Unbiased Estimates Research Articles

Compositing and regularization of drillhole data for geostatistical resource estimation

Compositing or regularization of drillhole data is common practice in mineral resource estimation and is deemed a necessary step in producing unbiased estimates of mineral resources and reserves. Commonly, data are collected over irregular distances due to the varying relative thicknesses of lithologies drilled or sampling/assaying strategies. This necessitates data transformation to regular lengths of equal size to ensure that all data have the same sample support. However, there have been few detailed publications on the effect of this process on the composited data that are subsequently taken forward for the estimation process. In this paper, three currently available compositing methods are reviewed and the effects of inappropriate compositing methodologies presented. It is shown through a case study that compositing samples to different lengths leads to changes in the average and variance of the grades in the drillcores in the dataset, which will impact the final estimated value. These differences are exacerbated by breaks or gaps in data where, for a variety of reasons, there has been no data collection or data have been lost. The importance of appropriately treating blank and zero data is also presented. Globally, these differences might be minimal, but locally may be substantial, affecting the efficiency of the estimation and subsequent use of the results in, for example, mine planning and reconciliation. Further detailed investigation of compositing practices is required if the full implications of compositing are to be understood and any induced bias effectively defined.

Hypothesis Testing for Progressive Kernel Estimation and VCM Framework.

Identifying an appropriate radius for unbiased kernel estimation is crucial for the efficiency of radiance estimation. However, determining both the radius and unbiasedness still faces big challenges. In this paper, we first propose a statistical model of photon samples and associated contributions for progressive kernel estimation, under which the kernel estimation is unbiased if the null hypothesis of this statistical model stands. Then, we present a method to decide whether to reject the null hypothesis about the statistical population (i.e., photon samples) by the F-test in the Analysis of Variance. Hereby, we implement a progressive photon mapping (PPM) algorithm, wherein the kernel radius is determined by this hypothesis test for unbiased radiance estimation. Second, we propose VCM+, a reinforcement of Vertex Connection and Merging (VCM), and derive its theoretically unbiased formulation. VCM+ combines hypothesis testing-based PPM with bidirectional path tracing (BDPT) via multiple importance sampling (MIS), wherein our kernel radius can leverage the contributions from PPM and BDPT. We test our new algorithms, improved PPM and VCM+, on diverse scenarios with different lighting settings. The experimental results demonstrate that our method can alleviate light leaks and visual blur artifacts of prior radiance estimate algorithms. We also evaluate the asymptotic performance of our approach and observe an overall improvement over the baseline in all testing scenarios.

Minimizing confounding in comparative observational studies with time-to-event outcomes: An extensive comparison of covariate balancing methods using Monte Carlo simulation.

Observational studies are frequently used in clinical research to estimate the effects of treatments or exposures on outcomes. To reduce the effects of confounding when estimating treatment effects, covariate balancing methods are frequently implemented. This study evaluated, using extensive Monte Carlo simulation, several methods of covariate balancing, and two methods for propensity score estimation, for estimating the average treatment effect on the treated using a hazard ratio from a Cox proportional hazards model. With respect to minimizing bias and maximizing accuracy (as measured by the mean square error) of the treatment effect, the average treatment effect on the treated weighting, fine stratification, and optimal full matching with a conventional logistic regression model for the propensity score performed best across all simulated conditions. Other methods performed well in specific circumstances, such as pair matching when sample sizes were large (n = 5000) and the proportion treated was < 0.25. Statistical power was generally higher for weighting methods than matching methods, and Type I error rates were at or below the nominal level for balancing methods with unbiased treatment effect estimates. There was also a decreasing effective sample size with an increasing number of strata, therefore for stratification-based weighting methods, it may be important to consider fewer strata. Generally, we recommend methods that performed well in our simulations, although the identification of methods that performed well is necessarily limited by the specific features of our simulation. The methods are illustrated using a real-world example comparing beta blockers and angiotensin-converting enzyme inhibitors among hypertensive patients at risk for incident stroke.

Efficacy and safety of macitentan in Fontan-palliated patients: 52-week randomized, placebo-controlled RUBATO Phase 3 trial and open-label extension

ObjectivesThe efficacy and safety of macitentan, an endothelin receptor antagonist, were assessed in a 52-week, prospective, multicenter, double-blind, randomized, placebo-controlled, parallel-group study assessing the efficacy and safety of macitentan in Fontan-palliated adult and adolescent patients (RUBATO-DB) and an open-label extension trial (RUBATO-OL). MethodsPatients aged 12 years and older with New York Heart Association functional class II or III underwent total cavopulmonary connection more than 1 year before screening and showed no signs of Fontan failure/clinical deterioration. In RUBATO-DB, the primary efficacy end point was change in peak oxygen consumption from baseline to week 16; secondary end points were change from baseline over 52 weeks in peak oxygen consumption and change in mean count/minute of daily physical activity via accelerometer from baseline to week 16. Safety was assessed throughout both studies. ResultsIn RUBATO-DB, 137 patients were randomized to macitentan 10 mg (n = 68) or placebo (n = 69); 92.7% completed 52-week double-blind treatment. At week 16, mean ± SD change in peak oxygen consumption was −0.16 ± 2.86 versus −0.67 ± 2.66 mL/kg/minute with macitentan versus placebo (median unbiased treatment difference estimate, 0.62 mL/kg/minute [99% repeated CI, −0.62 to 1.85]; P = .19). No treatment effect was observed in either of the secondary end points. During RUBATO-DB, most common adverse events with macitentan were headache, nasopharyngitis, and pyrexia. Across RUBATO-DB and RUBATO-OL, most common adverse events were COVID-19, headache, and fatigue. RUBATO-OL was prematurely discontinued because RUBATO-DB did not meet its primary or secondary end point. ConclusionsThe primary end point of RUBATO-DB was not met; macitentan did not improve exercise capacity versus placebo in patients with Fontan palliation. Macitentan was generally well tolerated over long-term treatment.

Addressing Endogeneity in Meta-Analysis: Instrumental Variable Based Meta-Analytic Structural Equation Modeling

In management research, meta-analysis is often used to aggregate findings from observational studies that lack random assignment to predictors (e.g., surveys), which may pose challenges in making accurate inferences due to the correlational nature of effect sizes. To improve inferential accuracy, we show how instrumental variable (IV) methods can be integrated into meta-analysis to help researchers obtain unbiased estimates. Our IV-based meta-analytic structural equation modeling (IV-MASEM) method relies on the fact that IVs can be incorporated into SEM, and meta-analytic effect sizes from correlational research can be used for MASEM. Conveniently, IV-MASEM does not require that each primary study measures all relevant variables, and it can address typical types of endogeneity, such as omitted variable bias. We clarify how the principles of IV-SEM can be applied to MASEM and then conduct three simulations to study the validity of IV-MASEM versus Univariate Meta-Analyses (UMA) and MASEMs that exclude IVs when the instruments were appropriate, inappropriate, and missing from a subset of primary studies. We also offer an illustrative study to demonstrate how to apply IV-MASEM to address endogeneity concerns in meta-analysis, which includes a new R function to test the qualifying conditions for IVs. We conclude with limitations and future directions for IV-MASEM.

Estimation of density functionals via cross‐validation

AbstractIn density estimation, the mean integrated squared error (MISE) is commonly used as a measure of performance. In that setting, the cross‐validation criterion provides an unbiased estimator of the MISE minus the integral of the squared density. Since the minimum MISE is known to converge to zero, this suggests that the minimum value of the cross‐validation criterion could be regarded as an estimator of minus the integrated squared density. This novel proposal presents the outstanding feature that, unlike all other existing estimators, it does not need the choice of any tuning parameter. Indeed, it is proved here that this approach results in a consistent and efficient estimator, with remarkable performance in practice. Moreover, apart from this base case, it is shown how several other problems on density functional estimation can be similarly handled using this new principle, thus demonstrating full potential for further applications.

A New Approach to Composite Estimation for Repeated Surveys with Rotating Panels

Composite estimation in repeated surveys with rotating panels refers to methods of estimation that exploit correlations in the data in the sample overlap between survey times to improve the precision of estimates. In this article a novel approach to composite estimation is proposed, in which composite regression estimators of current totals for a number of key variables are generated from a simultaneous calibration of the sampling weights of the overlapping samples of the current and previous survey time. In this procedure, in addition to the usual calibration to known population totals, differences of estimates for the key variables based on the full sample and the common sample from the two consecutive times are calibrated to each other. The resulting multivariate composite regression estimator, which is constructed as an approximate best linear unbiased estimator, incorporates effectively information from the samples of both survey times for enhanced estimation efficiency. Unlike other composite regression estimators, the proposed estimator does not require micro-matching of data in the overlap sample, and, therefore, is free of potential issues associated with it. It is also considerably more practical than existing composite regression estimators and the traditional AK-composite estimator.

On the efficiency of misspecified Gaussian inference in nonlinear regression: Application to time-delay and Doppler estimation

Nonlinear regression plays a crucial role in various engineering applications. For the sake of mathematical tractability and ease of implementation, most of the existing inference procedures are derived under the assumption of independent and identically distributed (i.i.d.) Gaussian-distributed data. However, real-world situations often deviate from this assumption, with the true data generating process being a correlated, heavy-tailed and non-Gaussian one. The paper aims at providing the Misspecified Cramér–Rao Bound (MCRB) on the Mean Squared Error (MSE) of any unbiased (in a proper sense) estimator of the parameters of a nonlinear regression model derived under the i.i.d. Gaussian assumption in the place of the actual correlated, non-Gaussian data generating process. As a special case, the MCRB for an uncorrelated, i.i.d. Complex Elliptically Symmetric (CES) data generating process under Gaussian assumption is also provided. Consistency and asymptotic normality of the related Mismatched Maximum Likelihood Estimator (MMLE) will be discussed along with its connection with the Nonlinear Least Square Estimator (NLLSE) inherent to the nonlinear regression model. Finally, the derived theoretical findings will be applied in the well-known problem of time-delay and Doppler estimation for GNSS.

Statistical inference from partially nominated sets: An application to estimating the prevalence of osteoporosis among adult women

This paper focuses on drawing statistical inference based on a novel variant of maxima or minima nomination sampling (NS) designs. These sampling designs are useful for obtaining more representative sample units from the tails of the population distribution using the available auxiliary ranking information. However, one common difficulty in performing NS in practice is that the researcher cannot obtain a nominated sample unless he/she uniquely determines the sample unit with the highest or the lowest rank in each set. To overcome this problem, a variant of NS, which is called partial nomination sampling, is proposed, in which the researcher is allowed to declare that two or more units are tied in the ranks whenever he/she cannot find the sample unit with the highest or the lowest rank. Based on this sampling design, two asymptotically unbiased estimators are developed for the cumulative distribution function, which is obtained using maximum likelihood and moment-based approaches, and their asymptotic normalities are proved. Several numerical studies have shown that the proposed estimators have higher relative efficiencies than their counterparts in simple random sampling in analyzing either the upper or the lower tail of the parent distribution. The procedures that we developed are then implemented on a real dataset from the Third National Health and Nutrition Examination Survey (NHANES III) to estimate the prevalence of osteoporosis among adult women aged 50 and over. It is shown that in certain circumstances, the techniques that we have developed require only one-third of the sample size needed in SRS to achieve the desired precision. This results in a considerable reduction in time and cost compared to the standard SRS method.

Improved estimation of the sensitive proportion using a new randomization technique and the Horvitz–Thompson type estimator

Randomized response techniques efficiently collect data on sensitive subjects to protect individual privacy. This paper aims to introduce a new randomizing technique in the additive scrambled model so that privacy is well preserved and the estimator's efficiency for the sensitive population proportion is improved. Also, a Horvitz–Thompson type estimator is presented as an unbiased estimator of the sensitive proportion of the population, then convergence to the normal distribution for the Horvitz–Thompson type estimator is considered by the entropy of the inclusion indicators in the Poisson sampling. Eventually, using the new additive scrambled model, the ratio of taking addictive drugs is estimated among students of the University.

Classical and Bayesian estimations of performance measures in G e o / G e o / 1 queue

. In this article, we consider an early arrival G e o / G e o / 1 queue from the statistical perspective. The estimations of parameters and system performances under Classical and Bayesian frameworks are considered. Based on queue length data, we attempt to study the uniform minimum-variance unbiased estimators (UMVUEs) and the closed Bayesian estimators for various queueing characteristics. We compare their properties using Monte Carlo (MC) simulations. As a comparison and improvement, based on arrival and departure data over a period, we use a Bivariate Beta distribution as joint prior, and solve the performance estimators using the properties of Gaussian hypergeometric function. We derive Bayesian estimators and conduct numerical simulations using Markov Chain Monte Carlo (MCMC) method.

Osteological age-at-death estimation in an archaeological sample avoiding age-mimicry: a six-step approach

In human osteoarchaeology, individual age-at-death is traditionally assigned by scoring characteristic expressions of specific traits and applying formulas or algorithms. However, it is well known that the resulting age estimates in target samples suffer from bias due to the effect of age-mimicry, both at the individual and at the population level. A general statistical methodology to obtain unbiased estimates of the age-at-death distribution in skeletal samples has been available for more than two decades. Even so, the procedure is rarely used. This may be related to the fact that this methodology requires external input which has selection of distributional characteristics to be reported. In this paper, we translate the general methodology into a clearly stated six-step procedure to be followed. We illustrate the six steps using an archaeological sample of 675 adult individuals and 15 scoring methods from traditional age-estimation procedures. By clearly identifying the actions that are necessary for its application we intend to make the approach more accessible for osteoarchaeologists while at the same time highlighting some challenges that need to be addressed in the future. Our study demonstrates that the approach is feasible and illustrates the absence of age-mimicry. A combined analysis of five informative traits allowed to obtain estimates of several characteristics of the target sample age distribution. However, its routine use will benefit from improved input from relevant reference samples and improved statistical software.

A Fast Survival Support Vector Regression Approach to Large Scale Credit Scoring via Safe Screening.

Survival models have found wider and wider applications in credit scoring recently due to their ability to estimate the dynamics of risk over time. In this research, we propose a Buckley-James safe sample screening support vector regression (BJS4VR) algorithm to model large-scale survival data by combing the Buckley-James transformation and support vector regression. Different from previous support vector regression survival models, censored samples here are imputed using a censoring unbiased Buckley-James estimator. Safe sample screening is then applied to discard samples that guaranteed to be non-active at the final optimal solution from the original data to improve efficiency. Experimental results on the large-scale real lending club loan data have shown that the proposed BJS4VR model outperforms existing popular survival models such as RSFM, CoxRidge and CoxBoost in terms of both prediction accuracy and time efficiency. Important variables highly correlated with credit risk are also identified with the proposed method.

Feature engineering and parameter tuning: improving phenomic prediction ability in multi-environmental durum wheat breeding trials

Key Message Optimized phenomic selection in durum wheat uses near-infrared spectra, feature engineering and parameter tuning. Our study reports improvements in predictive ability and emphasizes customized preprocessing for different traits and models.The success of plant breeding programs depends on efficient selection decisions. Phenomic selection has been proposed as a tool to predict phenotype performance based on near-infrared spectra (NIRS) to support selection decisions. In this study, we test the performance of phenomic selection in multi-environmental trials from our durum wheat breeding program for three breeding scenarios and use feature engineering as well as parameter tuning to improve the phenomic prediction ability. In addition, we investigate the influence of genotype and environment on the phenomic prediction ability for agronomic and quality traits. Preprocessing, based on a grid search over the Savitzky–Golay filter parameters based on 756,000 genotype best linear unbiased estimate (BLUE) computations, improved the phenomic prediction ability by up to 1500% (0.02–0.3). Furthermore, we show that preprocessing should be optimized depending on the dataset, trait, and model used for prediction. The phenomic prediction scenarios in our durum breeding program resulted in low-to-moderate prediction abilities with the highest and most stable prediction results when predicting new genotypes in the same environment as used for model training. This is consistent with the finding that NIRS capture both the genotype and genotype-by-environment (G×E)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(G\ imes E)$$\\end{document} interaction variance.

Stylized Rendering as a Function of Expectation

We propose a generalization of the rendering equation that captures both the realistic light transport of physically-based rendering (PBR) and a subset of non-photorealistic rendering (NPR) stylizations in a principled manner. The proposed formulation is based on the key observation that both classical transport and certain NPR stylizations can be modeled as a function of expectation. Given this observation, we generalize the recursive integrals of the rendering equation to recursive functions of expectation. As estimating functions of expectation can be challenging, especially recursive ones, we provide a toolkit for unbiased and biased estimation comprising prior work, general strategies, and a novel build-your-own strategy for constructing more complex unbiased estimators from simpler unbiased estimators. We then use this toolkit to construct a complete estimator for the proposed recursive formulation, and implement a sampling algorithm that is both conceptually simple and leverages many of the components of an ordinary path tracer. To demonstrate the practicality of the proposed method we showcase how it captures several existing stylizations like color mapping, cel shading, and cross-hatching, fuses NPR and PBR visuals, and allows us to explore visuals that were previously challenging under existing formulations.

Proxy Tracing: Unbiased Reciprocal Estimation for Optimized Sampling in BDPT

Robust light transport algorithms, particularly bidirectional path tracing (BDPT), face significant challenges when dealing with specular or highly glossy involved paths. BDPT constructs the full path by connecting sub-paths traced individually from the light source and camera. However, it remains difficult to sample by connecting vertices on specular and glossy surfaces with narrow-lobed BSDF, as it poses severe constraints on sampling in the feasible direction. To address this issue, we propose a novel approach, called proxy sampling , that enables efficient sub-path connection of these challenging paths. When a low-contribution specular/glossy connection occurs, we drop out the problematic neighboring vertex next to this specular/glossy vertex from the original path, then retrace an alternative sub-path as a proxy to complement this incomplete path. This newly constructed complete path ensures that the connection adheres to the constraint of the narrow lobe within the BSDF of the specular/glossy surface. Unbiased reciprocal estimation is the key to our method to obtain a probability density function (PDF) reciprocal to ensure unbiased rendering. We derive the reciprocal estimation method and provide an efficiency-optimized setting for efficient sampling and connection. Our method provides a robust tool for substituting problematic paths with favorable alternatives while ensuring unbiasedness. We validate this approach in the probabilistic connections BDPT for addressing specular-involved difficult paths. Experimental results have proved the effectiveness and efficiency of our approach, showcasing high-performance rendering capabilities across diverse settings.

Evaluation of different estimator approaches based on COVID-19 data and a simulation study

Sampling is crucial in basic statistics due to the large size of certain populations. Sampling theory focuses on selecting samples based on appropriate population characteristics and approaches to estimating population characteristics from the sample. Firstly, we use the ratio-type estimator proposed by Prasad (1989). We adapt this unbiased ratio-type estimator to two new different estimators using the Hartley-Ross and non-response approaches. Finally, we combine these approaches and propose a new estimator. The theoretical results were supported by COVID-19 data and a simulation study with various scenarios. Based on the COVID-19 data result, it was concluded that the new tN3 estimator is the most effective estimator among those proposed and compared, with the minimum MSE and maximum PRE. Upon examining the changes in the COVID-19 data set in detail, it is evident that the PRE value increases with an increase in sample size, non-response rate, and k values. As in the COVID-19 dataset, the tN3 estimator was the most effective in the simulation study results. It is also important to note that these results are not applicable to only one scenario in simulation study. The tN2 estimator was the most effective in the scenario with rho=0.90, T=1000, n=400, non-response rate=0.30 and k equal to 2, 4 and 5.

Comparing camera‐based ungulate density estimates: a case study using island populations of bighorn sheep and mule deer

AbstractCamera‐based abundance estimators are an alternative methodology of growing interest in both research and management applications. The statistical formulations of camera‐based abundance estimators using time‐lapse data should theoretically produce precise and unbiased estimates; however, production of unbiased results also requires meeting several important assumptions, and real‐world case studies evaluating such results remain relatively few. We applied instantaneous sampling (IS) and space‐to‐event (STE) estimators to remote camera data collected in April 2021 via time‐lapse sampling of closed populations of bighorn sheep (Ovis canadensis) and mule deer (Odocoileus hemionus) on Wild Horse Island in western Montana, USA, and compared results for bighorn sheep to aerial and ground‐based counts. Point estimates from camera‐based approaches underestimated bighorn sheep populations by 32–44% (IS estimator) and 62–69% (STE estimator) relative to aerial and ground counts. Patchy spatial distribution and group‐living behavior of sheep resulted in a high degree of noise surrounding the IS estimate. In comparison, a low point estimate with relatively narrow confidence intervals suggested potential sensitivity of the STE estimator to violating assumptions of independence among individual animals and sampling occasions. Estimates of mule deer had improved precision over sheep estimates, as indicated by lower estimated coefficients of variation of the mean (CVmean) derived from the analytic SE estimator. Using 15‐m viewsheds and the IS estimators, mule deer density estimates came with a 26% CVmean compared to 43% CVmean for bighorn sheep. This discrepancy may be a result of differences in distribution, behavior, and relative abundance between the 2 species. Accounting for group size and increasing time between sampling may improve accuracy of density estimates and adhere better to model assumptions when estimating precision. In addition, factors influencing viewshed and resulting density extrapolations must be considered carefully. While camera‐based methods theoretically provide an alternative way to estimate density when traditional methods are impractical, our results suggest that more work is needed to ensure density estimates are accurate and precise enough to inform population management.

Stochastically accelerated perturbative triples correction in coupled cluster calculations.

We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster framework. By combining elements of randomness and determinism, our algorithm achieves a favorable balance between accuracy and computational cost. The main advantage of this algorithm is that it allows for the calculation to be stopped at any time, providing an unbiased estimate, with a statistical error that goes to zero as the exact calculation is approached. We provide evidence that our semi-stochastic algorithm achieves substantial computational savings compared to traditional deterministic methods. Specifically, we demonstrate that a precision of 0.5 millihartree can be attained with only 10% of the computational effort required by the full calculation. This work opens up new avenues for efficient and accurate computations, enabling investigations of complex molecular systems that were previously computationally prohibitive.

Latent Interaction Effect in the CLPM Model: A Two-Step Multiple Imputation Analysis

This study aims to estimate the latent interaction effect in the CLPM model through a two-step multiple imputation analysis. The estimation of within × within and between × within latent interaction under the CLPM model framework is compared between the one-step Bayesian LMS method and the two-step multiple imputation analysis through a simulation study. The analysis show that the two-step multiple imputation analysis can provide unbiased estimation parameter, similar to the one-step Bayesian LMS method. This study also uses self-esteem and depression data from NLSY79 to perform a two-step multiple imputation analysis of the CLPM model, as well as an empirical example of latent interaction analysis. Mplus syntax is provided for researchers’ reference.