Presence Of Zeros Research Articles

Sufficient Reduction Method for Bivariate Zero-Inflated Poisson Process

The sufficient reduction (SR) method was developed for detecting a mean shift in a bivariate zero-inflated Poisson process. The derived sequence of statistics from the reduction was monitored with the EWMA and EWMA-SN charts for monitoring a mean shift in a process. The detection performance was compared against other SR methods developed for a Poisson process and evaluated via the simulations under the different shift sizes and proportions of zero in the process. The results showed that the presence of zeros in the process influenced the performance of SR methods by delaying shift detection and reducing the detection accuracy, especially when shift size was small. The proposed method with the EWMA chart gave the shortest delay for detecting a small to moderate shift and gave the highest true alarm rate and the lowest non-detection rate for detecting a small shift compared to other methods.

How to measure mast seeding?

The periodic production of large seed crops, or masting, is a widespread phenomenon in perennial plants. This behavior can enhance the reproductive efficiency of plants, leading to increased fitness, and produce ripple effects on food webs. While variability from year to year is a defining characteristic of masting, the methods used to quantify this variability are highly debated. The commonly used coefficient of variation lacks the ability to account for the serial dependence in mast data and can be influenced by zeros, making it a less suitable choice for various applications based on individual-level observations, such as phenotypic selection, heritability, and climate change studies, which rely on individual-plant-level datasets that often contain numerous zeros. To address these limitations, we present three case studies and introduce volatility and periodicity, which account for the variance in the frequency domain by emphasizing the significance of long intervals in masting. By utilizing examples of Sorbus aucuparia, Pinus pinea, Quercus robur, Quercus pubescens, and Fagus sylvatica, we demonstrate how volatility captures the effects of variance at both high and low frequencies, even in the presence of zeros, leading to improved ecological interpretations of the results. The growing availability of long-term, individual-plant datasets promises significant advancements in the field, but requires appropriate tools for analysis, which the new metrics provide.

Effects of outliers on remote sensing‐assisted forest biomass estimation: A case study from the United States national forest inventory

Abstract Large‐scale ecological sampling networks, such as national forest inventories (NFIs), collect in situ data to support biodiversity monitoring, forest management and planning, and greenhouse gas reporting. Data harmonization aims to link auxiliary remotely sensed data to field‐collected data to expand beyond field sampling plots, but outliers that arise in data harmonization—questionable observations because their values differ substantially from the rest—are rarely addressed. In this paper, we review the sources of commonly occurring outliers, including random chance (statistical outliers), definitions and protocols set by sampling networks, and temporal and spatial mismatch between field‐collected and remotely sensed data. We illustrate different types of outliers and the effects they have on estimates of above‐ground biomass population parameters using a case study of 292 NFI plots paired with airborne laser scanning (ALS) and Sentinel‐2 data from Sawyer County, Wisconsin, United States. Depending on the criteria used to identify outliers (sampling year, plot location error, nonresponse, presence of zeros and model residuals), as many as 53 of the 292 Forest Inventory and Analysis plot observations (18%) were identified as potential outliers using a single criterion and 111 plot observations (38%) if all criteria were used. Inclusion or removal of potential outliers led to substantial differences in estimates of mean and standard error of the estimate of biomass per unit area. The simple expansion estimator, which does not rely on ALS or other auxiliary data, was more sensitive to outliers than model‐assisted approaches that incorporated ALS and Sentinel‐2 data. Including Sentinel‐2 predictors showed minimal increases to the precision of our estimates relative to models with ALS predictors alone. Outliers arise from many causes and can be pervasive in data harmonization workflows. Our review and case study serve as a note of caution to researchers and practitioners that the inclusion or removal of potential outliers can have unintended consequences on population parameter estimates. When used to inform large‐scale biomass mapping, carbon markets, greenhouse gas reporting and environmental policy, it is necessary to ensure the proper use of NFI and remotely sensed data in geospatial data harmonization.

Geometric phase of quantum wave function and singularities of Bohm dynamics in a one-dimensional system

The interpretation of the quantum mechanics proposed by de Broglie and Bohm postulates that the time evolution of the position and the momentum of a quantum particle can be described by a trajectory in the phase-space. The evolution equation coincides with the classical one except for the presence of a nonlinear correction to the total energy of the particle denoted by Bohm potential. The particle momentum is associated to the derivative of the phase of the quantum wave function. The phase of a quantum wave function ceases to be globally well defined in the presence of zeros (nodes) and the Bohm potential becomes singular. We develop a geometrical interpretation of the Bohm dynamics based on the Ehresmann theory of the fiber bundles and we express the number of total rotations of the quantum phase around a node in terms of holonomy maps.

Semi-Automated Inversion-Specific Data Selection for Volcano Tomography

Active seismic experiments allow reconstructing the subsurface structure of volcanoes with unprecedented resolution and are vital to improve the interpretation of volcanic processes. They require a quality assessment for thousands of seismic waveforms recorded at hundreds of stations in the shortest amount of time. However, the processing necessary to obtain reliable images from such massive datasets demands signal processing and selection strategies specific to the inversions attempted. Here, we present a semi-automated workflow for data selection and inversion of amplitude-dependent information using the original TOMODEC2005 dataset, recorded at Deception Island (Antarctica). The workflow is built to tomographic techniques using amplitude information, and can be generalised to passive seismic imaging. It first selects data depending on standard attributes, like the presence of zeroes across all seismic waveforms. Then, waveform selections depend on inversion-specific attributes, like the delay of the maximum amplitude of the waveform or the quality of coda-wave decays. The automatic workflow and final visual selections produce a dataset reconstructing anomalies at a node spacing of 2 km, imaging a high-attenuation anomaly in the centre of the Deception Island bay, consistent with previously-published maps. Attenuation models are then obtained at a node spacing of 1 km, highlighting bodies of highest attenuation scattered across the island and a NW-SE trend in the high-attenuation anomaly in the central bay. These results show the effect of the local extension regime on volcanic structures, providing details on the eruptive history and evolution of the shallow magmatic and hydrothermal systems. The selection workflow can be easily generalised to other amplitude-dependent tomographic techniques when applied to active seismic surveys. Image improvements from the original dataset are minor when selecting data using standard attributes, like signal-to-noise ratios. Tomographic maps become drastically more stable and consistent between different frequencies and resolutions when data selection targets attributes specific to the inversion.

On Weil sums, conjectures of Helleseth, and Niho exponents

Let F be a finite field, μ be a fixed additive character and s be an integer coprime to |F×|. For any a∈F, the corresponding Weil sum is defined to be WF,s(a)=∑x∈Fμ(xs−ax). The Weil spectrum counts distinct values of the Weil sum as a runs through the invertible elements in the finite field. The value of these sums and the size of the Weil spectrum are of particular interest, as they link problems in coding and information theory to other areas of math such as number theory and arithmetic geometry. In the setting of Niho exponents, we examine the Weil sum, its bounds and its spectrum. As a consequence, we give a new proof to the Vanishing Conjecture of Helleseth (1971) on the presence of zero in the Weil spectrum in the case of Niho exponents. We also state a conjecture for when the Weil spectrum contains at least five elements, and prove it for a certain class of Weil sums.

Augmented-limited regression models with an application to the study of the risk perceived using continuous scales

Studies of risk perceived using continuous scales of [0,100] were recently introduced in psychometrics, which can be transformed to the unit interval, but the presence of zeros or ones are commonly observed. Motivated by this, we introduce a full inferential set of tools that allows for augmented and limited data modeling. We considered parameter estimation, residual analysis, influence diagnostic and model selection for zero-and/or-one augmented beta rectangular (ZOABR) regression models and their particular nested models, which is based on a new parameterization of the beta rectangular distribution. Different from other alternatives, we performed maximum-likelihood estimation using a combination of the EM algorithm (for the continuous part) and Fisher scoring algorithm (for the discrete part). Also, we perform an additional step, by considering other link functions, besides the usual logistic link, for modeling the response mean. By considering randomized quantile residuals, (local) influence diagnostics and model selection tools, we identified that the ZOABR regression model is the best one. We also conducted extensive simulations studies, which indicate that all developed tools work properly. Finally, we discuss the use of this type of models to treat psychometric data. It is worthwhile to mention that applications of the developed methods go beyond to Psychometric data. Indeed, they can be useful when the response variable in bounded, including or not the respective limits.

How McFadden Met Rockafellar and Learnt to Do More With Less

We study the additive random utility model of discrete choice under minimal assumptions. We make no assumptions regarding the distribution of random utility components or the functional form of systematic utility components. Exploiting the power of convex analysis, we are nevertheless able to generalize a range of important results. We characterize demand with a generalized Williams-Daly-Zachary theorem. A similarly generalized version of Hotz-Miller inversion yields constructive partial identification of systematic utilities. Estimators based on our partial identification result remain well defined in the presence of zeros in demand. We also provide necessary and sufficient conditions for point identification.

On Unknown Input Observers of Linear Systems: Asymptotic Unknown Input Decoupling Approach

This note presents a new unknown input observer (UIO) with adjustable performances for linear systems. It focuses on state estimation in the presence of zeros with slow dynamics. It is known that if the system has stable invariant zeros and satisfies the decoupling condition then a UIO exists. However, the invariant zeros constrain the pole placement and consequently the state estimation error convergence rate, especially, when the zeros dynamics are slow. In the proposed UIO, the exact decoupling condition is relaxed by the introduction of the asymptotic decoupling notion which allows to act on the invariant zeros and then enhance the convergence rate of the state estimation error. Numerical examples are provided to illustrate the performances of the UIO.

Comparing GLM, GLMM, and GEE modeling approaches for catch rates of bycatch species: A case study of blue shark fisheries in the South Atlantic

AbstractModeling and understanding the catch rate dynamics of marine species is extremely important for fisheries management and conservation. For oceanic highly migratory species in particular, usually only fishery‐dependent data are available which have limitations in the assumption of independence and if often zero‐inflated and/or overdispersed. We tested different modeling approaches applied to the case study of blue shark in the South Atlantic, by using generalized linear models (GLMs), generalized linear mixed models (GLMMs), and generalized estimating equations (GEEs), as well as different error distributions to deal with the presence of zeros in the data. We used fractional polynomials to deal with non‐linearity in some of the explanatory variables. Operational (set level) data collected by onboard fishery observers, covering 762 longline sets (1,014,527 hooks) over a 9‐year period (2008–2016), were used. One of the most important variables affecting catch rates is leader material, with increasing catches when wire leaders are used. Spatial and seasonal variables are also important, with higher catch rates expected toward temperate southern waters and eastern longitudes, particularly between July and September. Environmental variables, especially SST, also affect catches. There were no major differences in the parameters estimated with GLMs, GLMMs, or GEEs; however, the use of GLMMs or GEEs should be more appropriate due to fishery dependence in the data. Comparing those two approaches, GLMMs seem to perform better in terms of goodness‐of‐fit and model validation.

Comparing Zero-inflated Poisson, Zero-inflated Negative Binomial and Zero-inflated Geometric in Count Data with Excess Zero

Count data often violate the assumptions of a normal distribution due to the fact that they are bounded by their lowest value which is zero. The Poison distribution is sometimes suggested but when the assumption of equal mean and variance is violated due to over-dispersion and presence of zeros we tend to look in the direction of other models. Zero-inflated data falls in this category. The zero-inflated and hurdle models have been found to fit this scenario. The proportions of zero in the data often affect the choice of the models. Our study used the Monte Carlo design to sample 1000 cases from positively skewed distribution with 1.25 as mean vector and 0.10 as zero-inflation parameter. The data was analysed using the method of the maximum likelihood estimation. The Zero-Inflated Poisson, Zero-Inflated Negative Binomial and Zero-Inflated Geometric were fitted; the standard error and Akaike Information Criterion were obtained as measures of model validation with ZIP outperformed ZINB and ZIG.

Comparison of Computational Methods for Imputing Single-Cell RNA-Sequencing Data

Single-cell RNA-sequencing (scRNA-seq) is a recent breakthrough technology, which paves the way for measuring RNA levels at single cell resolution to study precise biological functions. One of the main challenges when analyzing scRNA-seq data is the presence of zeros or dropout events, which may mislead downstream analyses. To compensate the dropout effect, several methods have been developed to impute gene expression since the first Bayesian-based method being proposed in 2016. However, these methods have shown very diverse characteristics in terms of model hypothesis and imputation performance. Thus, large-scale comparison and evaluation of these methods is urgently needed now. To this end, we compared eight imputation methods, evaluated their power in recovering original real data, and performed broad analyses to explore their effects on clustering cell types, detecting differentially expressed genes, and reconstructing lineage trajectories in the context of both simulated and real data. Simulated datasets and case studies highlight that there are no one method performs the best in all the situations. Some defects of these methods such as scalability, robustness, and unavailability in some situations need to be addressed in future studies.

Zero-augmented accelerated spatial failure model for modeling hospital length of stay data

Hospital length of stay (LOS) is often used as an indicator for hospital efficiency and resource utilization. LOS is nonnegative with presence of zeros and typically positively skewed with a long right tail, which may not be adequately modelled by traditional distributions, such as lognormal. We developed a zero-augmented accelerated frailty model for modeling the extreme skewness with the presence of zeros. Levels of utilization of health services may vary geographically, so conditional autoregressive priors were used to provide spatial smoothing across neighboring hospital health districts. The random effect terms are further linked to investigate if the capacity for longer LOS are consistently higher or lower at the health district level. Modeling and inference used the Bayesian approach via Markov Chain Monte Carlo simulation techniques. We demonstrated the proposed model for modeling the LOS of patients admitted due to chronic lower respiratory disease in Saskatchewan, Canada.

Small area estimation for skewed data in the presence of zeroes

Skewed distributions with representative outliers pose a problem in many surveys. Various small area prediction approaches for skewed data based on transformation models have been proposed. However, in certain applications of those predictors, the fact that the survey data also contain a non-negligible number of zero-valued observations is sometimes dealt with rather crudely, for instance by arbitrarily adding a constant to each value (to allow zeroes to be considered as “positive observations, only smaller”, instead of acknowledging their qualitatively different nature). On the other hand, while a lognormal-logistic model has been proposed (to incorporate skewed distributions as well as zeroes), that model does not include any hierarchical aspects, and is therefore not explicitly adapted to small area prediction. In this paper, we consolidate the two approaches by extending one of the already established log-transformation mixed small area prediction models to incorporate a logistic component. This allows for the simultaneous, systematic treatment of domain effects, outliers and zero-valued observations in a single framework. We benchmark the resulting model-based predictors (against relevant alternatives) in applications to simulated data as well as empirical data from the Australian Agricultural and Grazing Industries Survey.

Small Area Estimation for Skewed Data in the Presence of Zeroes

Abstract Skewed distributions with representative outliers pose a problem in many surveys. Various small area prediction approaches for skewed data based on transformation models have been proposed. However, in certain applications of those predictors, the fact that the survey data also contain a non-negligible number of zero-valued observations is sometimes dealt with rather crudely, for instance by arbitrarily adding a constant to each value (to allow zeroes to be considered as “positive observations, only smaller”, instead of acknowledging their qualitatively different nature). On the other hand, while a lognormal-logistic model has been proposed (to incorporate skewed distributions as well as zeroes), that model does not include any hierarchical aspects, and is therefore not explicitly adapted to small area prediction. In this paper, we consolidate the two approaches by extending one of the already established log-transformation mixed small area prediction models to incorporate a logistic component. This allows for the simultaneous, systematic treatment of domain effects, outliers and zero-valued observations in a single framework. We benchmark the resulting model-based predictors (against relevant alternatives) in applications to simulated data as well as empirical data from the Australian Agricultural and Grazing Industries Survey.

The Zero-Inflated Promotion Cure Rate Regression Model Applied to Fraud Propensity in Bank Loan Applications

In this paper we extend the promotion cure rate model proposed by Chen et al (1999), by incorporating excess of zeros in the modelling. Despite allowing to relate the covariates to the fraction of cure, the current approach, which is based on a biological interpretation of the causes that trigger the event of interest, does not enable to relate the covariates to the fraction of zeros. The presence of zeros in survival data, unusual in medical studies, can frequently occur in banking loan portfolios, as presented in Louzada et al (2015), where they deal with propensity to fraud in lending loans in a major Brazilian bank. To illustrate the new cure rate survival method, the same real dataset analyzed in Louzada et al (2015) is fitted here, and the results are compared.

Pole Placement Using Genetic Algorithm with Integral Control

This paper presents the application of genetic algorithms to find the optimum feedback gains in pole placement with integral control to get the desired performance in control system. Performances are measured in terms of key parameters like settling time, peak overshoot, undershoot, rise time etc in control system. The major drawbacks of pole placement technique are to get optimum location of poles and we cannot place zeros at desired locations. Dominating concept of poles is enough for placing poles for systems which transfer functions are without zeros. But if there are zeros in transfer function then it is not enough to place pole with dominating pole concept because presence of zero can destroy the dynamic response of control system. In this paper genetic algorithm is used to find the optimum locations of poles to get the desired response and compensate the effect of zeros on transient in case zeros are present in transfer function. GA is a population based algorithm to find the global solution of a problem. This paper compares the unit step response of a plant with presence of zero in transfer function. The same GA based technique is used for finding optimum location of poles to get the desired response for magnetic levitation system. This analysis is well supported by the simulation and experimental results done using MATLAB and Simulink.

On Bias Correction in a Class of Inflated Beta Regression Models

Inflated beta regression models bear practical applicability in modeling rates and proportions measured continuously in the presence of zeros and/or ones. In this article, the second-order bias of maximum likelihood estimators for zero-or-one inflated beta regression model parameters is derived. This enables one to obtain corrected estimators that are approximately unbiased. Numerical results exhibit that corrected estimators show better performance in terms of mean-square error and bias when compared to maximum likelihood estimators.

Small Area Estimation for Skewed Data in Presence of Zeros

The standard approach for small area estimation (SAE) based on linear mixed models often yields inefficient estimates for skewed data. Chandra and Chambers (2011a) described SAE for skewed data that are linear following a log-log transformation. In this case, they extended the model-based direct estimation (MBDE) approach of SAE (Chandra and Chambers, 2009). In particular, they derived sample weights via model calibration (Wu and Sitter, 2001) based on a log-log transform model with random area effects. We discuss SAE for skewed data in presence of zeros. In this context, we extend the Chandra and Chambers (2011a) methods of SAE under a mixture model. Results generated by simulation studies show that the method works well and produces an efficient set of small area estimates.

A SPECTRAL METHOD FOR DECONVOLVING A DENSITY

We propose a new estimator for the density of a random variable observed with an additive measurement error. This estimator is based on the spectral decomposition of the convolution operator, which is compact for an appropriate choice of reference spaces. The density is approximated by a sequence of orthonormal eigenfunctions of the convolution operator. The resulting estimator is shown to be consistent and asymptotically normal. While most estimation methods assume that the characteristic function (CF) of the error does not vanish, we relax this assumption and allow for isolated zeros. For instance, the CF of the uniform and symmetrically truncated normal distributions have isolated zeros. We show that, in the presence of zeros, the density is identified even though the convolution operator is not one-to-one. We propose two consistent estimators of the density. We apply our method to the estimation of the measurement error density of hourly income collected from survey data.