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This study investigates wind speed prediction using advanced machine learning techniques, comparing the performance of Vanilla long short-term memory (LSTM) and convolutional neural network (CNN) models, alongside the application of extreme value theory (EVT) using the r-largest order generalised extreme value distribution ( G E V D r ). Over the past couple of decades, the academic literature has transitioned from conventional statistical time series models to embracing EVT and machine learning algorithms for the modelling of environmental variables. This study adds value to the literature and knowledge of modelling wind speed using both EVT and machine learning. The primary aim of this study is to forecast wind speed in the Limpopo province of South Africa to showcase the dependability and potential of wind power generation. The application of CNN showcased considerable predictive accuracy compared to the Vanilla LSTM, achieving 88.66% accuracy with monthly time steps. The CNN predictions for the next five years, in m/s, were 9.91 (2024), 7.64 (2025), 7.81 (2026), 7.13 (2027), and 9.59 (2028), slightly outperforming the Vanilla LSTM, which predicted 9.43 (2024), 7.75 (2025), 7.85 (2026), 6.87 (2027), and 9.43 (2028). This highlights CNN's superior ability to capture complex patterns in wind speed dynamics over time. Concurrently, the analysis of the G E V D r across various order statistics identified G E V D r = 2 as the optimal model, supported by its favourable evaluation metrics in terms of Akaike information criteria (AIC) and Bayesian information criteria (BIC). The 300-year return level for G E V D r = 2 was found to be 22.89 m/s, indicating a rare wind speed event. Seasonal wind speed analysis revealed distinct patterns, with winter emerging as the most efficient season for wind, featuring a median wind speed of 7.96 m/s. Future research could focus on enhancing prediction accuracy through hybrid algorithms and incorporating additional meteorological variables. To the best of our knowledge, this is the first study to successfully combine EVT and machine learning for short- and long-term wind speed forecasting, providing a novel framework for reliable wind energy planning. [ABSTRACT FROM AUTHOR]

This study investigates wind speed prediction using advanced machine learning techniques, comparing the performance of Vanilla long short-term memory (LSTM) and convolutional neural network (CNN) models, alongside the application of extreme value theory (EVT) using the r-largest order generalised extreme value distribution (GEVDr). Over the past couple of decades, the academic literature has transitioned from conventional statistical time series models to embracing EVT and machine learning algorithms for the modelling of environmental variables. This study adds value to the literature and knowledge of modelling wind speed using both EVT and machine learning. The primary aim of this study is to forecast wind speed in the Limpopo province of South Africa to showcase the dependability and potential of wind power generation. The application of CNN showcased considerable predictive accuracy compared to the Vanilla LSTM, achieving 88.66% accuracy with monthly time steps. The CNN predictions for the next five years, in m/s, were 9.91 (2024), 7.64 (2025), 7.81 (2026), 7.13 (2027), and 9.59 (2028), slightly outperforming the Vanilla LSTM, which predicted 9.43 (2024), 7.75 (2025), 7.85 (2026), 6.87 (2027), and 9.43 (2028). This highlights CNN’s superior ability to capture complex patterns in wind speed dynamics over time. Concurrently, the analysis of the GEVDr across various order statistics identified GEVDr=2 as the optimal model, supported by its favourable evaluation metrics in terms of Akaike information criteria (AIC) and Bayesian information criteria (BIC). The 300-year return level for GEVDr=2 was found to be 22.89 m/s, indicating a rare wind speed event. Seasonal wind speed analysis revealed distinct patterns, with winter emerging as the most efficient season for wind, featuring a median wind speed of 7.96 m/s. Future research could focus on enhancing prediction accuracy through hybrid algorithms and incorporating additional meteorological variables. To the best of our knowledge, this is the first study to successfully combine EVT and machine learning for short- and long-term wind speed forecasting, providing a novel framework for reliable wind energy planning.

The COVID-19 pandemic has had profound impact, necessitating a deeper understanding of factors influencing virus transmission. The negative impacts have weakened the economy and changed billions of lives around the world. COVID-19 is a new virus, and a lot of studies have tried to investigate its effect on, for example, the economy or environment. This research reveals new approaches to recognizing and stopping the spread of this virus with its connection to weather conditions and relevant parameters. By analyzing how temperature and humidity affect COVID-19 spread, alongside evaluating the effectiveness of initial public policies, this study addresses the critical gap in research by investigating the interplay between climate conditions and government regulations during the early stages of the pandemic in South Korea. This dual approach provides a comprehensive framework for understanding how environmental and policy factors jointly influence pandemic dynamics, offering valuable lessons for future global health crises. Although it focuses only on the first phase of South Korea COVID-19 regulations, outcomes show that these regulations were notably effective against the COVID-19 pandemic. The outcomes prove that higher temperature and higher relative humidity lead to lower transmission. Hence, based on the results during winter, the number of infections would be expected to speed up again.

Statistical hypothesis testing, as formalized by 20th century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in many scientific disciplines. We demonstrate in this paper how many of the worrisome aspects of statistical hypothesis testing can be ameliorated with concepts and methods from evidential analysis. The model family we treat is the familiar normal linear model with fixed effects, embracing multiple regression and analysis of variance, a warhorse of everyday science in labs and field stations. Questions about study design, the applicability of the null hypothesis, the effect size, error probabilities, evidence strength, and model misspecification become more naturally housed in an evidential setting. We provide a completely worked example featuring a two-way analysis of variance. [ABSTRACT FROM AUTHOR]

Earth's surface velocities are routinely extracted from Global Navigation Satellite System (GNSS) position time series. In addition to velocity estimates, acceleration may be a crucial parameter for modeling non-linear motion. Typically, a statistical hypothesis test is employed to evaluate the significance of the involved parameters and guide the selection of the appropriate model. In this contribution, we formulate a statistical test procedure from the generalized likelihood ratio test to analyze the significance of the acceleration in the model. The proposed procedure is compared with results obtained using the Akaike Information Criterion and Bayesian Information Criterion. Additionally, Minimal Detectable Horizontal Acceleration is provided as an indicator of the sensitivity of the acceleration detection. The GNSS time series of position estimates from the Nevada Geodetic Laboratory were used for this study. The experiments demonstrated a good agreement between the statistical test proposed and the information criteria approach. Therefore, the proposed statistical test may be another criterion to help the user in the important task of model selection. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has had profound impact, necessitating a deeper understanding of factors influencing virus transmission. The negative impacts have weakened the economy and changed billions of lives around the world. COVID-19 is a new virus, and a lot of studies have tried to investigate its effect on, for example, the economy or environment. This research reveals new approaches to recognizing and stopping the spread of this virus with its connection to weather conditions and relevant parameters. By analyzing how temperature and humidity affect COVID-19 spread, alongside evaluating the effectiveness of initial public policies, this study addresses the critical gap in research by investigating the interplay between climate conditions and government regulations during the early stages of the pandemic in South Korea. This dual approach provides a comprehensive framework for understanding how environmental and policy factors jointly influence pandemic dynamics, offering valuable lessons for future global health crises. Although it focuses only on the first phase of South Korea COVID-19 regulations, outcomes show that these regulations were notably effective against the COVID-19 pandemic. The outcomes prove that higher temperature and higher relative humidity lead to lower transmission. Hence, based on the results during winter, the number of infections would be expected to speed up again. [ABSTRACT FROM AUTHOR]

One of the primary issues that arises in statistical modeling pertains to the assessment of the relative importance of each variable in the model. A variety of techniques have been proposed to quantify variable importance for regression models. However, in the context of best subset selection, fewer satisfactory methods are available. With this motivation, we here develop a variable importance measure expressly for this setting. We investigate and illustrate the properties of this measure, introduce algorithms for the efficient computation of its values, and propose a procedure for calculating p-values based on its sampling distributions. We present multiple simulation studies to examine the properties of the proposed methods, along with an application to demonstrate their practical utility. [ABSTRACT FROM AUTHOR]

We consider the newly developed multinomial mixed-link models for a high-risk intestinal metaplasia (IM) study with DNA methylation data. Different from the traditional multinomial logistic models commonly used for categorical responses, the mixed-link models allow us to select the most appropriate link function for each category. We show that the selected multinomial mixed-link model (Model 1) using the total number of stem cell divisions (TNSC) based on DNA methylation data outperforms the traditional logistic models in terms of cross-entropy loss from ten-fold cross-validations with significant p-values 8.12 × 10 − 4 and 6.94 × 10 − 5 . Based on our selected model, the significance of TNSC's effect in predicting the risk of IM is justified with a p-value less than 10 − 6 . We also select the most appropriate mixed-link models (Models 2 and 3) when an additional covariate, the status of gastric atrophy, is available. When the status is negative, mild, or moderate, we recommend Model 2; otherwise, we prefer Model 3. Both Models 2 and 3 can predict the risk of IM significantly better than Model 1, which justifies that the status of gastric atrophy is informative in predicting the risk of IM. [ABSTRACT FROM AUTHOR]

We consider relative model comparison for the parametric coefficients of an ergodic Lévy driven model observed at high-frequency. Our asymptotics is based on the fully explicit two-stage Gaussian quasi-likelihood function (GQLF) of the Euler-approximation type. For selections of the scale and drift coefficients, we propose explicit Gaussian quasi-AIC and Gaussian quasi-BIC statistics through the stepwise inference procedure, and prove their asymptotic properties. In particular, we show that the mixed-rates structure of the joint GQLF, which does not emerge in the case of diffusions, gives rise to the non-standard forms of the regularization terms in the selection of the scale coefficient, quantitatively clarifying the relation between estimation precision and sampling frequency. Also shown is that the stepwise strategies are essential for both the tractable forms of the regularization terms and the derivation of the asymptotic properties of the Gaussian quasi-information criteria. Numerical experiments are given to illustrate our theoretical findings. [ABSTRACT FROM AUTHOR]

Latent class analysis (LCA) is a cross-sectional latent variable mixture modeling (LVMM) approach. Like all LVMM approaches, LCA aims to find heterogeneity within the population by identifying homogenous subgroups of individuals, with each subgroup (called latent class) possessing a unique set of characteristics that differentiate it from other subgroups. LCA can be carried out with categorical latent and indicator variables. But, LCA is unable to examine the association between respective items and the latent variable among categories of individuals. Multiple-group LCA, in particular, is a useful extension of LCA which enables the testing of homogeneity of the class patterns between groups of the individual through a series of constraints. In this paper, we have performed a multi-group latent class analysis for measuring self reported academic dishonesty among the students of University of Jammu. From the analysis, three general behaviors of academic cheaters are identified as rare, frequent, and instant cheaters. Further, from the multi-group LCA, it is envisaged that female students of University of Jammu are more instantaneous cheaters than male students. Students who are self-reported cheaters from sciences and humanities of the University of Jammu are persistent in cheating whereas from professional courses they are more occasional. [ABSTRACT FROM AUTHOR]

The number of deaths due to road accident is increasing day by day and has become an alarming global problem over the decades. India, with her rising motorization is no stranger to this global catastrophe. In this paper two relatively simple yet powerful and versatile techniques for forecasting time series data, autoregressive integrated moving average method (ARIMA) and exponential smoothing method are used to forecast the number of deaths due to road accidents in India from the year 2022-- 2031. The results based on the two methods are compared and it is found that they are in sync with each other and pre-existing literature. Furthermore, this is a unique attempt to use two time series analysis techniques on the same data and carry out a comparative analysis. The data was collected from the annual report of Ministry of Road Transport and Highways, India (2020) and Accidental Deaths & Suicides in India (ADSI) Report of National Crime Record Bureau (2021). After examining all the probable models, it is observed that ARIMA (2, 2, 2) model and exponential smoothing (M, A, N) model are suitable for the given data. Amongst the two, ARIMA (2, 2, 2) model has a lower AIC and BIC value. Thus, this comes out to be the best model as per our model selection criterion. Further, the study also reveals an upward trend of number of road accidental deaths for the upcoming 10 years in India. [ABSTRACT FROM AUTHOR]

The Auto-regressive Integrated Moving Averages (ARIMA) and Holt-Winters Exponential Smoothing Models are discussed in this article. We also used the AIC and BIC to find the best-fitting ARIMA model for the data and provide population and economic forecasts for future years. For forecasting, we also apply the Holt-Winters Exponential Smoothing Model. The ARIMA (0, 2, 5), (0, 2, 5), (0, 2, 4), (1, 2, 2) and (0, 2, 2) models were also found to be the best-fitting models for India's Total, Urban and Rural population, GDP and Age Dependency Ratio. The ARIMA model is the best-fitted model compared to the Holt-Winters model for the forecasting. The ARIMA model underestimates the total population, whereas the Holt-Winters model overestimates it. Both models overestimate for urban populations and GDP. Rural population and the Age Dependency Ratio are underestimated by both models. [ABSTRACT FROM AUTHOR]

This research study utilizes the Time Series Model analytical approach to investigate and predict the monthly records of female births at the General Hospital in Ukpom Abak, estimating the expected pattern of female births in the Abak Metropolis. Currently, there is a significant neglect of the documentation of female births, leading to a need for more reliable statistics on female births. This lack of data adversely affects the accuracy of predicting the number of daughters born to a female as she progresses through her reproductive age. Furthermore, with rapid population growth, government planners require assistance planning for various aspects such as workforce, education, healthcare facilities, and other essential amenities. Despite the efforts of government agencies such as the Bureau of Statistics to ensure proper birth records, parents have shown reluctance to provide the necessary information. The researcher suggests using time series analysis, which involves collecting well-defined data items obtained through repeated measurements over time, to gain reliable insights into the trends and patterns of female births. The analysis's findings could prove invaluable to governmental planners and other stakeholders managing the population. [ABSTRACT FROM AUTHOR]

PurposeThe association between CVD risk factors and mortality is well established, however, current tools for addressing subgroups have focused on the overall burden of disease. The identification of risky combinations of characteristics may lead to a better understanding of physiologic pathways that underlie morbidity and mortality in older adults.MethodsParticipants included 5067 older adults from the Cardiovascular Health Study, followed for up to 6 years. Using latent class analysis (LCA), we created CV damage phenotypes based on probabilities of abnormal brain infarctions, major echocardiogram abnormalities, N-terminal probrain natriuretic peptide, troponin T, interleukin-6, c reactive-protein, galectin-3, cystatin C. We assigned class descriptions based on the probability of having an abnormality among risk factors, such that a healthy phenotype would have low probabilities in all risk factors. Participants were assigned to phenotypes based on the maximum probability of membership. We used Cox-proportional hazards regression to evaluate the association between the categorical CV damage phenotype and all-cause and CVD-mortality.ResultsThe analysis yielded 5 CV damage phenotypes consistent with the following descriptions: healthy (59%), cardio-renal (11%), cardiac (15%), multisystem morbidity (6%), and inflammatory (9%). All four phenotypes were statistically associated with a greater risk of all-cause mortality when compared with the healthy phenotype. The multisystem morbidity phenotype had the greatest risk of all-cause death (HR: 4.02; 95% CI: 3.44, 4.70), and CVD-mortality (HR: 4.90, 95% CI: 3.95, 6.06).ConclusionsFive CV damage phenotypes emerged from CVD risk factor measures. CV damage across multiple systems confers a greater mortality risk compared to damage in any single domain.

Abstract Introduction The length of hospital stay (LOHS) caused by COVID-19 has imposed a financial burden, and cost on the healthcare service system and a high psychological burden on patients and health workers. The purpose of this study is to adopt the Bayesian model averaging (BMA) based on linear regression models and to determine the predictors of the LOHS of COVID-19. Methods In this historical cohort study, from 5100 COVID-19 patients who had registered in the hospital database, 4996 patients were eligible to enter the study. The data included demographic, clinical, biomarkers, and LOHS. Factors affecting the LOHS were fitted in six models, including the stepwise method, AIC, BIC in classical linear regression models, two BMA using Occam's Window and Markov Chain Monte Carlo (MCMC) methods, and GBDT algorithm, a new method of machine learning. Results The average length of hospitalization was 6.7 ± 5.7 days. In fitting classical linear models, both stepwise and AIC methods (R 2 = 0.168 and adjusted R 2 = 0.165) performed better than BIC (R 2 = 0.160 and adjusted = 0.158). In fitting the BMA, Occam's Window model has performed better than MCMC with R 2 = 0.174. The GBDT method with the value of R 2 = 0.64, has performed worse than the BMA in the testing dataset but not in the training dataset. Based on the six fitted models, hospitalized in ICU, respiratory distress, age, diabetes, CRP, PO2, WBC, AST, BUN, and NLR were associated significantly with predicting LOHS of COVID-19. Conclusion The BMA with Occam's Window method has a better fit and better performance in predicting affecting factors on the LOHS in the testing dataset than other models.

Introduction and Objective Droughts have a set of negative environmental, social and economic effects in a region or country. Using a monthly index and its analysis that, in addition to precipitation values, takes into account the effect of evaporation on the numerical value of the index, is very useful in determining drought parameters. Different indices are also a combination of variables with different marginal distributions, and for this purpose, their statistical analysis is difficult. Therefore, in order to determine the structure of dependence between two or more random variables, copula functions can be used, the distribution of margins is separated from the modeling of the structure of dependence between variables.Materials and Methods In this study, RDI index was used to determine the severity and duration of drought in 6 stations of North Khorasan province between 1988-2018 and Copula functions were used to analyze the severiy and duration. 26 different Copula functions were investigated using different statistical values. Also, two methods of local optimization and Monte Carlo Markov chain simulation with Bayesian estimator were used to numerically estimate the posterior distribution of selected Copula parameters. In order to evaluate the fit of different copulas, the common criteria were used for measuring the fit of different copulas including mean squared error, Bayesian information criterion, Akaike information and Nash-Sutcliffe efficiency criterion.Results and Discussion In all stations, the values of correlation coefficient with Pearson and Kendall tests were positive and had the same trend. The results of the Kolmogorov-Smirnov test at a significance level of five percent for choosing the optimal distribution showed that the generalized Pareto distribution was selected for the intensity and duration of Bojnord station and the exponential distribution for other stations was selected as the appropriate fitted distribution. The optimal function for Bojnord, Maneh and Semelghan stations was Burr function, Jajarm and Shirvan stations, Joe function, Farouj station, Galambos function and Esfarayen station, BB1 function. The results of the local optimization method are highly consistent with the Markov chain Monte-Carlo method. For the 100-year return period, the drought severity at bojnord station is 6.8, at esfarayen station, drought severity is 7.8, at faruj station, drought severity is 7.5, at jajarm station, drought severity is 7.8, at the station in manesemelghan, the drought severity was 8 and in shirvan station, the drought intensity was 2.8.Conclusion and Suggestions The current study shows the high capability of copula functions in solving two-variable problems and recommends the use of all possible functions in choosing marginal distributions and copula in solving problems. Also, the high correspondence between the two methods of local optimization and Markov chain Monte Carlo for estimating the parameters of the functions is probably due to the short statistical period used. Investigating the capabilities of these functions in solving multivariate problems, implementing other Monte Carlo Markov chain estimators, and using longer data to compare different optimization algorithms are suggested in future researches.

Random effects contain crucial information to understand the variability of the processes under study in mixed-effects models with crossed random effects (MEMs-CR). Given that model selection makes all-or-nothing decisions regarding to the inclusion of model parameters, we evaluated if model averaging could deal with model uncertainty to recover random effects of MEMs-CR. Specifically, we analyzed the bias and the root mean squared error (RMSE) of the estimations of the variances of random effects using model averaging with Akaike weights and Bayesian model averaging with BIC posterior probabilities, comparing them with two alternative analytical strategies as benchmarks: AIC and BIC model selection, and fitting a full random structure. A simulation study was conducted manipulating sample sizes for subjects and items, and the variance of random effects. Results showed that model averaging, especially Akaike weights, can adequately recover random variances, given a minimum sample size in the modeled clusters. Thus, we endorse using model averaging to deal with model uncertainty in MEMs-CR. An empirical illustration is provided to ease the usability of model averaging.

Introduction: The length of hospital stay (LOHS) caused by COVID-19 has imposed a financial burden, and cost on the healthcare service system and a high psychological burden on patients and health workers. The purpose of this study is to adopt the Bayesian model averaging (BMA) based on linear regression models and to determine the predictors of the LOHS of COVID-19. Methods: In this historical cohort study, from 5100 COVID-19 patients who had registered in the hospital database, 4996 patients were eligible to enter the study. The data included demographic, clinical, biomarkers, and LOHS. Factors affecting the LOHS were fitted in six models, including the stepwise method, AIC, BIC in classical linear regression models, two BMA using Occam's Window and Markov Chain Monte Carlo (MCMC) methods, and GBDT algorithm, a new method of machine learning. Results: The average length of hospitalization was 6.7 ± 5.7 days. In fitting classical linear models, both stepwise and AIC methods (R2 = 0.168 and adjusted R2 = 0.165) performed better than BIC (R2 = 0.160 and adjusted = 0.158). In fitting the BMA, Occam's Window model has performed better than MCMC with R2 = 0.174. The GBDT method with the value of R2 = 0.64, has performed worse than the BMA in the testing dataset but not in the training dataset. Based on the six fitted models, hospitalized in ICU, respiratory distress, age, diabetes, CRP, PO2, WBC, AST, BUN, and NLR were associated significantly with predicting LOHS of COVID-19. Conclusion: The BMA with Occam's Window method has a better fit and better performance in predicting affecting factors on the LOHS in the testing dataset than other models. [ABSTRACT FROM AUTHOR]

We consider the newly developed multinomial mixed-link models for a high-risk intestinal metaplasia (IM) study with DNA methylation data. Different from the traditional multinomial logistic models commonly used for categorical responses, the mixed-link models allow us to select the most appropriate link function for each category. We show that the selected multinomial mixed-link model (Model 1) using the total number of stem cell divisions (TNSC) based on DNA methylation data outperforms the traditional logistic models in terms of cross-entropy loss from ten-fold cross-validations with significant p-values 8.12×10−4 and 6.94×10−5. Based on our selected model, the significance of TNSC’s effect in predicting the risk of IM is justified with a p-value less than 10−6. We also select the most appropriate mixed-link models (Models 2 and 3) when an additional covariate, the status of gastric atrophy, is available. When the status is negative, mild, or moderate, we recommend Model 2; otherwise, we prefer Model 3. Both Models 2 and 3 can predict the risk of IM significantly better than Model 1, which justifies that the status of gastric atrophy is informative in predicting the risk of IM.

Abstract Background Infant mortality is defined as the death of a child at any time after birth and before the child’s first birthday. Sub-Saharan Africa has the highest infant and child mortality rate in the world. Infant and child mortality rates are higher in Ethiopia. A study was carried out to estimate the risk factors that affect infant mortality in Ethiopia. Method The EDHS− 2016 data set was used for this study. A total of 10,547 mothers from 11 regions were included in the study’s findings. To estimate the risk factors associated with infant mortality in Ethiopia, several count models (Poisson, Negative Binomial, Zero-Infated Poisson, Zero-Infated Negative Binomial, Hurdle Poisson, and Hurdle Negative Binomial) were considered. Result The average number of infant deaths was 0.526, with a variance of 0.994, indicating over-dispersion. The highest mean number of infant death occurred in Somali (0.69) and the lowest in Addis Ababa (0.089). Among the multilevel log linear models, the ZINB regression model with deviance (17,868.74), AIC (17,938.74), and BIC (1892.97) are chosen as the best model for estimating the risk factors affecting infant mortality in Ethiopia. However, the results of a multilevel ZINB model with a random intercept and slope model revealed that residence, mother’s age, household size, mother’s age at first birth, breast feeding, child weight, contraceptive use, birth order, wealth index, father education level, and birth interval are associated with infant mortality in Ethiopia. Conclusion Infant deaths remains high and infant deaths per mother differ across regions. An optimal fit was found to the data based on a multilevel ZINB model. We suggest fitting the ZINB model to count data with excess zeros originating from unknown sources such as infant mortality.

In this paper, we introduced a new family of distributions by generalizing existing multimodal skew-normal distribution. Statistical properties of the new family of distributions are studied in detail. In particular, explicit expressions of the density and distribution function, moments, skewness, kurtosis and the moments generating function are derived. Furthermore, estimation of the parameters using the maximum likelihood method of the new family of distributions is considered. Finally, the paper ends with an illustration of real-life data sets and then comparing the value of Akaike Information Criterion and Bayesian information criterion of the new distribution with some other known distributions. For the nested models, the Likelihood Ratio Test is carried out. [ABSTRACT FROM AUTHOR]

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal likelihoods depend on the prior choice. For model selection, even diffuse priors can be actually very informative, unlike for the parameter estimation problem. Furthermore, when the prior is improper, the marginal likelihood of the corresponding model is undetermined. In this work, we discuss the issue of prior sensitivity of the marginal likelihood and its role in model selection. We also comment on the use of uninformative priors, which are very common choices in practice. Several practical suggestions are discussed and many possible solutions, proposed in the literature, to design objective priors for model selection are described. Some of them also allow the use of improper priors. The connection between the marginal likelihood approach and the well‐known information criteria is also presented. We describe the main issues and possible solutions by illustrative numerical examples, providing also some related code. One of them involving a real‐world application on exoplanet detection. This article is categorized under:Statistical Models > Bayesian ModelsStatistical Models > Fitting ModelsStatistical Models > Model Selection [ABSTRACT FROM AUTHOR]

Background: Infant mortality is defined as the death of a child at any time after birth and before the child's first birthday. Sub-Saharan Africa has the highest infant and child mortality rate in the world. Infant and child mortality rates are higher in Ethiopia. A study was carried out to estimate the risk factors that affect infant mortality in Ethiopia.Method: The EDHS- 2016 data set was used for this study. A total of 10,547 mothers from 11 regions were included in the study's findings. To estimate the risk factors associated with infant mortality in Ethiopia, several count models (Poisson, Negative Binomial, Zero-Infated Poisson, Zero-Infated Negative Binomial, Hurdle Poisson, and Hurdle Negative Binomial) were considered.Result: The average number of infant deaths was 0.526, with a variance of 0.994, indicating over-dispersion. The highest mean number of infant death occurred in Somali (0.69) and the lowest in Addis Ababa (0.089). Among the multilevel log linear models, the ZINB regression model with deviance (17,868.74), AIC (17,938.74), and BIC (1892.97) are chosen as the best model for estimating the risk factors affecting infant mortality in Ethiopia. However, the results of a multilevel ZINB model with a random intercept and slope model revealed that residence, mother's age, household size, mother's age at first birth, breast feeding, child weight, contraceptive use, birth order, wealth index, father education level, and birth interval are associated with infant mortality in Ethiopia.Conclusion: Infant deaths remains high and infant deaths per mother differ across regions. An optimal fit was found to the data based on a multilevel ZINB model. We suggest fitting the ZINB model to count data with excess zeros originating from unknown sources such as infant mortality. [ABSTRACT FROM AUTHOR]

Random effects contain crucial information to understand the variability of the processes under study in mixed-effects models with crossed random effects (MEMs-CR). Given that model selection makes all-or-nothing decisions regarding to the inclusion of model parameters, we evaluated if model averaging could deal with model uncertainty to recover random effects of MEMs-CR. Specifically, we analyzed the bias and the root mean squared error (RMSE) of the estimations of the variances of random effects using model averaging with Akaike weights and Bayesian model averaging with BIC posterior probabilities, comparing them with two alternative analytical strategies as benchmarks: AIC and BIC model selection, and fitting a full random structure. A simulation study was conducted manipulating sample sizes for subjects and items, and the variance of random effects. Results showed that model averaging, especially Akaike weights, can adequately recover random variances, given a minimum sample size in the modeled clusters. Thus, we endorse using model averaging to deal with model uncertainty in MEMs-CR. An empirical illustration is provided to ease the usability of model averaging. [ABSTRACT FROM AUTHOR]

Model selection is an omnipresent problem in signal processing applications. The Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are the most commonly used solutions to this problem. These criteria have been found to have satisfactory performance in many cases and had a dominant role in the model selection literature since their introduction several decades ago, despite numerous attempts to dethrone them. Model selection can be viewed as a multiple hypothesis testing problem. This simple observation makes it possible to use for model selection a number of powerful hypothesis testing procedures that control the false discovery rate (FDR) or the familywise error rate (FER). This is precisely what we do in this paper in which we follow the lead of the proposers of the said procedures and introduce two general rules for model selection based on FDR and FER, respectively. We show in a numerical performance study that the FDR and FER rules are serious competitors of AIC and BIC with significant performance gains in more demanding cases, essentially at the same computational effort.

A two-step model selection procedure is proposed for autoregressive and moving-average (ARMA) model class. It is an adaptive least absolute shrinkage and selection operator (adLASSO) type model selection method that simultaneously chooses both the orders and significant lagged variables when the autoregressive and moving-average (ARMA) time series is contaminated with a nonlinear trend. The adLASSO is applied not to the observations, but to the detrended residuals. The proposed two-step adLASSO model selection procedure under some conditions can identify the true model with probability approaching one as the sample size increases, and the asymptotic properties of estimators are not affected by the replacement of observations with detrended residuals. The simulation studies show that the proposed method performs well with sample size as small as 50. The application of the method is illustrated by the annual varve thickness data collected from a location in Massachusetts. [ABSTRACT FROM AUTHOR]

Background: The focus of many studies is to estimate the effect of risk factors on outcomes, yet results may be dependent on the choice of other risk factors or potential confounders to include in a statistical model. For complex and unexplored systems, such as the COVID-19 spreading process, where a priori knowledge of potential confounders is lacking, data-driven empirical variable selection methods may be primarily utilized. Published studies often lack a sensitivity analysis as to how results depend on the choice of confounders in the model. This study showed variability in associations of short-term air pollution with COVID-19 mortality in Germany under multiple approaches accounting for confounders in statistical models. Methods: Associations between air pollution variables PM2.5, PM10, CO, NO, NO2, and O3 and cumulative COVID-19 deaths in 400 German districts were assessed via negative binomial models for two time periods, March 2020–February 2021 and March 2021–February 2022. Prevalent methods for adjustment of confounders were identified after a literature search, including change-in-estimate and information criteria approaches. The methods were compared to assess the impact on the association estimates of air pollution and COVID-19 mortality considering 37 potential confounders. Results: Univariate analyses showed significant negative associations with COVID-19 mortality for CO, NO, and NO2, and positive associations, at least for the first time period, for O3 and PM2.5. However, these associations became non-significant when other risk factors were accounted for in the model, in particular after adjustment for mobility, political orientation, and age. Model estimates from most selection methods were similar to models including all risk factors. Conclusion: Results highlight the importance of adequately accounting for high-impact confounders when analyzing associations of air pollution with COVID-19 and show that it can be of help to compare multiple selection approaches. This study showed how model selection processes can be performed using different methods in the context of high-dimensional and correlated covariates, when important confounders are not known a priori. Apparent associations between air pollution and COVID-19 mortality failed to reach significance when leading selection methods were used. [ABSTRACT FROM AUTHOR]

In this paper, the Rayleigh-Rayleigh (RR) distribution is presented. The RR distribution is a new model which is constructed based on infinite mixture distribution and some properties are described. The model is applied to the motor insurance claims of 3 voluntary plans and compared to the current models that are derived from exponential and some traditional models. The maximum likelihood estimation (MLE) is the parameter estimation. The various measurements of model fitting are the Kolmogorov-Smirnov test (K-S test), the Anderson-Darling test (AD test), Akaike information criterion (AIC) and Bayesian information criterion (BIC). We have found that the RR distribution is more suitable for the data than some current distributions such as Weibull, Gamma, Exponential and Rayleigh. [ABSTRACT FROM AUTHOR]

In this study, we applied an Autoregressive Integrated Moving Average (ARIMA) model to predict the spread of Diabetes disease infection in Taraba State, Nigeria. The monthly recorded cases of Diabetes between January 2010 and December 2020 in Federal Medical Centre, Jalingo was used to fit and validate the ARIMA model. A seasonal fluctuation and a slightly increasing pattern of a long-term trend were revealed in the time series of Diabetes disease. ARIMA (0,1,1) was selected as the best optimal model which has the lowest value of AIC/BIC. The root mean square error (RMSE) was used to assessed the predictive capability of the optimal model. The twenty-four (24) months forecast of Diabetes disease infection in Taraba State, Nigeria was also presented. The ARIMA model could be applied to effectively predict the short-term Diabetes disease infections in Taraba State, Nigeria and provide support for the development of interventions for disease control and prevention. [ABSTRACT FROM AUTHOR]

In various scientific fields, researchers make use of partitioning methods (e.g., K-means) to disclose the structural mechanisms underlying object by variable data. In some instances, however, a grouping of objects into clusters that are allowed to overlap (i.e., assigning objects to multiple clusters) might lead to a better representation of the underlying clustering structure. To obtain an overlapping object clustering from object by variable data, Mirkin's ADditive PROfile CLUStering (ADPROCLUS) model may be used. A major challenge when performing ADPROCLUS is to determine the optimal number of overlapping clusters underlying the data, which pertains to a model selection problem. Up to now, however, this problem has not been systematically investigated and almost no guidelines can be found in the literature regarding appropriate model selection strategies for ADPROCLUS. Therefore, in this paper, several existing model selection strategies for K-means (a.o., CHull, the Caliński-Harabasz, Krzanowski-Lai, Average Silhouette Width and Dunn Index and information-theoretic measures like AIC and BIC) and two cross-validation based strategies are tailored towards an ADPROCLUS context and are compared to each other in an extensive simulation study. The results demonstrate that CHull outperforms all other model selection strategies and this especially when the negative log-likelihood, which is associated with a minimal stochastic extension of ADPROCLUS, is used as (mis)fit measure. The analysis of a post hoc AIC-based model selection strategy revealed that better performance may be obtained when a different—more appropriate—definition of model complexity for ADPROCLUS is used. [ABSTRACT FROM AUTHOR]

Quantification of the dependence characteristics in hydrological time series is essential for understanding hydrological variability and for managing water resources. However, how determining a suitable model for describing the dependent components is still a challenge. In this article, we proposed a correlation coefficient‐based information criterion (CCIC) to determine the optimal model order of regression‐based models for quantifying the dependence characteristics in hydrological time series. CCIC was developed by combining the index of correlation coefficient and the information entropy index. The former was used to reflect the fitting error of the model and the latter was used as a penalty term to reflect the model uncertainty. They have similar roles as the two terms of the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) used commonly in hydrology. Results of Monte‐Carlo experiments verified higher and more stable accuracy of determining the true model order by CCIC than by AIC and BIC. Moreover, results indicated that the mean value of a time series had a big impact on the accuracy of CCIC. If the mean value of a time series was far from its initial value, the estimation of CCIC would have a big bias, causing low accuracy in the determination of suitable model order. The application of CCIC to annual precipitation from 520 stations in China further confirmed its advantages over AIC and BIC and indicated the significant short‐term dependence characteristics of annual precipitation in the Yangtze River basin. The proposed CCIC approach has potential for wider use in hydrometeorology. Key Points: Correlation coefficient‐based information criterion (CCIC) was proposed to determine the optimal order of regression models for quantifying dependence characteristics in hydrologic time seriesMC experiments verified higher and more stable accuracy of determining the true model order by CCIC than by Akaike Information Criterion and Bayesian Information Criterion used commonlyMean value of a time series had a big impact on the accuracy of CCIC for determining optimal order for regression models [ABSTRACT FROM AUTHOR]

A new two-parameter negative binomial mixture distribution named as negative binomial-Akash distribution is introduced in this paper. The proposed distribution is attained by compounding the negative binomial distribution with the Akash distribution. Some of its special characteristics are also derived, including factorial moments, mean, variance, index of dispersion etc. Furthermore, the behaviour of mean, variance and index of dispersion are discussed. The parameters of the proposed distribution are estimated using the maximum likelihood estimation method. This distribution can be used for modeling overdispersed count data. The usefulness and application of the proposed distribution are illustrated using two actual count data sets. [ABSTRACT FROM AUTHOR]

Data available in software engineering for many applications contains variability and it is not possible to say which variable helps in the process of the prediction. Most of the work present in software defect prediction is focused on the selection of best prediction techniques. For this purpose, deep learning and ensemble models have shown promising results. In contrast, there are very few researches that deals with cleaning the training data and selection of best parameter values from the data. Sometimes data available for training the models have high variability and this variability may cause a decrease in model accuracy. To deal with this problem we used the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) for selection of the best variables to train the model. A simple ANN model with one input, one output and two hidden layers was used for the training instead of a very deep and complex model. AIC and BIC values are calculated and combination for minimum AIC and BIC values to be selected for the best model. At first, variables were narrowed down to a smaller number using correlation values. Then subsets for all the possible variable combinations were formed. In the end, an artificial neural network (ANN) model was trained for each subset and the best model was selected on the basis of the smallest AIC and BIC value. It was found that combination of only two variables' ns and entropy are best for software defect prediction as it gives minimum AIC and BIC values. While, nm and npt is the worst combination and gives maximum AIC and BIC values. [ABSTRACT FROM AUTHOR]

This paper is concerned with approximating the short-term spread of the COVID-19 virus at the country from January 1, 2021 to July 25, 2022, extracted from the approved website of the Ministry of Health in Iraq using GARCH models and L.S.M.E method. In addition, we will try to determine the hypothetical inflection point and the final volume of cases of COVID-19. Where the analysis is from two parts firstly by applying the conditions for stability to GARCH models, and secondly part in the application of the Long-Short terms memory network, and we have found that the best model according to AIC and BIC information criteria is GARCH (1,0) this is regarding data analysis using GARCH Models, while the analysis using L.S.M.E according to the same AIC and BIC criteria. The results are of a standard value less than GARCH models due to the lack of high fluctuation in the severity of the contrast, where the GARCH models are used for states of high fluctuation and insecure in the variation of error, due to the adaptive nature of the network models Nervousness made it preferred models to describe these data and get the lowest medium for errors. [ABSTRACT FROM AUTHOR]

Information-based model selection criteria such as the AIC and BIC employ check loss functions to measure the goodness of fit for quantile regression models. Model selection using a check loss function is robust due to its resistance to outlying observations. In the present study, we suggest modifying the check loss function to achieve a more efficient goodness of fit. Because the cusp of the check loss is quadratically adjusted in the modified version, greater efficiency (or variance reduction) in the model selection is expected. Because we focus on model selection here, we do not modify the model-fitting process. Generalized cross-validation is another common method for choosing smoothing parameters in quantile smoothing splines. We describe how this can be adjusted using the modified check loss to increase efficiency. The proposed generalized cross-validation is designed to reflect the target quantile and sample size. Two real data sets and simulation studies are presented to evaluate its performance using linear and nonlinear quantile regression models. [ABSTRACT FROM AUTHOR]

Abstract Background Vaccine clinical studies typically provide time-resolved data on adaptive response read-outs in response to the administration of that particular vaccine to a cohort of individuals. However, modeling such data is challenged by the properties of these time-resolved profiles such as non-linearity, scarcity of measurement points, scheduling of the vaccine at multiple time points. Linear Mixed Models (LMM) are often used for the analysis of longitudinal data but their use in these time-resolved immunological data is not common yet. Apart from the modeling challenges mentioned earlier, selection of the optimal model by using information-criterion-based measures is far from being straight-forward. The aim of this study is to provide guidelines for the application and selection of LMMs that deal with the challenging characteristics of the typical data sets in the field of vaccine clinical studies. Methods We used antibody measurements in response to Hepatitis-B vaccine with five different adjuvant formulations for demonstration purposes. We built piecewise-linear, piecewise-quadratic and cubic models with transformations of the axes with pre-selected or optimized knot locations where time is a numerical variable. We also investigated models where time is categorical and random effects are shared intercepts between different measurement points. We compared all models by using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Deviance Information Criterion (DIC), variations of conditional AIC and by visual inspection of the model fit in the light of prior biological information. Results There are various ways of dealing with the challenges of the data which have their own advantages and disadvantages. We explain these in detail here. Traditional information-criteria-based measures work well for the coarse selection of the model structure and complexity, however are not efficient at fine tuning of the complexity level of the random effects. Conclusions We show that common statistical measures for optimal model complexity are not sufficient. Rather, explicitly accounting for model purpose and biological interpretation is needed to arrive at relevant models. Trial Registration Clinical trial registration number for this study: NCT00805389, date of registration: December 9, 2008 (pro-active registration).

In this article we apply the normal, truncated normal, and Weibull distributions for modelling the annual extreme wind load obtained from the Kazan-"Basic" meteorological station for years 1905–2004. The statistical modelling of extreme wind load is important in the design of structures such as city buildings. More generally, it provides information about weather for modification and monitoring climate change. In particular, meteorologists can fit various statistical frequency distributions to historical wind data in order to estimate the magnitude of maximum wind. [ABSTRACT FROM AUTHOR]

Recently, multiple systems estimation (MSE) has been applied to estimate the number of victims of human trafficking in different countries. The estimation procedure consists of a log-linear analysis of a contingency table of population registers and covariates. As the number of potential models increases exponentially with the number of registers and covariates, it is practically impossible to fit and compare all models. Therefore, the model search needs to be restricted to a small subset of all potential models. This paper addresses principles and criteria for model assessment and selection for MSE of human trafficking with special attention to sparsity which is typical to human trafficking data. The concepts are illustrated on data from Slovakia and Romania. [ABSTRACT FROM AUTHOR]

In this study, we introduce the integrated deviance information criterion (DIC) for nested and non-nested model selection problems in heteroskedastic spatial autoregressive models. In a Bayesian estimation setting, we assume that the idiosyncratic error terms of our spatial autoregressive model have a scale mixture of normal distributions, where the scale mixture variables are latent variables that induce heteroskedasticity. We first derive the integrated likelihood function by analytically integrating out the scale mixture variables from the complete-data likelihood function. We then use the integrated likelihood function to formulate the integrated DIC measure. We investigate the finite sample performance of the integrated DIC in selecting the true model in a simulation study. The simulation results show that the integrated DIC performs satisfactorily and can be useful for selecting the correct model in specification search exercises. Finally, in a spatially augmented economic growth model, we use the integrated DIC to choose the spatial weights matrix that leads to better predictive accuracy. [ABSTRACT FROM AUTHOR]

Model order estimation is the most important but challenging step for system identification using an autoregressive moving average (ARMA) model. In this paper, we propose an artificial neural network (ANN) structure to estimate the best model order for ARMA modeling of linear, time-invariant systems using the system's input and output data. The proposed algorithm creates an equivalent ANN structure corresponding to an ARMA model and chooses the best model order using the neural network's mean squared error (MSE) loss function. The proposed method is validated on simulated ARMA model data and the performance is compared with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). We considered three hypothetical linear systems and performed 100 Monte Carlo simulations for each model, with different data lengths, and with additive noise. For each of the three simulation models, the proposed method significantly outperformed the AIC and BIC in terms of the correct model order selection. Finally, the proposed ANN-based model order estimator was successfully applied to determine the dynamic relationship between heart rate (HR) and instantaneous lung volume (ILV) using an ARMA model. The results indicate that physiological and biological systems can be modeled with appropriate ARMA models obtained by the proposed algorithm to better understand the system dynamics.

In Psychology, it is common to find situations in which some kind of classification of people in subgroups or classes is needed. There are multivariate analysis techniques such as Hierarchical Cluster Analysis (HCA) that are commonly used for this purpose. Currently, there is a growing interest in the technique of Latent Class Analysis (LCA), although it is a relatively little known and used technique. Several authors have pointed out that the LCA has important advantages with respect to HCA, especially that the LCA allows for measures of goodness of fit. The aim of this paper is to present several applications of the LCA both from a simulation study and from real data and compare the performance of this technique against the HCA. The results from the simulation indicate that the LCA has a high performance to detect class structures. The results of the study from real data show that the different classes or mixtures present in the data may be overlapping, which makes grouping classes more difficult when applying LCA. The HCA can be a good analysis tool for the applied researcher since it can guide on the best model of LCA that should be interpreted. In research contexts in which the theoretical model is not clear, it is recommended to use both techniques in order to seek convergence of results.

Abstract The insurance industry uses mathematical models to estimate the risks due to future natural catastrophes. For climate‐related risks, historical climate data are a key ingredient used in making the models. Historical data for temperature and sea level often show clear and readily quantified climate change driven trends, and these trends would typically be accounted for when building risk models by adjusting earlier values to render the earlier data relevant to the future climate. For other climate variables, such as rainfall in many parts of the world, the questions of whether there are climate change driven trends in the historical data, and how to quantify them if there are, are less simple to answer. We investigate these questions in the context of European rainfall with a specific focus on how to deal with the uncertainty around trend estimates. We compare 10 empirical methodologies that one might use to model and predict trends, including traditional statistical testing and alternatives to statistical testing based on standard methods from model selection and model averaging. We emphasize prediction and risk assessment, rather than detection of trends, as our goal. Viewed in terms of this goal, the methods we consider each have qualitative and quantitative advantages and disadvantages. Understanding these advantages and disadvantages can help risk modellers make a choice as to which method to use, and based on the results we present, we believe that in many common situations model averaging methods, as opposed to statistical testing or model selection, are the most appropriate.