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Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure of a group sequential design is constructed with support for all possible outcome events, as is useful for designing an experiment prior to having data. This construction identifies impossible events that are not part of the support. The overall probability distribution is dissected into stage specific components. These components are sub-densities of interim test statistics first described by Armitage, McPherson and Rowe (1969) that are commonly used to create stopping boundaries given an $\alpha$-spending function and a set of interim analysis times. Likelihood expressions conditional on reaching a stage are given to connect pieces of the probability anatomy together. The reduction of the support caused by the adoption of an early stopping rule induces sequential truncation (not nesting) in the probability distributions of possible events. Multiple testing induces mixtures on the adapted support. Even asymptotic distributions of inferential statistics are mixtures of truncated distributions. In contrast to the classical result on local asymptotic normality (Le Cam 1960), statistics that are asymptotically normal without stopping options have asymptotic distributions that are mixtures of truncated normal distributions under local alternatives with stopping options; under fixed alternatives, asymptotic distributions of test statistics are degenerate., Comment: 23 pages

As one of the earliest crucial applications of Bayesian statistics, credibility theory (see Buhlmann and Gisler, 2006) was first developed for net premium calibration in insurance by optimally combining individual claim history with other claim histories from the whole population; for a century, this research direction has become a major discipline in the interplay among actuarial science, operational research and statistics. Traditionally, for the ease of calibration, the credibility formula is a linear functional of historical observations, which greatly simplifies the underlying computational complexity; yet, its downside is the resulting high sensitivity towards outliers. To remedy this shortcoming, De Vylder (1976) proposed to first transform the observations collected by truncation in particular, and this semi-linear approach was further investigated in Buhlmann & Gisler (2006) . Gisler (1980) suggested that the L 2 -optimal truncation point can be determined in an ad hoc manner, but the derivation of its general explicit formula is difficult. In our present work, to strike a balance between practical usage and mathematical tractability, we focus on heterogeneous risks all coming from possibly different maximum domain of attractions of the extreme value distributions, which well suffices in practice. By incorporating the satisficing method commonly used in operational research, we close the gap by providing the explicit formula for the aforementioned optimal truncation point up to a slowly varying function of the sample size in an asymptotic sense. A comprehensive numerical study also illuminates that with the aid of this newly obtained truncation point, the corresponding semi-linear credibility formula outperforms the classical Buhlmann model.

Human failure event (HFE) dependency analysis is a part of human reliability analysis (HRA). For efficient HFE dependency analysis, a maximum number of minimal cut sets (MCSs) that have HFE combinations are generated from the fault trees for the probabilistic safety assessment (PSA) of nuclear power plants (NPPs). After collecting potential HFE combinations, dependency levels of subsequent HFEs on the preceding HFEs in each MCS are analyzed and assigned as conditional probabilities. Then, HFE recovery is performed to reflect these conditional probabilities in MCSs by modifying MCSs. Inappropriate HFE dependency analysis and HFE recovery might lead to an inaccurate core damage frequency (CDF). Using the above process, HFE recovery is performed on MCSs that are generated with a non-zero truncation limit, where many MCSs that have HFE combinations are truncated. As a result, the resultant CDF might be underestimated. In this paper, a new method is suggested to incorporate HFE recovery into the MCS generation stage. Compared to the current approach with a separate HFE recovery after MCS generation, this new method can (1) reduce the total time and burden for MCS generation and HFE recovery, (2) prevent the truncation of MCSs that have dependent HFEs, and (3) avoid CDF underestimation. This new method is a simple but very effective means of performing MCS generation and HFE recovery simultaneously and improving CDF accuracy. The effectiveness and strength of the new method are clearly demonstrated and discussed with fault trees and HFE combinations that have joint probabilities.

The combined use of deuterium and tritium to determine travel time distributions (TTDs) in streams is an important development in catchment hydrology (Rodriguez et al, 2021). This comment takes issue with Rodriguez et al.'s general rejection of the truncation hypothesis, i.e. that the almost exclusive use of stable isotopes has truncated our vision of streamflow TTDs and caused us to miss the long tails of old water often shown by tritium. We discuss reasons why this hypothesis may not hold for the catchment described by Rodriguez et al. (2021), but could still apply to a large proportion of all catchments. We also discuss more generally future applications of tritium in northern and southern hemisphere catchments.

The Finite-Difference Method (FDM) despite being old and simple is not being used as rigorously as its counterpart Finite Element Method (FEM) for solving partial differential equations. This study aims to examine and improve the accuracy of FDM by eliminating significant sources of error. Since an expression for exact potential from the most accurate Method of Moment (MoM) is available in 3-D electrostatics, the classical form of Poisson equation is chosen for this study such that the error due to boundary conditions can be eliminated. The error due to the source term in the Poisson equation is studied with a single source and different grid densities by applying FDM in 3-D. Since the error is only present in the immediate surroundings of the source, a Distributed Source Scheme (DSS) has been proposed to reduce error due to the source term. A modified DSS i.e., Truncated Distributed Source Scheme (TDSS) is applied for the practical implementation of DSS. The maximum error in FDM when the source term is present has been reduced from 8.151% to 0.00091% with DSS. With the application of TDSS, it is shown that the maximum error can be maintained well below 0.1% for truncation values n > 15. The error due to source at off-center and off-grid positions was computed using TDSS and the maximum error is observed to be less than 0.05% and 0.01%, respectively. With off-grid error being low due to TDSS, it is shown that sources in TDSS can now take any position irrespective of grid nodes, which is forbidden in FDM with an average maximum error of 0.026%. It is also shown that DSS can also be used to find the charge distribution for a given potential distribution. While still maintaining the simplicity, improved accuracy and unrestricted source positions are achieved in FDM with exact boundary conditions using DSS.

Purpose To introduce a study design and statistical analysis framework to assess the repeatability, reproducibility, and minimal detectable changes (MDCs) of metabolite concentrations determined by in vivo MRS. Methods An unbalanced nested study design was chosen to acquire in vivo MRS data within different repeatability and reproducibility scenarios. A spin-echo, full-intensity acquired localized (SPECIAL) sequence was employed at 7 T utlizing three different inversion pulses: a hyperbolic secant (HS), a gradient offset independent adiabaticity (GOIA), and a wideband, uniform rate, smooth truncation (WURST) pulse. Metabolite concentrations, Cramer-Rao lower bounds (CRLBs) and coefficients of variation (CVs) were calculated. Both Bland-Altman analysis and a restricted maximum-likelihood estimation (REML) analysis were performed to estimate the different variance contributions of the repeatability and reproducibility of the measured concentration. A Bland-Altmann analysis of the spectral shape was performed to assess the variance of the spectral shape, independent of quantification model influences. Results For the used setup, minimal detectable changes of brain metabolite concentrations were found to be between 0.40 µmol/g and 2.23 µmol/g. CRLBs account for only 16 % to 74 % of the total variance of the metabolite concentrations. The application of gradient-modulated inversion pulses in SPECIAL led to slightly improved repeatability, but overall reproducibility appeared to be limited by differences in positioning, calibration, and other day-to-day variations throughout different sessions. Conclusion A framework is introduced to estimate the precision of metabolite concentrations obtained by MRS in vivo, and the minimal detectable changes for 13 metabolite concentrations measured at 7 T using SPECIAL are obtained.

Data truncation is a common problem in computed tomography (CT). Truncation causes cupping artifacts inside the field-of-view (FOV) and anatomical structures missing outside the FOV. Deep learning has achieved impressive results in CT reconstruction from limited data. However, its robustness is still a concern for clinical applications. Although the image quality of learning-based compensation schemes may be inadequate for clinical diagnosis, they can provide prior information for more accurate extrapolation than conventional heuristic extrapolation methods. With extrapolated projection, a conventional image reconstruction algorithm can be applied to obtain a final reconstruction. In this work, a general plug-and-play (PnP) method for truncation correction is proposed based on this idea, where various deep learning methods and conventional reconstruction algorithms can be plugged in. Such a PnP method integrates data consistency for measured data and learned prior image information for truncated data. This shows to have better robustness and interpretability than deep learning only. To demonstrate the efficacy of the proposed PnP method, two state-of-the-art deep learning methods, FBPConvNet and Pix2pixGAN, are investigated for truncation correction in cone-beam CT in noise-free and noisy cases. Their robustness is evaluated by showing false negative and false positive lesion cases. With our proposed PnP method, false lesion structures are corrected for both deep learning methods. For FBPConvNet, the root-mean-square error (RMSE) inside the FOV can be improved from 92HU to around 30HU by PnP in the noisy case. Pix2pixGAN solely achieves better image quality than FBPConvNet solely for truncation correction in general. PnP further improves the RMSE inside the FOV from 42HU to around 27HU for Pix2pixGAN. The efficacy of PnP is also demonstrated on real clinical head data.

Truncated singular value decomposition is a reduced version of the singular value decomposition in which only a few largest singular values are retained. This paper presents a novel perturbation analysis for the truncated singular value decomposition for real matrices. First, we describe perturbation expansions for the singular value truncation of order $r$. We extend perturbation results for the singular subspace decomposition to derive the first-order perturbation expansion of the truncated operator about a matrix with rank greater than or equal to $r$. Observing that the first-order expansion can be greatly simplified when the matrix has exact rank $r$, we further show that the singular value truncation admits a simple second-order perturbation expansion about a rank-$r$ matrix. Second, we introduce the first-known error bound on the linear approximation of the truncated singular value decomposition of a perturbed rank-$r$ matrix. Our bound only depends on the least singular value of the unperturbed matrix and the norm of the perturbation matrix. Intriguingly, while the singular subspaces are known to be extremely sensitive to additive noises, the newly established error bound holds universally for perturbations with arbitrary magnitude. Finally, we demonstrate an application of our results to the analysis of the mean squared error associated with the TSVD-based matrix denoising solution., Comment: Accepted to Linear Algebra and Its Applications

Cross-population applicability of osteological and dental methods is a known issue in forensic anthropology, but very little is known about whether differences between populations are due to ancestry, environment effects, or even the statistical approach utilized for developing the methods. This study wishes to add to the discussion of population-specificity of dental age estimation methods and examine the impact of their statistical basis on their accuracy and precision. These parameters were estimated by testing 12 different dental age estimation techniques on a sample of 182 panoramic radiographs of children between the ages of 6 and 15 years (110 girls and 72 boys) from the city of Merida in Yucatan, Mexico. None of the 12 methods selected is based on Mexican samples. Dental maturation was scored following and methods tested employed two dental scoring schemes: Moorrees, Fanning, and Hunt’s (MFH) 13-/14-stage system and Demirjian’s 8-stage system. Results show that methods derived from more geographically specific groups do not fare better or worse than methods developed on more diverse and inclusive international samples, even if no methods specific to Mexicans were tested. While some of the methods performed very well, and they were not based on a Mexican sample, this suggests that population-specific dental age estimation methods may be relatively unimportant or that population differences in dental maturation are very small. Other issues seemed to have a greater impact on accuracy and precision, such as age dependency, inclusion of the third molar in age assessments, age truncation and age heaping in reference samples, the dental scoring scheme used, and how predicted age is calculated mathematically. As such, findings in this study suggest that validation tests of age estimation methods may not be a useful or reliable means to assess population differences and that these differences need to be more systematically assessed if an argument is to be made for the increased accuracy and precision of population-specific methods. The statistical basis of dental prediction methods seems to have a more significant role in their accuracy and precision outside of their reference sample.

Background The 2021 NIJ recidivism forecasting challenge asks participants to construct predictive models of recidivism while balancing false positive rates across groups of Black and white individuals through a multiplicative fairness score. We investigate the performance of several models for forecasting 1-year recidivism and optimizing the NIJ multiplicative fairness metric. Methods We consider standard linear and logistic regression, a penalized regression that optimizes a convex surrogate loss (that we show has an analytical solution), two post-processing techniques, linear regression with re-balanced data, a black-box general purpose optimizer applied directly to the NIJ metric and a gradient boosting machine learning approach. Results For the set of models investigated, we find that a simple heuristic of truncating scores at the decision threshold (thus predicting no recidivism across the data) yields as good or better NIJ fairness scores on held out data compared to other, more sophisticated approaches. We also find that when the cutoff is further away from the base rate of recidivism, as is the case in the competition where the base rate is 0.29 and the cutoff is 0.5, then simply optimizing the mean square error gives nearly optimal NIJ fairness metric solutions. Conclusions The multiplicative metric in the 2021 NIJ recidivism forecasting competition encourages solutions that simply optimize MSE and/or use truncation, therefore yielding trivial solutions that forecast no one will recidivate.

Uncovering hidden mixture dependencies among variables has been investigated in the literature using mixture R-vine copula models. They provide considerable flexibility for modeling multivariate data. As the dimensions increase, the number of the model parameters that need to be estimated is increased dramatically, which comes along with massive computational times and efforts. This situation becomes even much more complex and complicated in the regular vine copula mixture models. Incorporating the truncation method with a mixture of regular vine models will reduce the computation difficulty for the mixture-based models. In this paper, the tree-by-tree estimation mixture model is joined with the truncation method to reduce computational time and the number of parameters that need to be estimated in the mixture vine copula models. A simulation study and real data applications illustrated the performance of the method. In addition, the real data applications show the effect of the mixture components on the truncation level.

We consider density deconvolution with zero-mean Laplace noise in the context of an error component regression model. We adapt the minimax deconvolution methods of Meister (2006) to allow estimation of the unknown noise variance. We propose a semi-uniformly consistent estimator for an ordinary-smooth target density and a modified "variance truncation device” for the unknown noise variance. We provide a simulation study and practical guidance for the choice of smoothness parameters of the ordinary-smooth target density. We apply restricted versions of our estimator to a stochastic frontier model of US banks and to a measurement error model of daily saturated fat intake.

Weighted scoring rules, perhaps the most common procedures for multi-candidate, single-winner elections, are defined by score vectors, of which the Borda Count is the best known example. The concept of Borda dominance identifies candidates who cannot win under any score vector; we assess its usefulness in the context of single-winner elections. We propose several families of score vectors that can accommodate any number of candidates, asking whether any of them can improve on Borda Count. Using large-scale simulation, we compare score vectors on Condorcet efficiency, or ability to find a Condorcet winner when one exists, on resilience to ballot truncation, and on ability to maximize the Copeland score using both complete and uniformly truncated ballots. Borda performs well on criteria related to Condorcet winner and Copeland score but, depending on the preference model, may not be optimal. Convex score vectors are the most resilient to ballot truncation.

The linearity of the distribution of city sizes is often assumed in the existing literature. Although different functional forms were tried, almost all of them impose a certain functional shape. In this study, we investigate the urban hierarchy and Zipf’s law using data for 973 Turkish subprovincial cities in 2019. We contribute to the literature in several ways. We force no definite functional form to observe the natural shape and employ nonparametric and quadratic regressions. We incorporate formal procedures of spatial dependence in regression models. We demonstrate that the linear model overestimates the Pareto exponent for small cities and underestimates it for bigger cities. We show that city sizes are unevenly distributed in Turkey. The rank–size rule is not valid in Turkey, either above or below a certain city‐size truncation level. Thus, the Pareto exponent estimated from the linear model is not a reliable indicator as quadratic regressions perform much better.

We study a selective sampling scheme in which survival data are observed during a data collection period if and only if a specific failure event is experienced. Individual units belong to one of a finite number of subpopulations, which may exhibit different survival behaviour, and thus cause heterogeneity. Based on a Poisson process model for individual emergence of population units, we derive a semiparametric likelihood model, in which the birth distribution is modeled nonparametrically and the lifetime distributions parametrically, and define maximum likelihood estimators. We propose a Newton–Raphson-type optimization method to address numerical challenges caused by the high-dimensional parameter space. The finite-sample properties and computational performance of the proposed algorithms are assessed in a simulation study. Personal insolvencies are studied as a special case of double truncation and we fit the semiparametric model to a medium-sized dataset to estimate the mean age at insolvency and the birth distribution of the underlying population.

In recent literature, a new class of unbiased Monte Carlo estimators have been proposed, which is based on truncating a telescopic representation of the expectation of a functional of the stochastic process at an independent random level. The generality of the method lies in that it can translate any sequence of asymptotically unbiased estimators into a truly unbiased estimator. However, since any independent truncation level can lead to an unbiased estimator, its optimal choice is crucial for the successful implementation of this unbiased Monte Carlo method in financial engineering applications. We develop a novel efficient algorithm to locate the optimal distribution of the random truncation level in general, which answers positively an open question posted in Rhee and Glynn (2015), and we rigorously establish the convergence and optimality of the algorithm and derive its exact complexity. Our algorithm has a much lower complexity as compared to the literature, and numerical examples confirm our findings. The proposed algorithm is shown to be also applicable to optimization problems arising in contextual areas of supply chain management.

This paper describes the design and synthesis of Strathclyde minor groove binders (S-MGBs) that have been truncated by the removal of a pyrrole ring in order to mimic the structure of the natural product, disgocidine. S-MGBs have been found to be active against many different organisms, however, selective antiparasitic activity is required. A panel of seven truncated S-MGBs was prepared and the activities examined against a number of clinically relevant organisms including several bacteria and parasites. The effect of the truncation strategy on S-MGB aggregation in aqueous environment was also investigated using 1H inspection and DOSY experiments. A lead compound, a truncated S-MGB, which possesses significant activity only against trypanosomes and Leishmania has been identified for further study and was also found to be less affected by aggregation compared to its full-length analogue., This paper describes the design and synthesis of Strathclyde minor groove binders (S-MGBs) that have been truncated by the removal of a pyrrole ring in order to mimic the structure of the natural product, disgocidine.

PURPOSE We aim to quantify differences between a new maximum likelihood (ML) background scaling (MLBS) algorithm and two conventional scatter scaling methods for clinical PET/CT. A common source of reduced image quantification with conventional scatter corrections is attributed to erroneous scaling of the initial scatter estimate to match acquired scattered events in the sinogram. MLBS may have performance advantages over conventional methods by using all available data intersecting the subject. METHODS A retrospective analysis was performed on subjects injected with 18 F-FDG (N = 71) and 68 Ga-DOTATATE (N = 11) and imaged using time-of-flight (TOF) PET/CT. The scatter distribution was estimated with single scatter simulation approaches. Conventional scaling algorithms included (a) tail fitted background scaling (TFBS), which scales the scatter to "tails" outside the emission support, and (b) absolute scatter correction (ABS), which utilizes the simulated scatter distribution with no scaling applied. MLBS consisted of an alternating iterative reconstruction with a TOF-based ML activity image update allowing negative values (NEG-ML) and nested loop ML scatter scaling estimation. Scatter corrections were compared using reconstructed images as follows: (a) normalized relative difference images were generated and used for voxel-wise analysis, (b) liver and suspected lesion ROIs were drawn to compute mean SUVs, and (c) a qualitative analysis of overall diagnostic image quality, impact of artifacts, and lesion conspicuity was performed. Absolute quantification and normalized relative differences were also assessed with an 18 F-FDG phantom study. RESULTS For human subjects 18 F-FDG data, Bland-Altman plots demonstrated that the largest normalized voxel-wise differences were observed close to the lower limit (SUV = 1.0). MLBS reconstructions trended towards higher scatter fractions compared to TFBS and ABS images, with median voxel differences across all subjects for TFBS-MLBS measured at 1.7% and 7.6% for 18 F-FDG and 68 Ga-DOTATATE, respectively. For mean SUV analysis, there was a high degree of correlation between the scatter corrections. For 18 F-FDG, ABS scatter correction reconstructions trended towards higher liver mean SUVs relative to MLBS. The qualitative image analysis revealed no significant differences between TFBS and MLBS image reconstructions. For a uniformly filled relatively large 37 cm diameter phantom, MLBS produced the lowest bias in absolute quantification, while normalized voxel-wise differences showed a trend in scatter correction performance consistent with the human subjects study. CONCLUSIONS For 18 F-FDG, MLBS is at least a valid substitute to TFBS, providing reconstructed image performance comparable to TFBS in most subjects but exhibiting quantitative differences in cases where TFBS is typically prone to inaccuracies (e.g., due to patient motion and CT-based attenuation map truncation). Particularly for low contrast regions, quantification differs for ABS compared to MLBS and TFBS, and caution should be taken when utilizing ABS for decision-making based on quantitative metrics.

We introduce a new approximation procedure to improve the accuracy of matrix analytic methods when using truncated queueing models to analyse infinite buffer systems. This is accomplished through emulating the presence of unobserved waiting customers beyond the finite buffer that are able to immediately enter the system following an observed customer’s departure. We show that this procedure results in exact steady-state probabilities at queue lengths below the buffer for truncated versions of the classic M/M/1, $$M/M/1+M$$ , $$M/M/\infty $$ , and M/PH/1 queues. We also present two variants of the basic procedure for use within a $$M/PH/1+M$$ queue and a N-queue polling system with exhaustive service, phase-type service and switch-in times, and exponential impatience timers. The accuracy of these two variants in the context of the polling model are compared through several numerical examples.

Data visualizations and graphs are increasingly common in both scientific and mass media settings. While graphs are useful tools for communicating patterns in data, they also have the potential to mislead viewers. In five studies, we provide empirical evidence that y-axis truncation leads viewers to perceive illustrated differences as larger (i.e., a truncation effect). This effect persisted after viewers were taught about the effects of y-axis truncation and was robust across participants, with 83.5% of participants across these 5 studies showing a truncation effect. We also found that individual differences in graph literacy failed to predict the size of individuals’ truncation effects. PhD students in both quantitative fields and the humanities were susceptible to the truncation effect, but quantitative PhD students were slightly more resistant when no warning about truncated axes was provided. We discuss the implications of these results for the underlying mechanisms and make practical recommendations for training critical consumers and creators of graphs.

Max-stable processes are a natural extension of multivariate extreme value theory important for modeling the spatial dependence of environmental extremes. Inference for max-stable processes observed at several spatial locations is challenging due to the intractability of the full likelihood function. Composite likelihood methods avoid these difficulties by combining a number of low-dimensional likelihood objects, typically defined on pairs or triplets of spatial locations. This work develops a new truncation procedure based on ℓ1-penalty to reduce the complexity and computational cost associated with the composite likelihood function. The new method is shown to achieve a favorable trade-off between computational burden and statistical efficiency by dropping a number of noisy sub-likelihoods. The properties of the new method are illustrated through numerical simulations and an application to real extreme temperature data.

Success on many tasks depends on a trade-off between speed and accuracy. In a novel variant, a speed-accuracy trade-off with sample-based decisions in which both speed and accuracy jointly depend on (self-truncated) sample size, we found strong accuracy biases. On every trial of a sequential investment game, participants chose between 2 investment funds based on binary samples of the funds' past outcomes. Participants could stop sampling and decide whenever they felt sufficiently informed. Total payoff was the product of choice accuracy and number of choices completed within the available time (speed). Participants' failure to understand the dominance of speed over accuracy-that speed decreases more than accuracy improves with increasing sample size-led to dramatic oversampling. Our research aimed to examine to what extent metacognitive functions of monitoring and control could correct for the accuracy bias. Experiments 1a through 1c demonstrated similarly strong accuracy biases and payoff losses in psychology and economics students, depressed, and control patients. In Experiments 2 through 4, the accuracy bias persisted despite several manipulations (feedback, sample limit, choice difficulty, payoff, sampling truncation as default) that underlined the speed advantage, reflecting a conspicuous metacognitive deficit. Even when participants faced no risk of losing on incorrect trials but could still win on correct trials (Experiment 3) and when sampling was contingent on the active solicitation of every new element (Experiment 4), participants continued to sample too much and failed to overcome the accuracy bias. The final discussion focuses on psychological reasons and possible remedies for the metacognitive deficit in trade-off regulation. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

This paper presents a data-driven measurement model for extended object tracking (EOT) with automotive radar. Specifically, the spatial distribution of automotive radar measurements is modeled as a hierarchical truncated Gaussian (HTG) with structural geometry parameters that can be learned from the training data. The HTG measurement model provides an adequate resemblance to the spatial distribution of real-world automotive radar measurements. Moreover, large-scale radar datasets can be leveraged to learn the geometry-related model parameters and offload the computationally demanding model parameter estimation from the state update step. The learned HTG measurement model is further incorporated into a random matrix based EOT approach with two (multi-sensor) measurement updates: one is based on a factorized Gaussian inverse-Wishart density representation and the other is based on a Rao-Blackwellized particle density representation. The effectiveness of the proposed approaches is verified on both synthetic data and real-world nuScenes dataset over 300 trajectories.

Sporting careers observed over a preset time interval can be partitioned into two distinct subsamples. These samples consist of individuals whose careers had already commenced at the start of the time interval (prevalent subsample) and individuals whose careers began during the time interval (incident subsample) as well the respective individual-level covariate data such as salary, height, weight, performance statistics, draft position, etc. Under the assumption of a proportional hazards model, we propose a partial likelihood estimator to model the effect of covariates on survival via an adjusted risk set sampling procedure for when the incident cohort data is used in conjunction with the prevalent cohort data. We use simulated failure time data to validate the combined cohort proportional hazards methodology and illustrate our model using an NBA data set for career durations measured between 1990 and 2008.

Women in Colombia face difficulties related to the patriarchal traits of their societies and well-known conflict afflicting the country since 1948. In this critical context, our aim is to study the relationship between baseline socio-demographic factors and variables associated to fertility, partnership patterns, and work activity. To best exploit the explanatory structure, we propose a Bayesian multivariate density regression model, which can accommodate mixed responses with censored, constrained, and binary traits. The flexible nature of the models allows for nonlinear regression functions and non-standard features in the errors, such as asymmetry or multi-modality. The model has interpretable covariate-dependent weights constructed through normalization, allowing for combinations of categorical and continuous covariates. Computational difficulties for inference are overcome through an adaptive truncation algorithm combining adaptive Metropolis-Hastings and sequential Monte Carlo to create a sequence of automatically truncated posterior mixtures. For our study on Colombian women's life patterns, a variety of quantities are visualised and described, and in particular, our findings highlight the detrimental impact of family violence on women's choices and behaviors., to appear in Bayesian analysis

Available literature reveals that the use of truncated pile would be a good solution to increase the stability of slope which is introduced to date for homogeneous soil. Here an attempt is made to perform both experimental and numerical studies introducing truncated piles in layered soil. Both top and bottom layers are cohesive-friction soil. The sand layer is sandwiched between these layers. The influential factors include water content variation, frequency of base shaking, types of reinforcement used, and depth of the truncation. Slopes are manually prepared and tested using a shake table instrument. The horizontal deformation, root means square acceleration, and crest deformation are evaluated and shown at different water content, frequency, and types of reinforcement. In practical engineering, the piles could be truncated reasonably while ensuring the reinforcement effect. The truncated part of piles is filled with the cement sand mortar. A 2D finite element analysis has been done to validate the results obtained from the experimental investigations. The results show that the introduction of truncated piles increases the stability of the slope. Also, the more increase in the truncated part of the pile, the more will be the effectiveness of the pile.

In this paper, we consider forward stochastic nonlinear parabolic equations, with a control localized in the drift term. Under suitable assumptions, we prove the small-time global null-controllability, with a truncated nonlinearity. We also prove the statistical local null-controllability of the true system. The proof relies on a precise estimation of the cost of null-controllability of the stochastic heat equation and on an adaptation of the source term method to the stochastic setting. The main difficulty comes from the estimation of the nonlinearity in the fixed point argument due to the lack of regularity (in probability) of the functional spaces where stochastic parabolic equations are well-posed. This main issue is tackled through a truncation procedure. As relevant examples that are covered by our results, let us mention the stochastic Burgers equation in the one dimensional case and the Allen-Cahn equation up to the three-dimensional setting.

We study single machine scheduling problems with general truncated sum-of-actual-processing-time-based learning effect. In the general truncated learning model, the actual processing time of a job is affected by the sum of actual processing times of previous jobs and by a job-dependent truncation parameter. We show that the single machine problems to minimize makespan and to minimize the sum of weighted completion times are both at least ordinary NP-hard and the single machine problem to minimize maximum lateness is strongly NP-hard. We then show polynomial solvable cases and approximation algorithms for these problems. Computational experiments are also conducted to show the effectiveness of our approximation algorithms.

Inspired by L.Peng’s work on estimating the mean of heavy-tailed distribution in the case of completed data. we propose an alternative estimator and study its asymptotic normality when it comes to the right truncated random variable. A simulation study is executed to evaluate the finite sample behavior on the proposed estimator

In the present article, we derive an explicit expression for the truncated mean and variance for the multivariate normal distribution with arbitrary rectangular double truncation. We use the moment generating approach of Tallis (1961) and extend it to general μ, Σ and all combinations of truncation. As part of the solution, we also give a formula for the bivariate marginal density of truncated multinormal variates. We also prove an invariance property of some elements of the inverse covariance after truncation. Computer algorithms for computing the truncated mean, variance and the bivariate marginal probabilities for doubly truncated multivariate normal variates have been written in R and are presented along with three examples.

A randomly truncated sample appears when the independent variables T and L are observable if L ＜ T. The truncated version Kaplan-Meier estimator is known to be the standard estimation method for the marginal distribution of T or L. The inverse probability weighted (IPW) estimator was suggested as an alternative and its agreement to the truncated version Kaplan-Meier estimator has been proved. This paper centers on the weak convergence of IPW estimators and variance decomposition. The paper shows that the asymptotic variance of an IPW estimator can be decomposed into two sources. The variation for the IPW estimator using known weight functions is the primary source, and the variation due to estimated weights should be included as well. Variance decomposition establishes the connection between a truncated sample and a biased sample with know probabilities of selection. A simulation study was conducted to investigate the practical performance of the proposed variance estimators, as well as the relative magnitude of two sources of variation for various truncation rates. A blood transfusion data set is analyzed to illustrate the nonparametric inference discussed in the paper.

This paper introduces a new julia package, LRMoE, a statistical software tailor-made for actuarial applications, which allows actuarial researchers and practitioners to model and analyse insurance loss frequencies and severities using the Logit-weighted Reduced Mixture-of-Experts (LRMoE) model. LRMoE offers several new distinctive features which are motivated by various actuarial applications and mostly cannot be achieved using existing packages for mixture models. Key features include a wider coverage on frequency and severity distributions and their zero inflation, the flexibility to vary classes of distributions across components, parameter estimation under data censoring and truncation and a collection of insurance ratemaking and reserving functions. The package also provides several model evaluation and visualisation functions to help users easily analyse the performance of the fitted model and interpret the model in insurance contexts.

Doubly truncated data arise when an individual is potentially observed only if its failure-time lies within a certain interval, unique to that individual. In this paper, we consider the pseudo-observations approach for estimating regression coefficients when data is subject to double truncation. The pseudo-observations generated from the nonparametric maximum likelihood estimates (NPMLE) of the survival function are used as response variables in a generalized estimating equation to estimate the parameters of the model. We look at two estimators for regression parameters of survival probabilities based on different ways of defining pseudo-observations, namely, the simple pseudo-observations (SPO) and stopped pseudo-observations (STPO). We establish asymptotic properties of the two estimators under some conditions. Simulations results show that the proportion of failed estimation based on STPO are smaller than that based on SPO. The estimator based on STPO performs adequately for finite samples while the estimator based on SPO can be very unstable when sample size is not large enough.

In this follow up article of Arnold and Ghosh, we re-visit and study in details one of the two special cases of multivariate hidden truncation -(a) single variable truncation from above in a trivar...

The NPMLE of a distribution function from doubly truncated data was introduced in the seminal paper of Efron and Petrosian (J Am Stat Assoc 94:824–834, 1999). The consistency of the NPMLE depends however on the assumption of independent truncation. In this work we introduce an extension of the Efron–Petrosian NPMLE when the variable of interest and the truncation variables may be dependent. The proposed estimator is constructed on the basis of a copula function which represents the dependence structure between the variable of interest and the truncation variables. Two different iterative algorithms to compute the estimator in practice are introduced, and their performance is explored through an intensive Monte Carlo simulation study. We illustrate the use of the estimators on two real data examples.

The paper presents a hybrid active-learning approach for structural reliability analysis via adaptive Kriging surrogate models. The quasi first-order reliability method is first proposed for characteristic truncation point of a structural performance function. This is used to define a truncation boundary via the joint probability distribution function of input random variables. To reduce simulation time for new training samples, a U-function based criterion is further implemented to refine the candidate sample set. Since the reliability-based expected improvement function and U functions are combined together to evaluate new training samples, it finalizes a hybrid active-learning Kriging (HALK) to develop adaptive surrogate models for the structural reliability analysis. Several numerical examples are presented to demonstrate potential applications of the proposed HALK algorithm. Compared to benchmark results provided by the brutal force Monte-Carlo simulation method, the effectiveness of the HALK approach has been justified by dealing with various structural reliability problems.

International audience; Travel cost (TC) data are often collected on-site, raising the question of on-site sampling bias. In addition, the motivations behind visiting a recreational area are diverse and differ across individuals, with the potential implications that preferences for trips are heterogenous. This is particularly true for recreational fishing areas that include multiple sites and within which multiple fishing activities are pursued. Comparing four single-site negative binomial models, this paper shows the importance of accounting for on-site sampling and heterogenous preferences simultaneously. The magnitude of the bias resulting from addressing these two issues separately is examined in terms of variation in consumer surplus, predicted mean trip and price elasticity. The paper further proposes an empirical strategy that addresses the issue of missing income bias. This bias occurs when respondents who do not report their income are significantly different in terms of their trip behavior from those with an average income level.

The CAPS PMssa monitor is a recently commercialized instrument designed to measure aerosol single-scattering albedo (SSA) with high accuracy (Onasch et al., 2015). The underlying extinction and scattering coefficient measurements made by the instrument also allow calculation of aerosol absorption coefficients via the extinction-minus-scattering (EMS) method. Care must be taken with EMS measurements due to the occurrence of large subtractive error amplification, especially for the predominantly scattering aerosols that are typically found in the ambient atmosphere. Practically this means that although the CAPS PMssa can measure scattering and extinction coefficients with high accuracy (errors on the order of 1 %–10 %), the corresponding errors in EMS-derived absorption range from ∼10 % to greater than 100 %. Therefore, we examine the individual error sources in detail with the goal of constraining these as tightly as possible. Our main focus is on the correction of the scattered light truncation effect (i.e., accounting for the near-forward and near-backward scattered light that is undetectable by the instrument), which we show to be the main source of underlying error in atmospheric applications. We introduce a new, modular framework for performing the truncation correction calculation that enables the consideration of additional physical processes such as reflection from the instrument's glass sampling tube, which was neglected in an earlier truncation model. We validate the truncation calculations against comprehensive laboratory measurements. It is demonstrated that the process of glass tube reflection must be considered in the truncation calculation, but that uncertainty still remains regarding the effective length of the optical cavity. Another important source of uncertainty is the cross-calibration constant that quantitatively links the scattering coefficient measured by the instrument to its extinction coefficient. We present measurements of this constant over a period of ∼5 months that demonstrate that the uncertainty in this parameter is very well constrained for some instrument units (2 %–3 %) but higher for others. We then use two example field datasets to demonstrate and summarize the potential and the limitations of using the CAPS PMssa for measuring absorption. The first example uses mobile measurements on a highway road to highlight the excellent responsiveness and sensitivity of the instrument, which enables much higher time resolution measurements of relative absorption than is possible with filter-based instruments. The second example from a stationary field site (Cabauw, the Netherlands) demonstrates how truncation-related uncertainties can lead to large biases in EMS-derived absolute absorption coefficients. Nevertheless, we use a subset of fine-mode-dominated aerosols from the dataset to show that under certain conditions and despite the remaining truncation uncertainties, the CAPS PMssa can still provide consistent EMS-derived absorption measurements, even for atmospheric aerosols with high SSA. Finally, we present a detailed list of recommendations for future studies that use the CAPS PMssa to measure absorption with the EMS method. These recommendations could also be followed to obtain accurate measurements (i.e., errors less than 5 %–10 %) of SSA and scattering and extinction coefficients with the instrument.

We estimate a travel cost model for the George Washington & Jefferson National Forests using an On-Site Latent Class Poisson Model. We show that the constraints of ad-hoc truncation and homogenous preferences significantly impact consumer surplus estimates derived from the on-site travel cost model. By relaxing the constraints, we show that more than one class of visitors with unique preferences exists in the population. The resulting demand functions, price responsive behaviors, and consumer surplus estimates reflect differences across these classes of visitors. With heterogeneous preferences, a group of ‘local residents’ exists with a probability of 8% and, on average take 113 visits.

As a result of studies demonstrating a correlation between a patent’s value and its forward citation count, patent valuation using forward citations has been increasingly used by practitioners when a patent’s value has not been otherwise established. Although potential limitations of patent citation analysis have been discussed in the past, there is little empirical research demonstrating the sensitivity of estimated patent values to various assumptions embedded within the method. We first summarize an approach that has been used by prior practitioners to estimate the relative value of patents within a portfolio using forward citations, and then perform various analyses to investigate the sensitivity of the approach to certain assumptions. We find that some concerns of prior literature are well-founded, while others are less so. For example, we confirm that biased valuations will result from failure to properly control for patent age and technology. Our analysis also finds that truncation bias is a problem when analyzing recently issued patents, which confirms findings from existing literature. We estimate the rate at which such truncation bias dissipates as patents age and find that the bias for the median patent is reduced to below 10% within five years from the date of publication, although additional variation can remain on an individualized level. Regarding the issue of self-citations, we find that the valuation approach using forward citation analysis can be (but is not always) sensitive to the issue of self-citations, with a median difference of 16.8%. Finally, the valuation approach using forward citation analysis appears to be robust to assumptions underlying patent cohort construction.

The outbreak of COVID-19 has become a global public health event. Many researchers have proposed many epidemiological models to predict the outbreak trend of COVID-19, but all use confirmed cases to predict “onset cases.” In this article, a total of 5434 cases were collected from National Health Commission and other provincial Health Commission in China, spanning from 1 December 2019 to 23 February 2020. We studied the delayed distribution of patients from onset to be confirmed. The delay is divided into two stages, which takes about 15 days or even longer. Therefore, considering the right truncation of the data, we proposed a “predict-in-advance” method, used the number of “visiting hospital cases” to predict the number of “onset cases.” The results not only show that our prediction shortens the delay of the second stage, but also the predicted value of onset cases is quite close to the real value of onset cases, which can effectively predict the epidemic trend of sudden infectious diseases, and provide an important reference for the government to formulate control measures in advance. Supplementary Information The online version contains supplementary material available at 10.1007/s11356-020-11859-w.

We consider the problem of controlling the precision of the multiple-model multiple-hypothesis filter with Gaussian mixture reduction. The controller adaptively chooses the number of hypotheses kept by the filter to (sub)optimally seek a tradeoff between filter precision and computational effort. In order to quantify the approximation error due to hypotheses truncation, the controller employs probability divergence measures such as $f$ -divergences and the Wasserstein divergence. The proposed solution is tested on the problem of estimating the states of a networked control system with packet drops on the controller-actuator channel. Theoretical results demonstrate that our strategy leads to a divergence between the true Bayes posterior and the truncated one that remains bounded over time. Numerical results show a good improvement with respect to truncation with a constant number of hypotheses, specially as the number of modes increases and so does the problem dimensionality.

This work develops a recursive algorithm to estimate a given size sequence of Markov parameters for linear discrete-time systems, which is related to FIR models estimation. The discussion on FIR models in identification literature tends to be brief due to its poor prediction error for low order models, although Markov parameter sequence of shorter length can be used, e.g., as the input for data-driven MPC based on FIR models and for system identification combined with realization theory. Estimation of Markov parameters sequence of larger length can also be used in applications in which the prediction itself is not relevant, such as stability assessment or norm computations. The formulation is derived for SISO systems and then we extended it to the MIMO case. An analysis of the overall truncation and bias errors is also developed and illustrative examples are given to highlight the method’s performance. In the examples we also further illustrate the difference in estimation results for different inputs, since the input choice is affected by the identification method utilised.

Methods for measuring the bistatic RCS of objects using near-field scanning and near-field to far-field transformation by mathematical modeling are analyzed. A model two-dimensional problem of diffraction by extended scatterers is considered. A cylindrical scanner is used. One important issue in this case is the possibility of scanning on a truncated surface rather than on the full scanning surface in order to reduce the cost of measurements. Under such conditions the results of the classical method become poorly predictable and an adapted method is required. Two methods based on the expansion in cylindrical waves when scanning on a truncated surface are compared: the classical one, used to measure antenna radiation patterns (the field outside the scanning area is assumed to be zero) [1] and the method proposed by Kim, which allows one to strictly take the truncation of the scanning surface by angle into account [2]. Comparison of the obtained results of both methods confirms the prospects of using the second method.

Purpose Computed tomography image reconstruction using truncated or sparsely acquired projection data to reduce radiation dose, iodine volume, and patient motion artifacts has been widely investigated. To continue these efforts, we investigated the use of machine learning-based reconstruction techniques using deep convolutional generative adversarial networks (DCGANs) and evaluated its effect using standard imaging metrics. Methods Ten thousand head computed tomography (CT) scans were collected from the 2019 RSNA Intracranial Hemorrhage Detection and Classification Challenge dataset. Sinograms were simulated and then resampled in both a one-third truncated and one-third sparse manner. DCGANs were tasked with correcting the incomplete projection data, either in the sinogram domain where the full sinogram was recovered by the DCGAN and then reconstructed, or the reconstruction domain where the incomplete data were first reconstructed and the sparse or truncation artifacts were corrected by the DCGAN. Seventy-five hundred images were used for network training and 2500 were withheld for network assessment using mean absolute error (MAE), structural similarity index measure (SSIM), and peak signal-to-noise ratio (PSNR) between results of different correction techniques. Image data from a quality-assurance phantom were also resampled in the two manners and corrected and reconstructed for network performance assessment using line profiles across high-contrast features, the modulation transfer function (MTF), noise power spectrum (NPS), and Hounsfield Unit (HU) linearity analysis. Results Better agreement with the fully sampled reconstructions were achieved from sparse acquisition corrected in the sinogram domain and the truncated acquisition corrected in the reconstruction domain. MAE, SSIM, and PSNR showed quantitative improvement from the DCGAN correction techniques. HU linearity of the reconstructions was maintained by the correction techniques for the sparse and truncated acquisitions. MTF curves reached the 10% modulation cutoff frequency at 5.86 lp/cm for the truncated corrected reconstruction compared with 2.98 lp/cm for the truncated uncorrected reconstruction, and 5.36 lp/cm for the sparse corrected reconstruction compared with around 2.91 lp/cm for the sparse uncorrected reconstruction. NPS analyses yielded better agreement across a range of frequencies between the resampled corrected phantom and truth reconstructions. Conclusions We demonstrated the use of DCGANs for CT-image correction from sparse and truncated simulated projection data, while preserving imaging quality of the fully sampled projection data.

This article provides an exact algorithm for efficient computation of the time series of conditional variances, and hence the likelihood function, of models that have an ARCH(∞) representation. This class of models includes, for example, the fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model. Our algorithm is a variation of the fast fractional difference algorithm of Jensen, A.N. and M.O. Nielsen (2014), Journal of Time Series Analysis 35, 428–436. It takes advantage of the fast Fourier transform (FFT) to achieve an order of magnitude improvement in computational speed. The efficiency of the algorithm allows estimation (and simulation/bootstrapping) of ARCH(∞) models, even with very large data sets and without the truncation of the filter commonly applied in the literature. In Monte Carlo simulations, we show that the elimination of the truncation of the filter reduces the bias of the quasi‐maximum‐likelihood estimators and improves out‐of‐sample forecasting. Our results are illustrated in two empirical examples.

Restricted mean survival time (RMST) is a clinically interpretable and meaningful survival metric that has gained popularity in recent years. Several methods are available for regression modeling of RMST, most based on pseudo-observations or what is essentially an inverse-weighted complete-case analysis. No existing RMST regression method allows for the covariate effects to be expressed as functions over time. This is a considerable limitation, in light of the many hazard regression methods that do accommodate such effects. To address this void in the literature, we propose RMST methods that permit estimating time-varying effects. In particular, we propose an inference framework for directly modeling RMST as a continuous function of L. Large-sample properties are derived. Simulation studies are performed to evaluate the performance of the methods in finite sample sizes. The proposed framework is applied to kidney transplant data obtained from the Scientific Registry of Transplant Recipients (SRTR).

Truncation is one of the most commonly used approaches for circuit-level approximate computing. This paper proposes a scheme for error compensation of arithmetic circuits in which a so-called padding is utilized to compensate at the output for the truncated bits of the input operands. Compensation relies on adjusting the output results of an arithmetic circuit; the padding takes a value determined by utilizing statistical information based on profiling an arithmetic circuit to reduce the average signed difference between the inexact and exact values and so the mean square error. An extensive analysis and simulation-based evaluation of error metrics are performed on signed truncated adders, multipliers and dividers; an excellent agreement is found. Additional design metrics such as power consumption and circuit complexity are also assessed. Different applications of approximate arithmetic circuits with the proposed output error compensation scheme are presented. Matrix multiplication and image processing (changing detection) are investigated to show the effectiveness of the scheme proposed in this paper.