Sequential negative binomial problems and statistical ecology: A selected review with new directions

In the past sixty years various research methods have been proposed to help the researcher to collect reliable data to which theoretical analyses can be applied. In this paper it is investigated if artificial intelligence (AI)-generated translations of selected excerpts from literary works by ChatGPT can help the researcher to gain more insight into a linguistic phenomenon, viz. the acceptability of preverbal bare plural nouns in Romance, which have been argued to be much less acceptable than bare nouns in Germanic. The machine translations are checked against the official translations by the professional human translators. Furthermore, the chatbot is queried about its choices. A quantitative and qualitative comparison reveals that the machine’s translations approach those by the human translators. However, while the chatbot shows some metalinguistic knowledge and may explain some of its choices, for explanations for which some more analytical knowledge is required, it fails. The paper concludes that the chatbot’s observational adequacy may, however, help the researcher to do research on specific linguistic phenomena for which data are difficult to obtain.

Within the past sixty years marked progress has been made in the understanding of the environmental factors in the etiology of disease. But great though the advances have been, the fact that persons react differently to the same sort of trauma, bacterial, mechanical, chemical or psychologic, has kept alive the concept of constitution as a factor in the etiology and course of disease. Prior to 1870, though some progress had been made in the study of the individual, the term constitution had been widely used to designate factors, the exact nature of which was unknown, and it was only natural that, with the discovery of the facts of bacteriology and immunology, research should be directed toward these more promising fields and that the term constitution should become largely discredited. In America, where the traditional background is almost entirely lacking and where experimental medicine on a large scale is of comparatively

The Poisson regression model is widely used for count data. This model assumes equidispersion. In practice, equidispersion is seldom reflected in data. However, in real-life data, the variance usually exceeds the mean. This situation is known as overdispersion. Negative binomial distribution and other Poisson mix models are often used to model overdispersion count data. Another extension of the negative binomial distribution in another model for count data is the univariate generalized Waring. In addition, the model developed by Famoye can be used in the analysis of count data. When the count data contains a large number of zeros, it is necessary to use zero-inflated models. In this study, different generalized regression models are emphasized for the analysis of excessive zeros count data. For this purpose, a real data set was analysed with the generalized Poisson model, generalized negative binomial model, generalized negative binomial Famoye, generalized Waring model, and the foregoing zero-inflated models. Log-likelihood, Akaike information criterion, Bayes information criterion, Vuong statistics were used for model comparisons.

This paper introduced a new mixed distribution, namely the negative binomial-generalized exponential (NB-GE) distribution, which it obtained by mixing the negative binomial (NB) distribution with a generalized exponential (GE) distribution. The NB-GE distribution offers the advantage of being able to handle this kind of data sets, while still maintaining similar characteristics as the traditional negative binomial. The closed form and the factorial moment of the NB-GE distribution are derived. The NB-GE distribution appropriate when we find the one related to count data which have a large number of zeros and overdispersion in Poisson distribution. In addition, we present the basic properties of the new distribution such as mean, variance, skewness and kurtosis. Including, the negative binomial-exponential distributions are presented as special cases of this NB-GE distribution. Parameters estimation is also implemented using maximum likelihood method and the usefulness of the NB-GE distribution is illustrated by real data set. When using a goodness of fit test, the results show that the NB-GE distribution can provide a better fit than the NB distribution and Poisson distribution for count data that contain a large number of zeros.

Statistical modelling for falls count data

The Negative Binomial distribution (NBD) is used for modeling many types of count data, including gene expression counts obtained by RNA sequencing technologies (RNA-Seq). Finding outliers in this type of data has been shown in recent research to help in identifying rare genetic disorders in humans. Existing Bayesian approaches to detecting outliers in data following the NBD are either computationally inefficient or too general and hence do not leverage the NBD’s specificities in an optimal way. We present a novel Bayesian outlier score for data following the NBD, relying on recent advances in the inference of its dispersion parameter through a special method of Gibbs sampling. The novel Bayesian model on which our score is based — OutPyRX (Outlier detection in Python for RNA-Seq, eXtended version) — improves the model of its predecessor OutPyR by introducing novel parameters that are derived from OutPyR’s. These novel parameters allow more than 6 times faster convergence of the novel outlier score compared to OutPyR’s while having a negligible computational impact on the Gibbs sampling procedure. We show that, in terms of area under precision-recall curve (AUC) values, the novel score outcompetes existing scores on 21 out of 24 datasets that we derived from 4 real datasets by injecting artificial outliers. However, OutPyRX does not perform confounder control which is required for some datasets containing biological outliers. The model is general and can be applied to other similar count data. The code for our model is available at https://github.com/esalkovic/outpyrx .

Methodologic Challenges in the Analysis of Count Data in Radiology Health Services Research

The foliage in a fully-leafed deciduous forest canopy is clumped. Consequently, theory indicates that the probability of beam penetration will be estimated more accurately with a model based on the negative binomial distribution than with a model based on the Poisson distribution, incorporating an assumption of a spherical leaf inclination angle distribution. Flux densities of photosynthetically active radiation (PAR) were measured in and above a deciduous forest canopy and were computed with the canopy radiative transfer models based on the negative binomial and Poisson distributions. These radiation values were used to compute canopy photosynthesis and stomatal conductance. Canopy photosynthesis and stomatal conductance, based on the negative binomial model, overestimated values computed from measured PAR profiles by 8 and 9%. respectively. The canopy photosynthesis and stomatal conductance values computed with the spherical Poisson model under-estimated measured values by 17 and 10%, respectively. Thus, the negative binomial radiative transfer model improves estimates of canopy photosynthesis and, to a lesser extent, stomatal conductance, inside a deciduous forest.

Count data, including zero counts arise in a wide variety of application, hence models for counts have become widely popular in many fields. In the statistics field, one may define the count data as that type of observation which takes only the non-negative integers value. Sometimes researchers may Counts more zeros than the expected. Excess zero can be defined as Zero-Inflation. Data with abundant zeros are especially popular in health, marketing, finance, econometric, ecology, statistics quality control, geographical, and environmental fields when counting the occurrence of certain behavioral and natural events, such as frequency of alcohol use, take drugs, number of cigarettes smoked, the occurrence of earthquakes, rainfall, and etc. Some models have been used to analyzing count data such as the zero-inflated Poisson (ZIP) model and the negative binomial model. In this paper, the models, Poisson, Negative Binomial, ZIP, and ZINB were been used to analyze rainfall data.

A semiparametric negative binomial generalized linear model for modeling over-dispersed count data with a heavy tail: Characteristics and applications to crash data

From the bestselling author of Cultural Literacy, a passionate and cogent argument for reforming the way we teach our children Why, after decades of commissions, reforms, and efforts at innovation, do our schools continue to disappoint us? In this comprehensive and thought-provoking book, educational theorist E. D. Hirsch, Jr. offers a masterful analysis of how American ideas about education have veered off course, what we must do to right them, and most importantly why. He argues that the core problem with American education is that educational theorists, especially in the early grades, have for the past sixty years rejected academic content in favor of child-centered and how-to learning theories that are at odds with how children really learn. The result is failing schools and widening inequality, as only children from content-rich (usually better-off) homes can take advantage of the schools' educational methods. Hirsch unabashedly confronts the education establishment, arguing that a content-based curriculum is essential to addressing social and economic inequality. A nationwide, specific, grade-by-grade curriculum established in the early school grades can help fulfill one of America's oldest and most compelling dreams: to give all children, regardless of language, religion, or origins, the opportunity to participate as equals and become competent citizens. Hirsch not only reminds us of these inspiring ideals, he offers an ambitious and specific plan for achieving them.

Abstract: This essay proposes a movements-based method for studying the development of US literature after World War II. It argues that the cultural materialist and institutionalist frameworks that have dominated post-1945 US literary studies in recent years have systematically overlooked the role of social movements as catalysts for cultural change. Through readings of the literary magazine n+1, the archival materials of Octavia Butler, and novels by a range of other major postwar US authors, it offers an account of how the collective mobilizations of the past sixty years—from Civil Rights, the New Left, and the Women's Movement to Occupy Wall Street, Black Lives Matter, and #MeToo—have decisively shifted the contours of the US literary field.

Application of the Conway–Maxwell–Poisson generalized linear model for analyzing motor vehicle crashes

More than 60% of accidents in Iran occur within 30 kilometers of cities entrance roads. Therefore the number of accidents per kilometer in these regions, in contrast to the other parts of roads is very considerable. The city of Tehran, as the capital of Iran, is the cross point of major arterials of passenger and freight transportation. Thus the evaluation of road safety, entering and exiting the city in the 30 kilometers buffer, can be considered to improve countrywide road safety. To investigate the effects of roadway characteristics and traffic conditions, including number of traffic violations, on accident frequency within 30 km of Tehran entrance roads, Poisson and Negative Binomial regression model were calibrated in this study. Although the goodness of fit index in Poisson model is much greater than the Negative Binomial model, the accident data dispersion in this study implies that Negative Binomial model is more appropriate to show the influences of effective variables. According to results of modeling, the variables including average daily volume, share of heavy vehicles, average daily speed violations and number of direct accesses and interchanges have effective influence on accident frequencies. Controlling access to roads and using effective actions to reduce the speed and number of speed violation can be accounted as effective policies to reduce accident frequencies within 30 km of Tehran entrance roads.

Modeling over-dispersed crash data with a long tail: Examining the accuracy of the dispersion parameter in Negative Binomial models