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The tree-based scan statistic is a data mining method used to identify signals of adverse drug reactions in a database of spontaneous reporting systems. It is particularly beneficial when dealing with hierarchical data structures. One may use a retrospective case–control study design from spontaneous reporting systems (SRS) to investigate whether a specific adverse event of interest is associated with certain drugs. However, the existing Bernoulli model of the tree-based scan statistic may not be suitable as it fails to adequately account for dependencies within matched pairs. In this article, we propose signal detection statistics for matched case–control data based on McNemar's test, Wald test for conditional logistic regression, and the likelihood ratio test for a multinomial distribution. Through simulation studies, we demonstrate that our proposed methods outperform the existing approach in terms of the type I error rate, power, sensitivity, and false detection rate. To illustrate our proposed approach, we applied the three methods and the existing method to detect drug signals for dizziness-related adverse events related to antihypertensive drugs using the database of the Korea Adverse Event Reporting System. [ABSTRACT FROM AUTHOR]

The research aims to develop and verify a real-time digital learning platform for diagnosing the degree of mathematical competency of seventh-grade students. A total of 1,559 students from four regions of Thailand and six experts participated in this research. The researchers employed a design-based approach and the Multidimensional Coefficient Multinomial Logit Model to evaluate the effectiveness of the real-time digital learning platform. The measurement tool consists of two aspects, namely mathematical measures and the construction of knowledge dimensions, with 58 items to simulate students' responses to the three respective content constituents: number and algebra, measurement and geometry, and statistics and probability. The findings showed that the multidimensional model offered a significantly better statistical fit in measurement, geometry, statistics, and probability, while numbers and algebra fit better in the unidimensional model. There were positive, strong, and significant correlations between the dimensions. The findings indicated that all items fit the OUTFIT MNSQ and INFIT MNSQ, which are between 0.75-1.33. The findings revealed that the internal structure when it came to evaluating the degrees of students' mathematical competency using the Wright map and the Multidimensional Test Response Model conformed with the quality of the digital learning platform in terms of its usefulness, accuracy, and feasibility. This real-time digital learning platform for diagnosing the degree of mathematical competency can be accessed from anywhere with an internet connection, making education more accessible to a wider audience, including individuals in remote areas or those with physical disabilities. [ABSTRACT FROM AUTHOR]

Simultaneous confidence intervals (SCI) for multinomial proportions are a corner stone in count data analysis and a key component in many applications. A variety of schemes were introduced over the years, mostly focussing on an asymptotic regime where the sample is large and the alphabet size is relatively small. In this work we introduce a new SCI framework which considers the large alphabet setup. Our proposed framework utilises bootstrap sampling with the Good-Turing probability estimator as a plug-in distribution. We demonstrate the favourable performance of our proposed method in synthetic and real-world experiments. Importantly, we provide an exact analytical expression for the bootstrapped statistic, which replaces the computationally costly sampling procedure. Our proposed framework is publicly available at the first author's Github page. [ABSTRACT FROM AUTHOR]

Longitudinal studies involving nominal outcomes are carried out in various scientific areas. These outcomes are frequently modelled using a generalized linear mixed modelling (GLMM) framework. This widely used approach allows for the modelling of the hierarchy in the data to accommodate different degrees of overdispersion. In this article, a combined model (CM) that takes into account overdispersion and clustering through two separate sets of random effects is formulated. Maximum likelihood estimation with analytic-numerical integration is used to estimate the model parameters. To examine the relative performance of the CM and the GLMM, simulation studies were carried out, exploring scenarios with different sample sizes, types of random effects, and overdispersion. Both models were applied to a real dataset obtained from an experiment in agriculture. We also provide an implementation of these models through SAS code. [ABSTRACT FROM AUTHOR]

The article focuses on the detailed formulation of the generative process for SpCoSLAM and SpCoNavi as represented by their graphical models. Topics include the use of various probability distributions in defining the models, the motion and measurement models in SLAM, and the approximation of probability distributions for specific components.

The multivariate inverse hypergeometric (MIH) distribution is an extension of the negative multinomial (NM) model that accounts for sampling without replacement in a finite population. Even though most studies on longitudinal count data with a specific number of 'failures' occur in a finite setting, the NM model is typically chosen over the more accurate MIH model. This raises the question: How much information is lost when inferring with the approximate NM model instead of the true MIH model? The loss is quantified by a measure called deficiency in statistics. In this paper, asymptotic bounds for the deficiencies between MIH and NM experiments are derived, as well as between MIH and the corresponding multivariate normal experiments with the same mean-covariance structure. The findings are supported by a local approximation for the log-ratio of the MIH and NM probability mass functions, and by Hellinger distance bounds. [ABSTRACT FROM AUTHOR]

Trend scoring constructed response items (i.e. rescoring Time A responses at Time B) gives rise to two-way data that follow a product multinomial distribution rather than the multinomial distribution that is usually assumed. Recent work has shown that the difference in sampling model can have profound negative effects on statistics usually used to monitor rater drift. In this paper, three statistics, termed E-statistics, that account for the product-multinomial sampling by comparing conditional distributions, are introduced. A simulation compares performance with the paired t-test and Stuart's Q in detecting rater drift. Both the paired t-test and Q suffered extreme Type I error inflation for certain rescore study designs. The new E-statistics maintained good Type I error control and had good power to detect rater drift across occasions. [ABSTRACT FROM AUTHOR]

The 2×2$$ 2\times 2 $$ table with a structural zero represents a common scenario in clinical trials and epidemiology, characterized by a specific empty cell. In such cases, the risk ratio serves as a vital parameter for statistical inference. However, existing confidence intervals, such as those constructed through the score test and Bayesian methods, fail to achieve the prescribed nominal level. Our focus is on numerically constructing exact confidence intervals for the risk ratio. We achieve this by optimally combining the modified inferential model method and the h$$ h $$‐function method. The resulting interval is then compared with intervals generated by four existing methods: the score method, the exact score method, the Bayesian tailed‐based method and the inferential model method. This comparison is conducted based on the infimum coverage probability, average interval length and non‐coverage probability criteria. Remarkably, our proposed interval outperforms other exact intervals, being notably shorter. To illustrate the effectiveness of our approach, we discuss two examples in detail. [ABSTRACT FROM AUTHOR]

Non‐invasive methods have largely replaced biopsy to identify advanced fibrosis in hepatitis C virus (HCV). Guidelines vary regarding testing strategy to balance accuracy, costs and loss to follow‐up. Although individual test characteristics are well‐described, data comparing the accuracy of using two tests together are limited. We calculated combined test characteristics to determine the utility of combined strategies. This study synthesizes empirical data from fibrosis staging trials and the literature to estimate test characteristics for Fibrosis‐4 (FIB4), APRI or a commercial serum panel (FibroSure®), followed by transient elastography (TE) or FibroSure®. We simulated two testing strategies: (1) second test only for those with intermediate first test results (staged approach), and (2) second test for all. We summarized empiric data with multinomial distributions and used this to estimate test characteristics of each strategy on a simulated population of 10,000 individuals with 4.2% cirrhosis prevalence. Negative predictive value (NPV) for cirrhosis from a single test ranged from 98.2% (95% CB 97.6–98.8%) for FIB‐4 to 99.4% (95% CB 99.0–99.8%) for TE. Using a staged approach with TE second, sensitivity for cirrhosis rose to 93.3–96.9%, NPV to 99.7–99.8%, while PPV dropped to <32%. Using TE as a second test for all minimally changed estimated test characteristics compared with the staged approach. Combining two non‐invasive fibrosis tests barely improves NPV and decreases or does not change PPV compared with a single test, challenging the utility of serial testing modalities. These calculated combined test characteristics can inform best methods to identify advanced fibrosis in various populations. [ABSTRACT FROM AUTHOR]

Shannon entropy is the most common metric for assessing the degree of randomness of time series in many fields, ranging from physics and finance to medicine and biology. Real-world systems are typically non-stationary, leading to entropy values fluctuating over time. This paper proposes a hypothesis testing procedure to test the null hypothesis of constant Shannon entropy in time series data. The alternative hypothesis is a significant variation in entropy between successive periods. To this end, we derive an unbiased sample entropy variance, accurate up to the order O (n - 4) with n the sample size. To characterize the variance of the sample entropy, we first provide explicit formulas for the central moments of both binomial and multinomial distributions describing the distribution of the sample entropy. Second, we identify the optimal rolling window length to estimate time-varying Shannon entropy. We optimize this choice using a novel self-consistent criterion based on counting significant entropy variations over time. We corroborate our findings using the novel methodology to assess time-varying regimes of entropy for stock price dynamics by presenting a comparative analysis between meme and IT stocks in 2020 and 2021. We show that low entropy values correspond to periods when profitable trading strategies can be devised starting from the symbolic dynamics used for entropy computation, namely periods of market inefficiency. [ABSTRACT FROM AUTHOR]

Applying analytic approximations for computing multivariate normal cumulative distribution functions has led to a substantial improvement in the estimability of mixed multinomial probit models, both in terms of accuracy and especially in terms of computation time. This paper makes a contribution by presenting a possible way to improve the accuracy of estimating mixed multinomial probit model covariances based on the idea of parameter selection using cross-validation. Comparisons to the MACML approach indicate that the proposed parameter selection approach is able to recover covariance parameters more accurately, even when there is a moderate degree of independence between the random coefficients. The approach also estimates parameters efficiently, with standard errors tending to be smaller than those of the MACML approach, which can be observed by means of a real data case. [ABSTRACT FROM AUTHOR]

This research discusses the effects of large round‐off errors on the performance of control charts for means when a process is normally distributed with a known variance and a fixed sample size. Quality control in practice uses control charts for means as a process monitoring tool, even when the data is significantly rounded. The objective of this research is to demonstrate how ignoring the round‐off errors and using a standard Shewhart chart affects the quality control of a measured process. The first part of the research includes theoretical calculations for estimating the values of alpha and beta, relating to the unrounded data and the large‐rounded data. For the rounded data, normality can no longer be assumed because the data is discrete; therefore, the multinomial distribution is used. The results show that given an in‐control process, alpha indicates that false alarms are more frequent, whereas given an out‐of‐control process, the influence on beta is minor and inconsistent. For some rounding levels, there is a decline in the control chart performances, and in others, there is an improvement. In the second part, a simulation study is used to evaluate the performances of the control chart based on a single sample, checking whether the conclusion (reject or fail to reject) for a sample is consistent for rounded and unrounded data. The results of the simulation match the theoretical calculations. [ABSTRACT FROM AUTHOR]

Clustered competing risks data are a complex failure time data scheme. Its main characteristics are the cluster structure, which implies a latent within-cluster dependence between its elements, and its multiple variables competing to be the one responsible for the occurrence of an event, the failure. To handle this kind of data, we propose a full likelihood approach, based on generalized linear mixed models instead the usual complex frailty model. We model the competing causes in the probability scale, in terms of the cumulative incidence function (CIF). A multinomial distribution is assumed for the competing causes and censorship, conditioned on the latent effects that are accommodated by a multivariate Gaussian distribution. The CIF is specified as the product of an instantaneous risk level function with a failure time trajectory level function. The estimation procedure is performed through the R package Template Model Builder, an C++ based framework with efficient Laplace approximation and automatic differentiation routines. A large simulation study was performed, based on different latent structure formulations. The model fitting was challenging and our results indicated that a latent structure where both risk and failure time trajectory levels are correlated is required to reach reasonable estimation. [ABSTRACT FROM AUTHOR]

This note presents a refined local approximation for the logarithm of the ratio between the negative multinomial probability mass function and a multivariate normal density, both having the same mean–covariance structure. This approximation, which is derived using Stirling's formula and a meticulous treatment of Taylor expansions, yields an upper bound on the Hellinger distance between the jittered negative multinomial distribution and the corresponding multivariate normal distribution. Upper bounds on the Le Cam distance between negative multinomial and multivariate normal experiments ensue. [ABSTRACT FROM AUTHOR]

Remaining useful life (RUL) prediction is an important issue in prognostics and health management (PHM). Numerous studies have been conducted to construct degradation models for RUL prediction. However, their models fail to handle the scenarios where multiple failure modes exist, especially when the failure modes are unknown (unlabeled) beforehand and need to be recognized. This paper develops a multimodal recognition and prognostic method based on features extracted via multisensor degradation modeling. Specifically, we assume the failure mode of a unit follows a multinomial distribution. Given the failure mode distribution, we characterize the degradation status of the unit via degradation models based on each sensor signal and a constructed health index (HI). Our innovative idea is to extract features as the derivatives of the degradation status to comprehensively utilize information from multiple sensors for more effective failure mode recognition and RUL prediction. We develop a fusion coefficient-integrated expectation-maximization (FCIEM) algorithm to estimate model parameters by using data from historical units. Finally, we recognize the failure mode and predict the RUL of in-service units based on their extracted features and degradation status. Numerical experiments and a case study of aircraft engines were conducted to evaluate the performance of our proposed method. [ABSTRACT FROM AUTHOR]

As a sustainable mode of travel, carpooling is an effective solution to environmental and energy problems, but it has not been fully utilized. The research on carpooling attitudes, especially for college students, still needs to be improved. In response to this problem, this paper aims to investigate the effect of personal attributes, travel attributes, attitude attributes and other attributes of students on carpooling attitudes in China. To collect the data, an online questionnaire survey was implemented at Shenzhen University, and 514 students participated. Based on the samples, the multinomial logit model is used to explore the contribution of all variables. The model results showed that personal attributes such as sex and age had no significant effect on the attitude of college students towards carpooling. The safety of carpooling and its high cost make college students have a neutral attitude towards it. The most concerning factor for college students in carpooling is comfort. These findings can provide valuable suggestions for measures to be taken in response to different attributes affecting students' attitudes and are particularly important for the university and government to make optimal decisions to motivate students to select carpooling. [ABSTRACT FROM AUTHOR]

We use transaction data of active individual investors in mutual funds to examine whether investors are momentum or contrarian by combining binomial distribution with the multinomial logit model. We find that individual investors adopt different trading strategies in making their purchase and redemption decisions, whereby they act as momentum buyers and contrarian sellers. Different fund styles do not affect investors' trading decisions based on historical returns, and investors' trading behaviours in value and dividend funds are consistent. After identifying each investor's trading strategy, we examine the impact of demographics on trading behaviour for the first time. We find that older individual investors in mutual funds are more likely to be momentums, as are those with stock trading experience. Individual investors with large transaction sizes are more likely to be momentum buyers, while investors of small sizes are contrarian. Our research not only helps managers understand the trading behaviour of individual investors but also provides some help to regulators. [ABSTRACT FROM AUTHOR]

Based on the decoupling theory, this paper analyzes the relationship between the embodied carbon productivity and the embodied value added in China's industrial sectors, evaluates the development mode of the sectors, and explores a reasonable path to promote the green and low-carbon transformation of the sectors based on the panel multinomial logit model. The empirical conclusions are as follows: (i) Except for the decrease in 2002–2005, the embodied carbon productivity achieved rapid growth in other time periods; during the period of 2002–2020, the embodied value added increased by 339.59 percentage points, with an average annual growth rate of 8.57%, and the embodied carbon productivity increased by 70.59 percentage points, with an average annual growth rate of 3.01%. (ii) As the embodied value added of the 28 industrial subsectors expanded, the changes in their embodied carbon productivity were different. This process can be roughly classified into three main phases: The first phase is the extensive growth period of 2002–2005, in which the embodied carbon productivity of most industrial subsectors declined while the embodied value added expanded; the second phase is the low-carbon transformation and development period of 2005–2012, during which the recessive positive-efficiency emission reduction became the dominant mode; and the third phase is the low-carbon development period of 2012–2020, in which the high-efficiency emission reduction became the dominant mode. (iii) When the industrial sectors are in an expansive state, increasing the substitution of capital for energy factors will make the transformation of industrial sectors more inclined to expansive high-efficiency emission reduction mode, and when the industrial sectors fall into recession, optimizing the energy structure will produce the same effect. [ABSTRACT FROM AUTHOR]

The goal of the paper is to analyze a Gaudin model for a polynomial representation of the Kohno–Drinfeld Lie algebra associated with the multinomial distribution. The main result is the construction of an explicit basis of the space of polynomials consisting of common eigenfunctions of Gaudin operators in terms of Aomoto–Gelfand hypergeometric series. The construction shows that the polynomials in this basis are also common eigenfunctions of the operators for a dual Gaudin model acting on the degree indices, and therefore, they provide a solution to a multivariate discrete bispectral problem. [ABSTRACT FROM AUTHOR]

The probabilistic topic model imposes a low-rank structure on the expectation of the corpus matrix. Therefore, singular value decomposition (SVD) is a natural tool of dimension reduction. We propose an SVD-based method for estimating a topic model. Our method constructs an estimate of the topic matrix from only a few leading singular vectors of the data matrix, and has a great advantage in memory use and computational cost for large-scale corpora. The core ideas behind our method include a pre-SVD normalization to tackle severe word frequency heterogeneity, a post-SVD normalization to create a low-dimensional word embedding that manifests a simplex geometry, and a post-SVD procedure to construct an estimate of the topic matrix directly from the embedded word cloud. We provide the explicit rate of convergence of our method. We show that our method attains the optimal rate in the case of long and moderately long documents, and it improves the rates of existing methods in the case of short documents. The key of our analysis is a sharp row-wise large-deviation bound for empirical singular vectors, which is technically demanding to derive and potentially useful for other problems. We apply our method to a corpus of Associated Press news articles and a corpus of abstracts of statistical papers. for this article are available online. [ABSTRACT FROM AUTHOR]

Sentiment analysis is increasingly pivotal in natural language processing (NLP), crucial for deciphering public opinions across diverse sectors. This research conducts a comparative examination of rule-based and machine learning (ML) methods in sentiment analysis, specifically targeting the Kazakh language. Given the Kazakh language's limited exposure in computational linguistics, the study meticulously evaluates datasets from news articles, literature, and Amazon product reviews, aiming to compare the efficiency, adaptability, and overall performance of these distinct approaches. Employing a detailed set of evaluation metrics such as accuracy, precision, recall, and computational efficiency, the study provides a comprehensive analysis of the strengths and limitations of rule-based techniques versus ML models like Logistic Regression, Multinomial Naive Bayes, Decision Trees, Random Forest, and XGBoost. The findings suggest rule-based methods excel in identifying nuanced emotional expressions within literary texts, while ML models demonstrate superior adaptability and robustness, particularly effective in handling the linguistic variations found in news and reviews. Despite the strengths identified, the study also reveals significant limitations of the rulebased approach, especially in broader contexts beyond literary analysis. This highlights an imperative for future research to integrate sentiment dictionaries or domain-specific lexicons that cater to a wider array of linguistic styles, potentially enhancing sentiment analysis tools' applicability in Kazakh and similar less-studied languages. This investigation contributes significantly to the sentiment analysis discourse, offering invaluable insights for both researchers and practitioners by elucidating the complexities of applying NLP technologies across diverse linguistic landscapes, thus advancing the understanding and methodologies of sentiment analysis in the Kazakh language context. [ABSTRACT FROM AUTHOR]

This paper presents a new probabilistic coordinated search technique for finding a randomly located target in n-disjoint known regions using n-searchers. Each region contains one searcher. The searchers use advanced technology to communicate with each other. This paper aims to obtain the candidate utility function, namely the expected value of the time for detecting the target, and minimize this expected value considering a restricted amount of time. We present a particular case when the target has a multinomial distribution, which is essential for searching for a valuable target that is missing at sea or lost in a wilderness area. [ABSTRACT FROM AUTHOR]

We study the asymptotic behaviour of the expectation of the maxima and minima of a random assignment process generated by a large matrix with multinomial entries. A variety of results is obtained for different sparsity regimes. [ABSTRACT FROM AUTHOR]

How animals use the diel period (24‐h light–dark cycle) is of fundamental importance to understand their niche. While ecological and evolutionary literature abound with discussion of diel phenotypes (e.g. diurnal, nocturnal, crepuscular, cathemeral), they lack clear and explicit quantitative definitions. As such, inference can be confounded when evaluating hypotheses of animal diel niche switching or plasticity across studies because researchers may be operating under different definitions of diel phenotypes.We propose quantitative definitions of diel phenotypes using four alternative hypothesis sets (maximizing, traditional, general and selection) aimed at achieving different objectives. Each hypothesis set is composed of mutually exclusive hypotheses defined based on the activity probabilities in the three fundamental periods of light availability (twilight, daytime and night‐time).We develop a Bayesian modelling framework that compares diel phenotype hypotheses using Bayes factors and estimates model parameters using a multinomial model with linear inequality constraints. Model comparison, parameter estimation and visualizing results can be done in the Diel.Niche R package. A simplified R Shiny web application is also available.We provide extensive simulation results to guide researchers on the power to discriminate among hypotheses for a range of sample sizes (10–1280). We also work through several examples of using data to make inferences on diel activity, and include online vignettes on how to use the Diel.Niche package. We demonstrate how our modelling framework complements other analyses, such as circular kernel density estimators and animal movement modelling.Our aim is to encourage standardization of the language of diel activity and bridge conceptual frameworks and hypotheses in diel research with data and models. Lastly, we hope more research focuses on the ecological and conservation importance of understanding how animals use diel time. [ABSTRACT FROM AUTHOR]

The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is obtained through two approaches: one involves tracing out the environment from a bosonic eigenstate of the combined environment and system of interest (the empirical approach), while the other involves tracing out the environment from the mixed state of the combined environment and system of interest (the Bayesian approach). In the thermodynamic limit, the two coincide and are equal to the multinomial distribution. Furthermore, the paper proposes to identify the physical entropy of the bosonic system with the Shannon entropy of the occupancy numbers, fixing certain contradictions that arise in the classical analysis of thermodynamic entropy. Finally, by leveraging an information-theoretic inequality between the entropy of the multinomial distribution and the entropy of the multivariate hypergeometric distribution, Bayesianism of information theory and empiricism of statistical mechanics are integrated into a common "infomechanical" framework. [ABSTRACT FROM AUTHOR]

This manuscript provides a comprehensive exploration of Probabilistic latent semantic analysis (PLSA), highlighting its strengths, drawbacks, and challenges. The PLSA, originally a tool for information retrieval, provides a probabilistic sense for a table of co-occurrences as a mixture of multinomial distributions spanned over a latent class variable and adjusted with the expectation–maximization algorithm. The distributional assumptions and the iterative nature lead to a rigid model, dividing enthusiasts and detractors. Those drawbacks have led to several reformulations: the extension of the method to normal data distributions and a non-parametric formulation obtained with the help of Non-negative matrix factorization (NMF) techniques. Furthermore, the combination of theoretical studies and programming techniques alleviates the computational problem, thus making the potential of the method explicit: its relation with the Singular value decomposition (SVD), which means that PLSA can be used to satisfactorily support other techniques, such as the construction of Fisher kernels, the probabilistic interpretation of Principal component analysis (PCA), Transfer learning (TL), and the training of neural networks, among others. We also present open questions as a practical and theoretical research window. [ABSTRACT FROM AUTHOR]

Recent technological developments suggest that sooner or later, Artificial Intelligence (AI) will become an indispensable technology. With the developed countries leading in the development and deployment of AI, it is therefore a plausible claim that students and recent graduates of schools in the Global North may be familiar with the technology. For Africa, this is unclear. This paper therefore assesses the level of fresh graduates' awareness and their level of preparedness for prospects, issues and possible threat that AI may pose in their future work life. Specifically, the project profiles students according to their current level of AI understanding, assesses students' perception of its potential threat and assesses their level of preparedness to use the technology. A total of 112 recent graduates from various Nigerian tertiary institutions serving in the mandatory National Youths' Service Corps (NYSC) were randomly selected to respond to fill the survey. Descriptive Statistics and Multinomial Logit Model were analytical techniques. Results show that most of the graduates are essentially ignorant or unsure of the threat of AI to their lives and especially for the foreseeable future. These categories of graduates are within the ranks of class lower than First Class. Further, almost all the graduates are unaware of any policy concerns of the government on ICT and AI. Nevertheless, almost all of them were willing to pay to learn about AI. The apparent ignorance of the potentials -- positive or negative -- of AI among the graduates in the case study country of Nigeria reveals a deficiency in curricula and highlights the need for a more robust policy response from government. The study raises significant concerns and questions about not only the currency of higher education curricula in Nigeria, but also in Africa broadly, in addition to young people's readiness to survive and thrive in the digital future of work. [ABSTRACT FROM AUTHOR]

Species-abundance distribution (SAD) is essential in understanding the formation and maintenance mechanisms of species diversity. In alpine meadows, aspect affects almost all biological and ecological processes. Therefore, the soil ciliate data obtained by Illumina MiSeq sequencing were used to explore the characteristics of SADs to the soil ciliate communities on different aspects in alpine meadows (south aspect, southwest aspect, west aspect, northwest aspect, north aspect; SA, SWA, WA, NWA, NA, respectively). Statistical models: Log-series model (LSM) and Log-normal model (LNORM), Niche models: Broken stick model (BSM) and Geometric series model (GSM), and a neutral theory model: Meta-community zero-sum multinomial distribution model (MZSM) were selected to fit the soil ciliate data for analysis. The results showed that: (1) the number of common species increased and then decreased from SA to NA, the number of rare species changed in the opposite trend; (2) BSM and GSM were able to fit the SAD of overall soil ciliates species on different aspects, while MZSM was rejected on all aspects, indicating that the niche process dominated the formation of soil ciliate communities in the alpine meadows, and the resource allocation pattern was dominated by fixed allocation; (3) best-fit models for common species were GSM and BSM which were consistent with best-fit models for all species, while the best-fit model for rare species was LNORM, common species dominated the formation of SAD on different aspects and had an irreplaceable role in maintaining community productivity and stability. [ABSTRACT FROM AUTHOR]

Consider a finite sample from an unknown multinomial distribution. Inferring the underlying multinomial parameters is a basic problem in statistics and related fields. Currently known methods focus on classical regimes where the sample is large, or both the sample and the alphabet are small. In this work we study the complementary large alphabet regime, as we consider the case where the number of samples is comparable with (or even smaller than) the alphabet size. We introduce a novel inference scheme that significantly improves upon currently known methods. Our proposed scheme is robust, easy to apply and provides favourable performance guarantees. [ABSTRACT FROM AUTHOR]

Weighting data appropriately in stock assessment models is necessary to diagnose model mis-specification, estimate uncertainty, and when combining data sets. Age- and length-composition data are often fitted using a multinomial distribution and then reweighted iteratively, and the Dirichlet-multinomial ("DM") likelihood provides a model-based alternative that estimates an additional parameter and thereby "self-weights" data. However, the DM likelihood requires specifying an input sample size (n input), which is often unavailable and results are sensitive to n input. We therefore introduce the multivariate-Tweedie (MVTW) as alternative with three benefits: (1) it can identify both overdispersion (downweighting) or underdispersion (upweighting) relative to the n input; (2) proportional changes in ninput are exactly offset by parameters; and (3) it arises naturally when expanding data arising from a hierarchical sampling design. We use an age-structured simulation to show that the MVTW (1) can be more precise than the DM in estimating data weights, and (2) can appropriately upweight data when needed. We then use a real-world state-space assessment to show that the MVTW can easily be adapted to other software. We recommend that stock assessments explore the sensitivity to specifying DM, MVTW, and logistic-normal likelihoods, particularly when the DM estimates an effective sample size approaching ninput. [ABSTRACT FROM AUTHOR]

This article proposes a method for determining the p-value of correlations in compositional data, i.e., those data that arise as a result of dividing original values by their sum. Data organized in this way are typical for many fields of knowledge, but there is still no consensus on methods for interpreting correlations in such data. In the second decade of the new millennium, almost all newly emerging methods for solving this problem have become based on the log transformation of data. In the method proposed here, there are no log transformations. We return to the early stages of attempting to solve the problem and rely on negative shifts in correlations in the multinomial distribution. In modeling the data, we use a hybrid method that combines the hypergeometric distribution with the distribution of any other law. During our work on the calculation method, we found that the number of degrees of freedom in compositional data measures discretely only when all normalizing sums are equal and that it decreases when the sums are not equal, becoming a continuously varying quantity. Estimation of the number of degrees of freedom and the strength of its influence on the magnitude of the shift in the distribution of correlation coefficients is the basis of the proposed method. [ABSTRACT FROM AUTHOR]

We consider estimator and model choice when estimating abundance from capture–recapture data. Our work is motivated by a mark–recapture distance sampling example, where model and estimator choice led to unexpectedly large disparities in the estimates. To understand these differences, we look at three estimation strategies (maximum likelihood estimation, conditional maximum likelihood estimation, and Bayesian estimation) for both binomial and Poisson models. We show that assuming the data have a binomial or multinomial distribution introduces implicit and unnoticed assumptions that are not addressed when fitting with maximum likelihood estimation. This can have an important effect in finite samples, particularly if our data arise from multiple populations. We relate these results to those of restricted maximum likelihood in linear mixed effects models. [ABSTRACT FROM AUTHOR]

Background: Unplanned hospitalizations among patients with advanced cancer are often sentinel events prompting goals of care discussions and hospice transitions. Late referrals to hospice, especially those at the end of life, are associated with decreased quality of life and higher total health care costs. Inpatient management of patients with solid tumor malignancies is increasingly shifting from oncologists to oncology hospitalists. However, little is known about the impact of oncology hospitalists on the timing of transition to hospice. Objective: To compare hospice discharge rate and time to hospice discharge on an inpatient oncology service led by internal medicine‐trained hospitalists and a service led by oncologists. Methods: At Smilow Cancer Hospital, internal medicine‐trained hospitalists were integrated into one of two inpatient medical oncology services allowing comparison between the new, hospitalist‐led service (HS) and the traditional, oncologist‐led service (TS). Discharges from July 26, 2021, through January 31, 2022, were identified from the electronic medical record. The odds ratio for discharge disposition by team was calculated by logistic regression using a multinomial distribution. Adjusted length of stay before discharge was assessed using multivariable linear regression. Results: The HS discharged 47/400 (11.8%) patients to inpatient hospice, whereas the TS service discharged 18/313 (5.8%), yielding an adjusted odds ratio of 1.94 (95% CI, 1.07–3.51; p =.03). Adjusted average length of stay before inpatient hospice disposition was 6.83 days (95% CI, 4.22–11.06) for the HS and 16.29 days (95% CI, 7.73–34.29) for the TS (p =.003). Conclusions: Oncology hospitalists improve hospice utilization and time to inpatient hospice referral on an inpatient medical oncology service. Plain Language Summary: Patients with advanced cancer are often admitted to the hospital near the end of life. These patients generally have a poor chance of long‐term survival and may prefer comfort‐focused care with hospice.In this study, oncology hospitalists discharged a higher proportion of patients to inpatient hospice with less time spent in the hospital before discharge. Oncology hospitalists improve hospice utilization and time to hospice referral on an inpatient medical oncology service. [ABSTRACT FROM AUTHOR]

In this article, we explore how precise information about migrants' working conditions in their destination countries impacts their decision to migrate again upon returning home. Using household data from Kerala and Tamil Nadu from 2020–21, we study return emigrants (REM) who returned during the first COVID-19 lockdowns in the Gulf Cooperation Council (GCC) countries. Through a binary choice model, we discover that negative experiences in the destination country significantly influence the decision to re-migrate. Specifically, issues with salary payment and reduced working hours make re-migration less likely. We then apply a two-stage multinomial regression to identify the causes of these negative experiences and how they shape a migrant's future decisions. We conclude that such experiences discourage re-migration and increase the preference to work in the country of origin. Our research offers insights for shaping future migration policies in the region. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a hierarchical Bayesian version of the Mixture of Unigrams model for text clustering and approach its posterior inference through variational inference. We compute the explicit expression of the variational objective function for our hierarchical model under a mean-field approximation. We then derive the update equations of a suitable algorithm based on coordinate ascent to find local maxima of the variational target, and estimate the model parameters through the optimized variational hyperparameters. The advantages of variational algorithms over traditional Markov Chain Monte Carlo methods based on iterative posterior sampling are also discussed in detail. [ABSTRACT FROM AUTHOR]

We introduce a new algorithm to compute the difference between values of the log Γ -function in close points, where Γ denotes Euler's gamma function. As a consequence, we obtain a way of computing the Dirichlet-multinomial log-likelihood function which is more accurate, has a better computational complexity and a wider range of application than the previously known ones. [ABSTRACT FROM AUTHOR]

The Poisson multinomial distribution (PMD) describes the distribution of the sum of n independent but non-identically distributed random vectors, in which each random vector is of length m with 0/1 valued elements and only one of its elements can take value 1 with a certain probability. Those probabilities are different for the m elements across the n random vectors, and form an n × m matrix with row sum equals to 1. We call this n × m matrix the success probability matrix (SPM). Each SPM uniquely defines a PMD . The PMD is useful in many areas such as, voting theory, ecological inference, and machine learning. The distribution functions of PMD , however, are usually difficult to compute and there is no efficient algorithm available for computing it. In this paper, we develop efficient methods to compute the probability mass function (pmf) for the PMD using multivariate Fourier transform, normal approximation, and simulations. We study the accuracy and efficiency of those methods and give recommendations for which methods to use under various scenarios. We also illustrate the use of the PMD via three applications, namely, in ecological inference, uncertainty quantification in classification, and voting probability calculation. We build an R package that implements the proposed methods, and illustrate the package with examples. This paper has online supplementary materials. [ABSTRACT FROM AUTHOR]

In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distribution of the network and prove that it is necessary and sufficient for ergodicity that the expected occupancy time for each batch be finite. Further, we recover recurrence relations for the transient probability mass function formulated in terms of a distribution obtained by compounding the batch size with a multinomial distribution. [ABSTRACT FROM AUTHOR]

The multibridgeR package allows a Bayesian evaluation of informed hypotheses H r applied to frequency data from an independent binomial or multinomial distribution. multibridge uses bridge sampling to efficiently compute Bayes factors for the following hypotheses concerning the latent category proportions 휃: (a) hypotheses that postulate equality constraints (e.g., 휃1 = 휃2 = 휃3); (b) hypotheses that postulate inequality constraints (e.g., 휃1 < 휃2 < 휃3 or 휃1 > 휃2 > 휃3); (c) hypotheses that postulate combinations of inequality constraints and equality constraints (e.g., 휃1 < 휃2 = 휃3); and (d) hypotheses that postulate combinations of (a)–(c) (e.g., 휃1 < (휃2 = 휃3),휃4). Any informed hypothesis H r may be compared against the encompassing hypothesis H e that all category proportions vary freely, or against the null hypothesis H 0 that all category proportions are equal. multibridge facilitates the fast and accurate comparison of large models with many constraints and models for which relatively little posterior mass falls in the restricted parameter space. This paper describes the underlying methodology and illustrates the use of multibridge through fully reproducible examples. [ABSTRACT FROM AUTHOR]

When the cells are ordinal in the multinomial distribution, i.e., when cells have a natural ordering, guaranteeing that the borrowing information among neighboring cells makes sense conceptually. In this paper, we introduce a novel probability distribution for borrowing information among neighboring cells in order to provide reliable estimates for cell probabilities. The proposed smoothed Dirichlet distribution forces the probabilities of neighboring cells to be closer to each other than under the standard Dirichlet distribution. Basic properties of the proposed distribution, including normalizing constant, moments, and marginal distributions, are developed. Sample generation of smoothed Dirichlet distribution is discussed using the acceptance-rejection algorithm. We demonstrate the performance of the proposed smoothed Dirichlet distribution using 2018 Major League Baseball (MLB) batters data. [ABSTRACT FROM AUTHOR]

Abstract At some moment in our lives, we are probably faced with the following question: How likely is it that you would recommend [company X] to a friend or colleague?. This question is related to the Net Promoter Score (NPS), a simple measure used by several companies as indicator of customer loyalty. Even though it is a well-known measure in the business world, studies that address the statistical properties or the sample size determination problem related to this measure are still scarce. We adopt a Bayesian approach to provide point and interval estimators for the NPS and discuss the determination of the sample size. Computational tools were implemented to use this methodology in practice. An illustrative example with data from financial services is also presented.

ABSTRACT Sampling is an essential step in estimating a parameter: thus, cost and time associated to this step should be minimized. Sequential sampling is characterized by using samples of variable sizes given as a function of observations, and sequential sampling provides a smaller sample size than a fixed-size sample in most cases. In addition, the Bayesian decision theory can be incorporated into sequential sampling to perform parameter estimation because it allows the inclusion of a priori information about the parameter of interest, which optimizes the procedure. However, the great challenge to performing the Bayesian sequential estimation in establishing the stopping criteria. Most studies in this area investigate binomial distributions, while few analyze multinomial distributions. This study aimed to define the stopping criteria for the Bayesian sequential estimation of the parameters of multinomial distributions with conjugate Dirichlet priors. The proposed methodology was applied to a set of X-ray test data for quality control of maize seed lots. This test uses conventional sampling techniques in which a sample has a fixed size with 200 seeds. The influence of two priors on the stopping criteria was evaluated, one uniform and one conjugate, with hyperparameters based on reference information from the literature. The results indicated a reduction in the sample size in most lots evaluated.

Sentiment analysis is widely used in cases of text processing and comments. One of the case studies is about the analysis of a hotel review by the public. The method used in analyzing a sentiment from comments or reviews of a hotel is the Naïve Bayes Classifier. One that can be used is the Multinomial Naïve Bayes method. In improving the results of the accuracy of the method required an optimization method. There are many optimization methods that can be applied to algorithms in sentiment analysis case studies. One well-known method is Particle Swarm Optimization (PSO). This study aims to determine the effect of PSO optimization on the Multinomial Naïve Bayes algorithm in the case of sentiment analysis. From the results of optimization and model testing, the highest accuracy was obtained in the Multinomial Naïve Bayes test with PSO optimization as hyperparameter tunning and feature selection of 97%. [ABSTRACT FROM AUTHOR]

Ordinal patterns serve as a robust symbolic transformation technique, enabling the unveiling of latent dynamics within time series data. This methodology involves constructing histograms of patterns, followed by the calculation of both entropy and statistical complexity—an avenue yet to be fully understood in terms of its statistical properties. While asymptotic results can be derived by assuming a multinomial distribution for histogram proportions, the challenge emerges from the non-independence present in the sequence of ordinal patterns. Consequently, the direct application of the multinomial assumption is questionable. This study focuses on the computation of the asymptotic distribution of permutation entropy, considering the inherent patterns' correlation structure. Furthermore, the research delves into a comparative analysis, pitting this distribution against the entropy derived from a multinomial law. We present simulation algorithms for sampling time series with prescribed histograms of patterns and transition probabilities between them. Through this analysis, we better understand the intricacies of ordinal patterns and their statistical attributes. [ABSTRACT FROM AUTHOR]