Accurate Coverage Probabilities Research Articles

Towards automated animal density estimation with acoustic spatial capture-recapture.

Passive acoustic monitoring can be an effective way of monitoring wildlife populations that are acoustically active but difficult to survey visually, but identifying target species calls in recordings is non-trivial. Machine learning (ML) techniques can do detection quickly but may miss calls and produce false positives, i.e., misidentify calls from other sources as being from the target species. While abundance estimation methods can address the former issue effectively, methods to deal with false positives are under-investigated. We propose an acoustic spatial capture-recapture (ASCR) method that deals with false positives by treating species identity as a latent variable. Individual-level outputs from ML techniques are treated as random variables whose distributions depend on the latent identity. This gives rise to a mixture model likelihood that we maximize to estimate call density. We compare our method to existing methods by applying it to an ASCR survey of frogs and simulated acoustic surveys of gibbons based on real gibbon acoustic data. Estimates from our method are closer to ASCR applied to the dataset without false positives than those from a widely used false positive "correction factor" method. Simulations show our method to have bias close to zero and accurate coverage probabilities and to perform substantially better than ASCR without accounting for false positives.

Analyzing the influence of binary data clustering on relative risk within the context of inferential methods

In epidemiological cohort studies, the relative risk is a key measure to gauge the connection between two treatments or exposures. It quantifies the proportional change in the risk of disease due to the application of a specific treatment. However, the conventional methods for calculating relative risk, available in widely-used software, might yield inaccurate results when applied to correlated binary data from studies conducted over time or in clusters. Recently, various techniques have been proposed to estimate the risk ratio for correlated binary data. However, some methods exhibit a tradeoff between maintaining accurate coverage probability (CP) and ensuring an appropriate interval width or location. This paper introduces a new approach to confidently estimating the risk ratio using a hybrid method. This hybrid method combines two distinct confidence intervals (CIs) derived from single risk rates to establish a unified confidence interval for their ratio. Furthermore, we present a methodology to construct a confidence interval for the risk ratio, which builds upon established methods for correlated binary data. This extension incorporates principles such as the design effect and adequate sample sizes commonly used in representative sample surveys. An extensive simulation study is conducted to evaluate the effectiveness of these proposed methods. The performance of the methods is thoroughly examined in various scenarios. Additionally, the practicality of the proposed methods is showcased through three real-life examples. These examples involve comparing the side effects of low-dose tricyclic antidepressants with a placebo, assessing the efficacy of a treatment group in a teratological experiment, and evaluating the efficiency of active drugs in curing infections during clinical trials.

Computation of prediction intervals for forest aboveground biomass predictions using generalized linear models in a large-extent boreal forest region

Abstract Remotely sensed data have an important application for estimation of forest variables, e.g. height, volume, and aboveground biomass (AGB). The increased use of remotely sensed data implemented along with model-based inference has shown improved efficiency in prediction and mapping of such forest variables. In this study, plot-level airborne laser scanning data and Swedish National Forest Inventory field reference data were used to predict AGB using generalized linear models (GLMs) assuming Gamma and Tweedie distributions for the field observed AGB. The GLMs were selected considering the convenience of not correcting transformation bias as it is required in other regression models with transformed response variable. To overcome the challenge in providing reliable uncertainty estimates for the estimated forest variable map products at individual pixel-scale, we focused on computing 95% prediction intervals (PIs) for Gamma and Tweedie GLMs with a square root link function. The relative uncertainties were computed as the ratio between the half-width of the PIs and the predicted AGBs. The AGB-airborne laser scanning models were developed with root mean square error values of 22.6 Mgha−1 (26%) and 21.7 Mgha−1 (25%), respectively, for the Gamma and Tweedie GLMs. Two methods were applied to compute PIs for the Gamma GLM, one using the R package ‘ciTools’ and another derived through asymptotic theory. It was found that the 95% PIs computed using ‘ciTools’ had the most accurate coverage probability in comparison to the other method. An extended version of these PIs was also utilized for the Tweedie GLMs. The range of PIs associated with the prediction of AGB were narrower for lower predicted AGB values compared with the length of higher predicted AGB values. Comparing the two fitted models, the Gamma GLM showed lower relative uncertainties for the lower range of predicted AGBs, whereas the Tweedie GLM showed lower relative uncertainties for the higher range of predicted AGBs. Overall, the Tweedie GLM provided a better model fit for AGB predictions.

Conformal asymmetric multi-quantile generative transformer for day-ahead wind power interval prediction

With the rapid increase in the installed capacity of wind power, day-ahead wind power interval prediction is becoming more and more important. To solve such a challenging problem and provide intervals of higher quality, this paper proposes a prediction method based on conformal asymmetric multi-quantile generative transformer. Herein, the multi-quantile generative transformer is a deep learning model that generates multi-quantile forecast results for next day through one forward propagation process. Then, two quantiles, whose width is the smallest while satisfying the nominal confidence constraint, are selected from the predicted sequence as the upper bound and lower bound of the asymmetric interval. Furthermore, we introduce the conformal quantile regression to calibrate the bounds of the prediction interval to ensure that its coverage rate is as close as nominal confidence. The experiments show that the proposed method surpasses the benchmarks by providing narrower prediction intervals with more accurate empirical coverage probability. Under nominal confidence 90%, it gives prediction intervals with average empirical coverage probability of 90.50% and normalized average width of 0.44 on four wind farms. Compared with symmetric prediction intervals given by common benchmark quantile long short term memory network, the average width is reduced by 19.6%.

Objective Bayesian inference for the Capability index of the Weibull distribution and its generalization

The Weibull distribution plays an important role in reliability and quality control monitoring. This model has been widely used to describe the process capability index (PCI) when data do not follow a normal distribution. In this scenario, the current studies focus on estimating the parameters using classical inference. In this paper, we consider Bayesian methods to estimate the PCI denominated Cpk from an objective perspective using reference priors. The proposed inference is further extended to a generalized version of the Weibull distribution that provides a good fit for more complex data with non-monotone hazard behavior. The posterior distributions are constructed and Bayes estimators based on the median are proposed. In this case, Markov Chain Monte Carlo methods are used to achieve the estimates and from an extensive simulation study, we observe that good results are observed in terms of mean relative and squared errors. The proposed approach is also used to construct adequate credibility intervals with low computational cost and accurate coverage probabilities. A real data application is presented which confirms that our proposed approach outperforms the current methods.

Confidence interval localization of pipeline leakage via the bootstrap method

Much of the focus of transient-based pipeline leakage detection research has been on deterministic point estimation of leak location. This paper proposes a framework for extending deterministic leakage localization methods so that they can provide decision-makers with not only a point estimation of leak location, but also a confidence interval for the estimation. To address the complex nature of aleatoric uncertainties, a semi-parametric transient model is introduced and the empirical distribution of measurement is built via a limited number of transient tests. The stochastic characteristics of leakage localization are then explored by the bootstrap method. As a result, confidence intervals are constructed to predict the range of leak location. Experimental results demonstrate that the proposed method can localize the actual leak with an accurate coverage probability and satisfactorily match the ground-truth confidence intervals. In the considered scenario, the error of point localization is tolerable with seven transient tests only; with the same amount of data, the proposed bootstrap method provides additional information about the imprecision and uncertainty to the decision-making of pipeline maintenance.

Day-ahead probabilistic forecasting for French half-hourly electricity loads and quantiles for curve-to-curve regression

The probabilistic forecasting of electricity loads is crucial for effective scheduling and decision-making in volatile and competitive energy markets with ever-growing uncertainties. We propose a novel approach to construct the probabilistic predictors for curves (PPC) of electricity loads, which leads to properly defined predictive bands and quantiles in the context of curve-to-curve regression. The proposed predictive model provides not only accurate hourly load point forecasts, but also generates well-defined probabilistic bands and day-long trajectories of the loads at any probability level, pre-specified by managers. We also define the predictive quantile curves that exhibit future loads in extreme scenarios and provide insights for hedging risks in the supply management of electricity. When applied to the day-ahead forecasting for French half-hourly electricity loads, the PPC outperform several state-of-the-art time series and machine learning predictive methods with more accurate point forecasts (mean absolute percentage error of 1.10%, compared to 1.36%–4.88% for the alternatives), a higher coverage rate of the day-long trajectory of loads (coverage rate of 95.5%, against 31.9%–90.7% for the alternatives) and a narrower average length of the predictive bands. In a series of numerical experiments, the PPC further demonstrate robust performance and general applicability, achieving accurate coverage probabilities under a variety of data-generating mechanisms.

A statistical measure for the skewness of X chromosome inactivation for quantitative traits and its application to the MCTFR data

BackgroundX chromosome inactivation (XCI) is that one of two chromosomes in mammalian females is silenced during early development of embryos. There has been a statistical measure for the degree of the skewness of XCI for qualitative traits. However, no method is available for such task at quantitative trait loci.ResultsIn this article, we extend the existing statistical measure for the skewness of XCI for qualitative traits, and the likelihood ratio, Fieller’s and delta methods for constructing the corresponding confidence intervals, and make them accommodate quantitative traits. The proposed measure is a ratio of two linear regression coefficients when association exists. Noting that XCI may cause variance heterogeneity of the traits across different genotypes in females, we obtain the point estimate and confidence intervals of the measure by incorporating such information. The hypothesis testing of the proposed methods is also investigated. We conduct extensive simulation studies to assess the performance of the proposed methods. Simulation results demonstrate that the median of the point estimates of the measure is very close to the pre-specified true value. The likelihood ratio and Fieller’s methods control the size well, and have the similar test power and accurate coverage probability, which perform better than the delta method. So far, we are not aware of any association study for the X-chromosomal loci in the Minnesota Center for Twin and Family Research data. So, we apply our proposed methods to these data for their practical use and find that only the rs792959 locus, which is simultaneously associated with the illicit drug composite score and behavioral disinhibition composite score, may undergo XCI skewing. However, this needs to be confirmed by molecular genetics.ConclusionsWe recommend the Fieller’s method in practical use because it is a non-iterative procedure and has the similar performance to the likelihood ratio method.

Empirical likelihood meta-analysis with publication bias correction under Copas-like selection model

Meta-analysis is commonly used to synthesize multiple results from individual studies. However, its validation is usually threatened by publication bias and between-study heterogeneity, which can be captured by the Copas selection model. Existing inference methods under this model are all based on conditional likelihood and may not be fully efficient. In this paper, we propose a full likelihood approach to meta-analysis by integrating the conditional likelihood and a marginal semi-parametric empirical likelihood under a Copas-like selection model. We show that the maximum likelihood estimators (MLE) of all the underlying parameters have a jointly normal limiting distribution, and the full likelihood ratio follows an asymptotic central chi-square distribution. Our simulation results indicate that compared with the conditional likelihood method, the proposed MLEs have smaller mean squared errors and the full likelihood ratio confidence intervals have more accurate coverage probabilities. A real data example is analyzed to show the advantages of the full likelihood method over the conditional likelihood method.

Diagnostic test meta-analysis by empirical likelihood under a Copas-like selection model

The validation of diagnostic test meta-analysis is often threatened by publication bias, which can be commonly characterized by the Copas selection model. Under this model, conventional approaches to diagnostic meta-analysis are based on conditional likelihood. Since they may have efficiency loss, we propose a full likelihood diagnostic meta-analysis method by integrating the usual conditional likelihood and a marginal semi-parametric empirical likelihood. We show that the resulting maximum likelihood estimators (MLEs) have a jointly normal limiting distribution, and the resulting likelihood ratio follows a central chisquare limiting distribution. Our numerical studies indicate that the proposed MLEs often have smaller mean square errors than the conditional likelihood MLEs. The full likelihood ratio interval estimators generally have more accurate coverage probabilities than the conditional-likelihood-based Wald intervals. We re-study two real meta analyses on influenza and mental health respectively for illustration.

Modelling the Spread of COVID-19 in New York City

This paper proposes a methodology to predict the increase in the number of confirmed COVID-19 cases in the city of New York at the zip code level. We concentrate on the initial period of the pandemic spanning from March 31 to June 16, 2020. To do this, we propose a Poisson regression model for count data that includes a large set of covariates reflecting socioeconomic conditions at neighbourhood level and spatial effects. The sensitivity of the predictions of the number of cases to the specific choice of the regressors is controlled for by also considering an emsemble prediction model given by Bayesian model averaging. Our results extend related studies by showing that variables such as population size, its share of the elderly, the self-employment rate, income per capita, and the percentage of workers in the educational and healthcare sectors not only explain the cross-sectional variability in the number of new confirmed cases but also have out-of-sample predictive ability. Our pointwise forecasts display reasonable mean square prediction errors and the associated interval forecasts accurate empirical coverage probabilities suggesting the suitability of the methodology for prediction of the number of infections.

Empirical likelihood based on synthetic right censored data

In this paper, we develop a Mean Empirical Likelihood (MeanEL) method for right censored data. This MeanEL approach is based on traditional empirical likelihood methods but uses synthetic data to construct an EL ratio statistics, which is shown to have a χ2 limiting distribution. Different simulation studies show that the MeanEL confidence intervals tend to have more accurate coverage probabilities than other existing Empirical Likelihood methods. Theoretical comparisons of different EL methods are also provided under a general framework.

Maximum likelihood abundance estimation from capture-recapture data when covariates are missing at random.

In capture-recapture experiments, individual covariates may be subject to missingness, especially when the number of captures is small. When the covariate information is missing at random, the inverse probability weighting method and the multiple imputation method are widely used to obtain point estimators of the abundance. These estimators are then used to construct Wald-type confidence intervals. However, such intervals may have seriously inaccurate coverage probabilities. In this paper, we propose a maximum empirical likelihood (EL) estimation approach for the abundance in the presence of missing covariates. We show that the maximum EL estimator is asymptotically normal, and that the EL ratio statistic for the abundance has a chi-square limiting distribution with one degree of freedom. Simulations indicate that the proposed estimator has a smaller mean square error than existing estimators, and the proposed EL ratio confidence interval usually has more accurate coverage probabilities than the existing Wald-type confidence intervals. We illustrate the proposed method by analyzing data collected in Hong Kong for the yellow-bellied prinia, a birdspecies.

A Marginal Maximum Likelihood Approach for Extended Quadratic Structural Equation Modeling with Ordinal Data

ABSTRACT The literature on non-linear structural equation modeling is plentiful. Despite this fact, few studies consider interactions between exogenous and endogenous latent variables. Further, it is well known that treating ordinal data as continuous produces bias, a problem which is enhanced when non-linear relationships between latent variables are incorporated. A marginal maximum likelihood-based approach is proposed in order to fit a non-linear structural equation model including interactions between exogenous and endogenous latent variables in the presence of ordinal data. In this approach, the exact gradient of the approximated observed log-likelihood is calculated in order to attain the approximated maximum likelihood estimator. A simulation study shows that the proposed method provides estimates with low bias and accurate coverage probabilities.

Small area mean estimation after effect clustering

ABSTRACTProviding reliable estimates of subpopulation/area parameters has attracted increased attention due to their importance in applications such as policymaking. Due to low or even no samples from some areas, we must adopt indirect model approaches. Existing indirect small area estimation methods often assume that a single nested error regression model is suitable for all the small areas. In particular, the effects of the auxiliary variables are either fixed or have a single attraction center. In some applications, it can be more appropriate to cluster the small areas so that the effects of the auxiliary variables are fixed but have multiple centers in the nested error regression model. In this paper, we examine an extended nested error regression model in which the auxiliary variables have mixed effects with multiple centers. We use a penalty approach to identify these centers and estimate the model parameters simultaneously. We then propose two new small area mean estimators and construct estimators of their mean square errors. Simulations based on artificial and realistic finite populations show that the new estimators can be efficient. Furthermore, the confidence intervals based on the new methods have accurate coverage probabilities. We illustrate the proposed methods with the Survey of Labour and Income Dynamics conducted in Canada.

Confidence intervals for extreme Pareto‐type quantiles

AbstractIn this paper, we revisit the construction of confidence intervals for extreme quantiles of Pareto‐type distributions. A novel asymptotic pivotal quantity is proposed for these quantile estimators, which leads to new asymptotic confidence intervals that exhibit more accurate coverage probability. This pivotal quantity also allows for the construction of a saddle‐point approximation, from which a second set of new confidence intervals follows. The small‐sample properties and utility of these confidence intervals are studied using simulations and a case study from insurance.

A statistical measure for the skewness of X chromosome inactivation based on case-control design

BackgroundSkewed X chromosome inactivation (XCI), which is a non-random process, is frequently observed in both healthy and affected females. Furthermore, skewed XCI has been reported to be related to many X-linked diseases. However, no statistical method is available in the literature to measure the degree of the skewness of XCI for case-control design. Therefore, it is necessary to develop methods for such a task.ResultsIn this article, we first proposed a statistical measure for the degree of XCI skewing by using a case-control design, which is a ratio of two logistic regression coefficients after a simple reparameterization. Based on the point estimate of the ratio, we further developed three types of confidence intervals (the likelihood ratio, Fieller’s and delta methods) to evaluate its variation. Simulation results demonstrated that the likelihood ratio method and the Fieller’s method have more accurate coverage probability and more balanced tail errors than the delta method. We also applied these proposed methods to analyze the Graves’ disease data for their practical use and found that rs3827440 probably undergoes a skewed XCI pattern with 68.7% of cells in heterozygous females having the risk allele T active, while the other 31.3% of cells keeping the normal allele C active.ConclusionsFor practical application, we suggest using the Fieller’s method in large samples due to the non-iterative computation procedure and using the LR method otherwise for its robustness despite its slightly heavy computational burden.

A statistical measure for the skewness of X chromosome inactivation based on family trios

BackgroundX chromosome inactivation (XCI) is an important gene regulation mechanism in females to equalize the expression levels of X chromosome between two sexes. Generally, one of two X chromosomes in females is randomly chosen to be inactivated. Nonrandom XCI (XCI skewing) is also observed in females, which has been reported to play an important role in many X-linked diseases. However, there is no statistical measure available for the degree of the XCI skewing based on family data in population genetics.ResultsIn this article, we propose a statistical approach to measure the degree of the XCI skewing based on family trios, which is represented by a ratio of two genotypic relative risks in females. The point estimate of the ratio is obtained from the maximum likelihood estimates of two genotypic relative risks. When parental genotypes are missing in some family trios, the expectation-conditional-maximization algorithm is adopted to obtain the corresponding maximum likelihood estimates. Further, the confidence interval of the ratio is derived based on the likelihood ratio test. Simulation results show that the likelihood-based confidence interval has an accurate coverage probability under the situations considered. Also, we apply our proposed method to the rheumatoid arthritis data from USA for its practical use, and find out that a locus, rs2238907, may undergo the XCI skewing against the at-risk allele. But this needs to be further confirmed by molecular genetics.ConclusionsThe proposed statistical measure for the skewness of XCI is applicable to complete family trio data or family trio data with some paternal genotypes missing. The likelihood-based confidence interval has an accurate coverage probability under the situations considered. Therefore, our proposed statistical measure is generally recommended in practice for discovering the potential loci which undergo the XCI skewing.

Weighted empirical likelihood inference for dynamical correlations

A novel approach is proposed based on the weighted empirical likelihood to construct confidence intervals for dynamical correlation of random functions. The properties of the proposed confidence interval are investigated for random functions with regular or irregular observations. It is shown that the confidence interval using our new approach has a more accurate coverage probability than that using the traditional bootstrap method for random functions with irregular observations. Furthermore, simulation studies demonstrate that the new approach is considerably more efficient in computation than the bootstrap method. The new approach is illustrated with three applications. The first application investigates the dynamical correlation of air pollutants. The second application studies the dynamical correlation of EEG signals in different regions of the brain in response to some stimuli. The third application estimates the dynamical correlation of gene expressions during the activation of T-cells.

Downlink Coverage Analysis for a Finite 3D Wireless Network of Unmanned Aerial Vehicles

In this paper, we consider a finite network of unmanned aerial vehicles serving a given region. Modeling this network as a uniform binomial point process, we derive the downlink coverage probability of a reference receiver located at an arbitrary position on the ground assuming Nakagami- $m$ fading for all wireless links. The reference receiver is assumed to connect to its closest transmitting node as is usually the case in cellular systems. After deriving the distribution of distances from the reference receiver to the serving and interfering nodes, we derive an exact expression for downlink coverage probability in terms of the derivative of Laplace transform of interference power distribution. In the downlink of this system, it is not unusual to encounter scenarios in which the line-of-sight component is significantly stronger than the reflected multipath components. To emulate such scenarios, we also derive the coverage probability in the absence of fading from the results of Nakagami- $m$ fading by taking the limit $m \to \infty$ . Using asymptotic expansion of incomplete gamma function, we concretely show that this limit reduces to a redundant condition. Consequently, we derive an accurate coverage probability approximation for this case using dominant interferer-based approach in which the effect of dominant interferer is exactly captured and the residual interference from other interferers is carefully approximated. We then derive the bounds of the approximate coverage probability using Berry-Esseen theorem. Our analyses reveal several useful trends in coverage probability as a function of height of the transmitting nodes and the location of reference receiver on the ground.