coverage probabilities might be compromised, or intervals are inconclusively wide. Bayesian estimation with a sensibly chosen prior for between-trial heterogeneity may offer a promising compromise.

A comparison of methods for meta‐analysis of a small number of studies with binary outcomes

Abstract: Meta-analyses often include only a small number of studies (≤5). Estimating between-study heterogeneity is difficult in this situation. An inaccurate estimation of heterogeneity can result in biased effect estimates and too narrow confidence intervals. The beta-binominal model has shown good statistical properties for meta-analysis of sparse data. We compare the beta-binominal model with different inverse variance random (eg, DerSimonian-Laird, modified Hartung-Knapp, and Paule-Mandel) and fixed effects methods (Mantel-Haenszel and Peto) in a simulation study. The underlying true parameters were obtained from empirical data of actually performed meta-analyses to best mirror real-life situations. We show that valid methods for meta-analysis of a small number of studies are available. In fixed effects situations, the Mantel-Haenszel and Peto methods performed best. In random effects situations, the beta-binominal model performed best for meta-analysis of few studies considering the balance between coverage probability and power. We recommended the beta-binominal model for practical application. If very strong evidence is needed, using the Paule-Mandel heterogeneity variance estimator combined with modified Hartung-Knapp confidence intervals might be useful to confirm the results. Notable most inverse variance random effects models showed unsatisfactory statistical properties also if more studies (10-50) were included in the meta-analysis.

A Novel Hybrid Interval Prediction Approach Based on Modified Lower Upper Bound Estimation in Combination with Multi-Objective Salp Swarm Algorithm for Short-Term Load Forecasting

Abstract: Effective and reliable load forecasting is an important basis for power system planning and operation decisions. Its forecasting accuracy directly affects the safety and economy of the operation of the power system. However, attaining the desired point forecasting accuracy has been regarded as a challenge because of the intrinsic complexity and instability of the power load. Considering the difficulties of accurate point forecasting, interval prediction is able to tolerate increased uncertainty and provide more information for practical operation decisions. In this study, a novel hybrid system for short-term load forecasting (STLF) is proposed by integrating a data preprocessing module, a multi-objective optimization module, and an interval prediction module. In this system, the training process is performed by maximizing the coverage probability and by minimizing the forecasting interval width at the same time. To verify the performance of the proposed hybrid system, half-hourly load data are set as illustrative cases and two experiments are carried out in four states with four quarters in Australia. The simulation results verified the superiority of the proposed technique and the effects of the submodules were analyzed by comparing the outcomes with those of benchmark models. Furthermore, it is proved that the proposed hybrid system is valuable in improving power grid management.

Coverage Probability Analysis of UAV Cellular Networks in Urban Environments

Abstract: In this paper, we study coverage probabilities of the UAV-assisted cellular network modeled by 2-dimension (2D) Poisson point process. The cellular user is assumed to connect to the nearest aerial base station. We derive the explicit expressions for the downlink coverage probability for the Rayleigh fading channel. Furthermore, we explore the behavior of performance when taking the property of air-to-ground channel into consideration. Our analytical and numerical results show that the coverage probability is affected by UAV height, pathloss exponent and UAV density. To maximize the coverage probability, the optimal height and density of UAVs are studied, which could be beneficial for the UAV deployment design.

Quantifying uncertainty in short-term traffic prediction and its application to optimal staffing plan development

Abstract: In this paper, we aim to quantify uncertainty in short-term traffic volume prediction by enhancing a hybrid machine learning model based on Particle Swarm Optimization (PSO) and Extreme Learning Machine (ELM) neural network. Different from the previous studies, the PSO-ELM models require no statistical inference nor distribution assumption of the model parameters, but rather focus on generating the prediction intervals (PIs) that can minimize a multi-objective function which considers two criteria, reliability and interval sharpness. The improved PSO-ELM models are developed for an hourly border crossing traffic dataset and compared to: (1) the original PSO-ELMs; (2) two state of the art models proposed by Zhang et al. (2014) and Guo et al. (2014) separately; and (3) the traditional ARMA and Kalman filter models. The results show that the improved PSO-ELM can always keep the mean PI length the lowest, and guarantee that the PI coverage probability is higher than the corresponding PI nominal confidence, regardless of the confidence level assumed. The study also probes the reasons that led to a few points being not covered by the PIs of PSO-ELMs. Finally, the study proposes a comprehensive optimization framework to make staffing plans for border crossing authority based on bounds of PIs and point predictions. The results show that for holidays, the staffing plans based on PI upper bounds generated much lower total system costs, and that those plans derived from PI upper bounds of the improved PSO-ELM models, are capable of producing the lowest average waiting times at the border. For a weekday or a typical Monday, the workforce plans based on point predictions from Zhang et al. (2014) and Guo et al. (2014) models generated the smallest system costs with low border crossing delays. Moreover, for both holiday and normal Monday scenarios, if the border crossing authority lacked the required staff to implement the plans based on PI upper bounds or point predictions, the staffing plans based on PI lower bounds from the improved PSO-ELMs performed the best, with an acceptable level of service and total system costs close to the point prediction plans.

Uncertainty Quantification for Online Learning and Stochastic Approximation via Hierarchical Incremental Gradient Descent

Abstract: Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever- increasing volume of work on SGD, much less is known about the statistical inferential properties of SGD-based predictions. Taking a fully inferential viewpoint, this paper introduces a novel procedure termed HiGrad to conduct statistical inference for online learning, without incurring additional computational cost compared with SGD. The HiGrad procedure begins by performing SGD updates for a while and then splits the single thread into several threads, and this procedure hierarchically operates in this fashion along each thread. With predictions provided by multiple threads in place, a t-based confidence interval is constructed by decorrelating predictions using covariance structures given by a Donsker-style extension of the Ruppert--Polyak averaging scheme, which is a technical contribution of independent interest. Under certain regularity conditions, the HiGrad confidence interval is shown to attain asymptotically exact coverage probability. Finally, the performance of HiGrad is evaluated through extensive simulation studies and a real data example. An R package higrad has been developed to implement the method.

Mixed effects approach to the analysis of the stepped wedge cluster randomised trial—Investigating the confounding effect of time through simulation

Abstract: © 2018 Nickless et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Background A stepped wedge cluster randomised trial (SWCRT) is a multicentred study which allows an intervention to be rolled out at sites in a random order. Once the intervention is initiated at a site, all participants within that site remain exposed to the intervention for the remainder of the study. The time since the start of the study (“calendar time”) may affect outcome measures through underlying time trends or periodicity. The time since the intervention was introduced to a site (“exposure time”) may also affect outcomes cumulatively for successful interventions, possibly in addition to a step change when the intervention began. Methods Motivated by a SWCRT of self-monitoring for bipolar disorder, we conducted a simulation study to compare model formulations to analyse data from a SWCRT under 36 different scenarios in which time was related to the outcome (improvement in mood score). The aim was to find a model specification that would produce reliable estimates of intervention effects under different scenarios. Nine different formulations of a linear mixed effects model were fitted to these datasets. These models varied in the specification of calendar and exposure times. Results Modelling the effects of the intervention was best accomplished by including terms for both calendar time and exposure time. Treating time as categorical (a separate parameter for each measurement time-step) achieved the best coverage probabilities and low bias, but at a cost of wider confidence intervals compared to simpler models for those scenarios which were sufficiently modelled by fewer parameters. Treating time as continuous and including a quadratic time term performed similarly well, with slightly larger variations in coverage probability, but narrower confidence intervals and in some cases lower bias. The impact of misspecifying the covariance structure was comparatively small. Conclusions We recommend that unless there is a priori information to indicate the form of the relationship between time and outcomes, data from SWCRTs should be analysed with a linear mixed effects model that includes separate categorical terms for calendar time and exposure time. Prespecified sensitivity analyses should consider the different formulations of these time effects in the model, to assess their impact on estimates of intervention effects.

Coverage and Interference in D2D Networks With Poisson Cluster Process

Abstract: In this letter, we present an analytical framework for the coverage probability analysis in a device-to-device (D2D) network with the location of devices modeled as a Poisson cluster process. We consider Nakagami- $m$ fading between the D2D communication links, which provides a more realistic scenario for the performance analysis. We assume a standard singular path loss model and use stochastic geometry as a tool for the interference and coverage probability analysis. Furthermore, we derive a closed form approximate expression and a bound on the coverage probability, and also include the interference-limited case. Numerical results corroborate our analysis.

Modeling Infrastructure Sharing in mmWave Networks With Shared Spectrum Licenses

Abstract: Competing cellular operators aggressively share infrastructure in many major US markets If operators were also to share spectrum in next-generation millimeter-wave (mmWave) networks, intra-network interference will become correlated with inter-network interference We propose a mathematical framework to model a multi-operator mmWave cellular network with co-located base-stations (BSs) We then characterize the signal-to-interference-plus-noise ratio distribution for an arbitrary network and derive its coverage probability To understand how varying the spatial correlation between different networks affects coverage probability, we derive special results for the two-operator scenario, where we construct the operators’ individual networks from a single network via probabilistic coupling For external validation, we devise a method to quantify and estimate spatial correlation from actual BS deployments We compare our two-operator model against an actual macro-cell-dominated network and an actual network primarily comprising distributed-antenna-system (DAS) nodes Using the actual deployment data to set the parameters of our model, we observe that coverage probabilities for the model and actual deployments not only compare very well to each other, but also match nearly perfectly for the case of the DAS-node-dominated deployment Another interesting observation is that a network that shares spectrum and infrastructure has a lower rate coverage probability at low rate thresholds than a network of the same number of BSs that shares neither spectrum nor infrastructure, suggesting that the latter is more suitable for low-rate applications

On the Energy-Efficient Deployment for Ultra-Dense Heterogeneous Networks With NLoS and LoS Transmissions

Abstract: We investigate network performance of ultra-dense heterogeneous networks and study the maximum energy-efficient base station deployment incorporating probabilistic non-line-of-sight and line-of-sight transmissions. First, we develop an analytical framework with the maximum instantaneous received power and the maximum average received power association schemes to model the coverage probability and related performance metrics, e.g., the potential throughput and the energy efficiency (EE). Second, we formulate two optimization problems to achieve the maximum energy-efficient deployment solution with specific service criteria. Simulation results show that there are tradeoffs among the coverage probability, the total power consumption, and the EE. To be specific, the maximum coverage probability with ideal power consumption is superior to that with practical power consumption when the total power constraint is small and inferior to that with practical power consumption when the total power constraint becomes large. Moreover, the maximum EE is a decreasing function with respect to the coverage probability constraint.

Probability Interval Prediction of Wind Power Based on KDE Method With Rough Sets and Weighted Markov Chain

Abstract: Research on the uncertainty of wind power has a significant influence on power system planning and decision-making This paper proposes a novel method for wind power interval forecasting based on rough sets theory, weighted Markov chain, and kernel density estimation (KDE) method Since the wind power prediction is significantly correlated to its historical record, this method first applies the Markov chain method to predict the power at different steps based on historical power data, and then the overall power is calculated via rough set weighted summation Finally, the obtained forecasting power is fed into the KDE forecasting model to obtain both upper and lower bounds of the probability interval of the wind power at a certain confidence level The predicted interval coverage probability and average bandwidth are two of the criterions used to evaluate the proposed method Moreover, the simulation results obtained via the Markov chain-KDE method and the weighted Markov chain-KDE method are compared against the results of the proposed method These comparisons show that the proposed method based on rough set theory and weighted Markov chain KDE method offers unique advantages over the other methods for probability interval prediction of wind power, which are higher coverage, narrower average bandwidth, and a more accurate result

Optimize the Coverage Probability of Prediction Interval for Anomaly Detection of Sensor-Based Monitoring Series.

Abstract: Effective anomaly detection of sensing data is essential for identifying potential system failures. Because they require no prior knowledge or accumulated labels, and provide uncertainty presentation, the probability prediction methods (e.g., Gaussian process regression (GPR) and relevance vector machine (RVM)) are especially adaptable to perform anomaly detection for sensing series. Generally, one key parameter of prediction models is coverage probability (CP), which controls the judging threshold of the testing sample and is generally set to a default value (e.g., 90% or 95%). There are few criteria to determine the optimal CP for anomaly detection. Therefore, this paper designs a graphic indicator of the receiver operating characteristic curve of prediction interval (ROC-PI) based on the definition of the ROC curve which can depict the trade-off between the PI width and PI coverage probability across a series of cut-off points. Furthermore, the Youden index is modified to assess the performance of different CPs, by the minimization of which the optimal CP is derived by the simulated annealing (SA) algorithm. Experiments conducted on two simulation datasets demonstrate the validity of the proposed method. Especially, an actual case study on sensing series from an on-orbit satellite illustrates its significant performance in practical application.

Exact confidence limits for the response rate in two-stage designs with over- or under-enrollment in the second stage:

Abstract: Simon's two-stage design has been widely used in early phase clinical trials to assess the activity of a new investigated treatment. In practice, the actual sample sizes do not always follow the study design precisely, especially in the second stage. When over- or under-enrollment occurs in a study, the original critical values for the study design are no longer valid for making proper statistical inference in a clinical trial. The hypothesis for such studies is always one-sided, and the null hypothesis is rejected when only a few responses are observed. Therefore, a one-sided lower interval is suitable to test the hypothesis. The commonly used approaches for confidence interval construction are based on asymptotic approaches. These approaches generally do not guarantee the coverage probability. For this reason, Clopper-Pearson approach can be used to compute exact confidence intervals. This approach has to be used in conjunction with a method to order the sample space. The frequently used method is based on point estimates for the response rate, but this ordering has too many ties which lead to conservativeness of the exact intervals. We propose developing exact one-sided intervals based on the p-value to order the sample space. The proposed approach outperforms the existing asymptotic and exact approaches. Therefore, it is recommended for use in practice.

Confidence intervals for the mean and a percentile based on zero-inflated lognormal data

Abstract: The problems of estimating the mean and an upper percentile of a lognormal population with nonnegative values are considered. For estimating the mean of a such population based on data that include...

Optimal Base Station Deployment with Downlink Rate Coverage Probability Constraint

Abstract: The uncertainty in user locations and channel conditions makes the deployment and performance analysis of wireless networks challenging. Stochastic geometry has emerged as a powerful tool for analyzing the performance of wireless networks, assuming certain stochastic models for the distribution of both users and base stations (BSs). In this letter, seeking further precision, we derive the downlink rate coverage probability of a wireless network with deterministically known BS locations . Then, we use this result to optimize the placement of BSs while keeping the downlink rate coverage probability above a certain threshold.

The Frechet distribution: Estimation and Application an Overview

Abstract: In this article, we consider the problem of estimating the parameters of the Frechet distribution from both frequentist and Bayesian points of view. First we briefly describe different frequentist approaches, namely, maximum likelihood, method of moments, percentile estimators, L-moments, ordinary and weighted least squares, maximum product of spacings, maximum goodness-of-fit estimators and compare them with respect to mean relative estimates, mean squared errors and the 95\% coverage probability of the asymptotic confidence intervals using extensive numerical simulations. Next, we consider the Bayesian inference approach using reference priors. The Metropolis-Hasting algorithm is used to draw Markov Chain Monte Carlo samples, and they have in turn been used to compute the Bayes estimates and also to construct the corresponding credible intervals. Five real data sets related to the minimum flow of water on Piracicaba river in Brazil are used to illustrate the applicability of the discussed procedures.

Accuracy of Distance-Based Ranking of Users in the Analysis of NOMA Systems

Abstract: We characterize the accuracy of analyzing the performance of a NOMA system where users are ranked according to their distances instead of instantaneous channel gains, i.e., product of distance-based path-loss and fading channel gains. Distance-based ranking is analytically tractable and can lead to important insights. However, it may not be appropriate in a multipath fading environment where a near user suffers from severe fading while a far user experiences weak fading. Since the ranking of users in a NOMA system has a direct impact on coverage probability analysis, impact of the traditional distance-based ranking, as opposed to instantaneous signal power-based ranking, needs to be understood. This will enable us to identify scenarios where distance-based ranking, which is easier to implement compared to instantaneous signal power-based ranking, is acceptable for system performance analysis. To this end, in this paper, we derive the probability of the event when distance-based ranking yields the same results as instantaneous signal power-based ranking, which is referred to as the accuracy probability. We characterize the probability of accuracy considering Nakagami-m fading channels and three different spatial distribution models of user locations in NOMA. We illustrate the impact of accuracy probability on uplink and downlink coverage probability.

Inference on the Gamma Distribution

Abstract: This study develops inferential procedures for a gamma distribution. Based on the Cornish–Fisher expansion and pivoting the cumulative distribution function, an approximate confidence interval for ...

Confidence intervals for a two-parameter exponential distribution: One- and two-sample problems

Abstract: The problems of interval estimating the mean, quantiles, and survival probability in a two-parameter exponential distribution are addressed. Distribution function of a pivotal quantity whose percen...

Survival analysis with time-dependent covariates subject to missing data or measurement error: Multiple Imputation for Joint Modeling (MIJM)

Abstract: Modern epidemiological studies collect data on time-varying individual-specific characteristics, such as body mass index and blood pressure. Incorporation of such time-dependent covariates in time-to-event models is of great interest, but raises some challenges. Of specific concern are measurement error, and the non-synchronous updating of covariates across individuals, due for example to missing data. It is well known that in the presence of either of these issues the last observation carried forward (LOCF) approach traditionally used leads to bias. Joint models of longitudinal and time-to-event outcomes, developed recently, address these complexities by specifying a model for the joint distribution of all processes and are commonly fitted by maximum likelihood or Bayesian approaches. However, the adequate specification of the full joint distribution can be a challenging modeling task, especially with multiple longitudinal markers. In fact, most available software packages are unable to handle more than one marker and offer a restricted choice of survival models. We propose a two-stage approach, Multiple Imputation for Joint Modeling (MIJM), to incorporate multiple time-dependent continuous covariates in the semi-parametric Cox and additive hazard models. Assuming a primary focus on the time-to-event model, the MIJM approach handles the joint distribution of the markers using multiple imputation by chained equations, a computationally convenient procedure that is widely available in mainstream statistical software. We developed an R package "survtd" that allows MIJM and other approaches in this manuscript to be applied easily, with just one call to its main function. A simulation study showed that MIJM performs well across a wide range of scenarios in terms of bias and coverage probability, particularly compared with LOCF, simpler two-stage approaches, and a Bayesian joint model. The Framingham Heart Study is used to illustrate the approach.

Statistical Inference for Online Learning and Stochastic Approximation via Hierarchical Incremental Gradient Descent.

Abstract: Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large However, despite an ever-increasing volume of work on SGD, much less is known about the statistical inferential properties of SGD-based predictions Taking a fully inferential viewpoint, this paper introduces a novel procedure termed HiGrad to conduct statistical inference for online learning, without incurring additional computational cost compared with SGD The HiGrad procedure begins by performing SGD updates for a while and then splits the single thread into several threads, and this procedure hierarchically operates in this fashion along each thread With predictions provided by multiple threads in place, a t-based confidence interval is constructed by decorrelating predictions using covariance structures given by the Ruppert--Polyak averaging scheme Under certain regularity conditions, the HiGrad confidence interval is shown to attain asymptotically exact coverage probability Finally, the performance of HiGrad is evaluated through extensive simulation studies and a real data example An R package higrad has been developed to implement the method

Coverage analysis of finite cellular networks: A stochastic geometry approach

Abstract: This paper develops a tractable modeling and analysis framework for finite cellular wireless networks using stochastic geometry. Defining finite homogeneous Poisson point processes to model the number and locations of access points in a confined region, we study the coverage probability for an arbitrarily-located reference user that is served by the closest access point. The distance distribution and the Laplace transform (LT) of the interference are derived. We also derive a closed-form lower bound on the LT of the interference. Our analyses reveal that a higher path loss exponent improves the coverage probability and that there is a location where the coverage probability is maximized.

Bivariate random-effects meta-analysis models for diagnostic test accuracy studies using arcsine-based transformations.

Abstract: Diagnostic or screening tests are widely used in medical fields to classify patients according to their disease status. Several statistical models for meta-analysis of diagnostic test accuracy studies have been developed to synthesize test sensitivity and specificity of a diagnostic test of interest. Because of the correlation between test sensitivity and specificity, modeling the two measures using a bivariate model is recommended. In this paper, we extend the current standard bivariate linear mixed model (LMM) by proposing two variance-stabilizing transformations: the arcsine square root and the Freeman-Tukey double arcsine transformation. We compared the performance of the proposed methods with the standard method through simulations using several performance measures. The simulation results showed that our proposed methods performed better than the standard LMM in terms of bias, root mean square error, and coverage probability in most of the scenarios, even when data were generated assuming the standard LMM. We also illustrated the methods using two real data sets.

Estimation of an overall standardized mean difference in random-effects meta-analysis if the distribution of random effects departs from normal.

Abstract: The random-effects model, applied in most meta-analyses nowadays, typically assumes normality of the distribution of the effect parameters. The purpose of this study was to examine the performance of various random-effects methods (standard method, Hartung's method, profile likelihood method, and bootstrapping) for computing an average effect size estimate and a confidence interval (CI) around it, when the normality assumption is not met. For comparison purposes, we also included the fixed-effect model. We manipulated a wide range of conditions, including conditions with some degree of departure from the normality assumption, using Monte Carlo simulation. To simulate realistic scenarios, we chose the manipulated conditions from a systematic review of meta-analyses on the effectiveness of psychological treatments. We compared the performance of the different methods in terms of bias and mean squared error of the average effect estimators, empirical coverage probability and width of the CIs, and variability of the standard errors. Our results suggest that random-effects methods are largely robust to departures from normality, with Hartung's profile likelihood methods yielding the best performance under suboptimal conditions.