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Continuous time Bayesian networks (CTBNs) represent a class of stochastic processes, which can be used to model complex phenomena, for instance, they can describe interactions occurring in living processes, social science models or medicine. The literature on this topic is usually focused on a case when a dependence structure of a system is known and we are to determine conditional transition intensities (parameters of a network). In the paper, we study a structure learning problem, which is a more challenging task and the existing research on this topic is limited. The approach, which we propose, is based on a penalized likelihood method. We prove that our algorithm, under mild regularity conditions, recognizes a dependence structure of a graph with high probability. We also investigate properties of the procedure in numerical studies. [ABSTRACT FROM AUTHOR]

Conventional pharmacokinetic (PK) bioequivalence (BE) studies aim to compare the rate and extent of drug absorption from a test (T) and reference (R) product using non‐compartmental analysis (NCA) and the two one‐sided test (TOST). Recently published regulatory guidance recommends alternative model‐based (MB) approaches for BE assessment when NCA is challenging, as for long‐acting injectables and products which require sparse PK sampling. However, our previous research on MB‐TOST approaches showed that model misspecification can lead to inflated type I error. The objective of this research was to compare the performance of model selection (MS) on R product arm data and model averaging (MA) from a pool of candidate structural PK models in MBBE studies with sparse sampling. Our simulation study was inspired by a real case BE study using a two‐way crossover design. PK data were simulated using three structural models under the null hypothesis and one model under the alternative hypothesis. MB‐TOST was applied either using each of the five candidate models or following MS and MA with or without the simulated model in the pool. Assuming T and R have the same PK model, our simulation shows that following MS and MA, MB‐TOST controls type I error rates at or below 0.05 and attains similar or even higher power than when using the simulated model. Thus, we propose to use MS prior to MB‐TOST for BE studies with sparse PK sampling and to consider MA when candidate models have similar Akaike information criterion. [ABSTRACT FROM AUTHOR]

HEGY test is a commonly used procedure to test seasonal unit roots. However, the HEGY test is highly sensitive to the deterministic components of the model and the selected lag structure. Therefore, the test may give wrong results if the correct model is not used in terms of the lag structure and deterministic components. Moreover, there is a requirement in the HEGY test that unit roots at different frequencies should be tested separately. Lasso and Bridge estimators, which have been proposed recently with the arise of big data and artificial intelligence studies, are frequently used for model selection and parameter estimation for cross-sectional data. This study proposes a novel approach by adapting the Bridge estimator to the HEGY model and automatically selecting the correct model. Monte Carlo simulations have shown that this approach gives good results in terms of both choosing the correct model and automatically determining the frequencies with a seasonal unit root, with the help of the oracle feature of the Bridge estimator. Moreover, a real data example is provided to demonstrate the usage of our method and to provide a numerical comparison between the Bridge estimator and HEGY test to test the seasonal convergence hypothesis. [ABSTRACT FROM AUTHOR]

AbstractModel degrees of freedom ( df ) is a fundamental concept in statistics because it quantifies the flexibility of a fitting procedure and is indispensable in model selection. To investigate the gap between df and the number of independent variables in the fitting procedure, Tibshirani (2015) introduced the search degrees of freedom ( sdf ) concept to account for the search cost during model selection. However, this definition has two limitations: it does not consider fitting procedures in augmented spaces and does not use the same fitting procedure for sdf and df . We propose a modified search degrees of freedom ( msdf ) to directly account for the cost of searching in either original or augmented spaces. We check this definition for various fitting procedures, including classical linear regressions, spline methods, adaptive regressions (the best subset and the lasso), regression trees, and multivariate adaptive regression splines (MARS). In many scenarios when sdf is applicable, msdf reduces to sdf . However, for certain procedures like the lasso, msdf offers a fresh perspective on search costs. For some complex procedures like MARS, the df has been pre-determined during model fitting, but the df of the final fitted procedure might differ from the pre-determined one. To investigate this discrepancy, we introduce the concepts of nominal df and actual df , and define the property of self-consistency, which occurs when there is no gap between these two df ’s. We propose a correction procedure for MARS to align these two df ’s, demonstrating improved fitting performance through extensive simulations and two real data applications. [ABSTRACT FROM AUTHOR]

The Averaged One-Dependence Estimators (AODE) is a popular and effective method of Bayesian classification. In AODE, selecting the optimal sub-model based on a cross-validated risk minimization strategy can further enhance classification performance. However, existing cross-validation risk minimization strategies do not consider the differences in attributes in classification decisions. Consequently, this paper introduces an algorithm for Model Selection-based Weighted AODE (SWAODE). To express the differences in attributes in classification decisions, the ODE corresponding to attributes are weighted, with mutual information commonly used in the field of machine learning adopted as weights. Then, these weighted sub-models are evaluated and selected using leave-one-out cross-validation (LOOCV) to determine the best model. The new method can improve the accuracy and robustness of the model and better adapt to different data features, thereby enhancing the performance of the classification algorithm. Experimental results indicate that the algorithm merges the benefits of weighting with model selection, markedly enhancing the classification efficiency of the AODE algorithm. [ABSTRACT FROM AUTHOR]

Small‐angle scattering (SAS) is a key experimental technique for analyzing nanoscale structures in various materials. In SAS data analysis, selecting an appropriate mathematical model for the scattering intensity is critical, as it generates a hypothesis of the structure of the experimental sample. Traditional model selection methods either rely on qualitative approaches or are prone to overfitting. This paper introduces an analytical method that applies Bayesian model selection to SAS measurement data, enabling a quantitative evaluation of the validity of mathematical models. The performance of the method is assessed through numerical experiments using artificial data for multicomponent spherical materials, demonstrating that this proposed analysis approach yields highly accurate and interpretable results. The ability of the method to analyze a range of mixing ratios and particle size ratios for mixed components is also discussed, along with its precision in model evaluation by the degree of fitting. The proposed method effectively facilitates quantitative analysis of nanoscale sample structures in SAS, which has traditionally been challenging, and is expected to contribute significantly to advancements in a wide range of fields. [ABSTRACT FROM AUTHOR]

Personalized treatment planning in Molecular Radiotherapy (MRT) with accurately determining the absorbed dose is highly desirable. The absorbed dose is calculated based on the Time-Integrated Activity (TIA) and the dose conversion factor. A crucial unresolved issue in MRT dosimetry is which fit function to use for the TIA calculation. A data-driven population-based fitting function selection could help solve this problem. Therefore, this project aims to develop and evaluate a method for accurately determining TIAs in MRT, which performs a Population-Based Model Selection within the framework of the Non-Linear Mixed-Effects (NLME-PBMS) model. Biokinetic data of a radioligand for the Prostate-Specific Membrane Antigen (PSMA) for cancer treatment were used. Eleven fit functions were derived from various parameterisations of mono-, bi-, and tri-exponential functions. The functions' fixed and random effects parameters were fitted (in the NLME framework) to the biokinetic data of all patients. The goodness of fit was assumed acceptable based on the visual inspection of the fitted curves and the coefficients of variation of the fitted fixed effects. The Akaike weight, the probability that the model is the best among the whole set of considered models, was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit. NLME-PBMS Model Averaging (MA) was performed with all functions having acceptable goodness of fit. The Root-Mean-Square Error (RMSE) of the calculated TIAs from individual-based model selection (IBMS), a shared-parameter population-based model selection (SP-PBMS) reported in the literature, and the functions from NLME-PBMS method to the TIAs from MA were calculated and analysed. The NLME-PBMS (MA) model was used as the reference as this model considers all relevant functions with corresponding Akaike weights. The function f 3 a = A 1 e - λ 1 + λ phys t + A 2 e - λ phys t was selected as the function most supported by the data with an Akaike weight of (54 ± 11) %. Visual inspection of the fitted graphs and the RMSE values show that the NLME model selection method has a relatively better or equivalent performance than the IBMS or SP-PBMS methods. The RMSEs of the IBMS, SP-PBMS, and NLME-PBMS (f 3 a) methods are 7.4%, 8.8%, and 2.4%, respectively. A procedure including fitting function selection in a population-based method was developed to determine the best fit function for calculating TIAs in MRT for a given radiopharmaceutical, organ and set of biokinetic data. The technique combines standard practice approaches in pharmacokinetics, i.e. an Akaike-weight-based model selection and the NLME model framework. [ABSTRACT FROM AUTHOR]

The paper discusses the results of a selection of a set of monthly indicators to be used as predictors of the quarterly index of Italian service turnover. A mixed frequency approach based on sparse temporal disaggregation is used, which outperforms the classical methods of the Chow and Lin family, allowing both a high number of regressors by the LASSO method and stable estimates. The application refers to the turnover in transport, a sector strongly affected in 2020 by the dramatic movements due to the COVID-19 pandemic and the resurgence of inflation at the end of 2021. The monthly indicators are selected from 143 time series: 56 series of business surveys in transport about both the climate and frequency of the answers; 18 series from Assaeroporti about both passengers and cargo flights split by national and international routes; 69 series of monthly turnover in industry split by both sector of economic activity and reference market. The sample spans the months from January 2010 to December 2021 for both seasonally adjusted and unadjusted data. Several aspects of the estimation are considered: the stability of selected indicators over the quarters 2017–2021; their forecasting performance; the reliability of the estimates in terms of their monthly pattern. [ABSTRACT FROM AUTHOR]

A variety of change point estimation and detection algorithms have been developed for random variables observed over time. The acquisition of data in current practice often results in multiple subjects studied. The traditional treatment of such observations involves the assumption of their independence. In practice, however, this assumption is often inadequate or unrealistic. We propose an effective and modern computerized approach to estimating and detecting change points in linear model time series processes in the situation when the assumption of independent observations is not feasible. The developed methodology relies on the multivariate transformation and matrix normal distribution. The latter is used for separating the sources of variability. The application of the back-transform of the exponential transformation leads to a flexible distribution that effectively accounts for deviations from normality. The developed procedure has been successfully tested in various settings and applied to a crime rate data set. [ABSTRACT FROM AUTHOR]

In choosing a candidate model in likelihood-based inference by minimizing an information criterion, the practitioner is often faced with the difficult task of deciding how far up the ranked list to look. Motivated by this pragmatic necessity, we derive an approximation to the quantiles of a generalized (model selection) information criterion (ZIC), defined as a criterion for which the limit in probability is identical to that of the normalized log-likelihood, and which includes common special cases such as AIC and BIC. The method starts from the joint asymptotic normality of the ZIC values, and proceeds by deriving the (asymptotically) exact distribution of the minimum, which can be efficiently (numerically) computed. High quantiles can then be obtained by inverting this distribution function, resulting in what we call a certainty envelope (CE) of plausible models, intended to provide a heuristic upper bound on the location of the actual minimum. The theory is established for three data settings of perennial classical interest: (i) independent and identically distributed, (ii) regression, and (iii) time series. The development in the latter two cases invokes Lindeberg-Feller type conditions for, respectively, normalized: sums of conditional distributions and quadratic forms, in the observations. The performance of the methodology is examined on simulated data by assessing CE nominal coverage probabilities, and comparing them to the bootstrap. Both approaches give coverages close to nominal for large samples, but the bootstrap is on average two orders of magnitude slower. Finally, we hint at the possibility of producing confidence intervals for individual parameters by pivoting the distribution of the minimum ZIC, thus naturally accounting for post-model selection uncertainty. [ABSTRACT FROM AUTHOR]

Outlier detection stands as a critical cornerstone in the field of data mining, with a wide range of applications spanning from fraud detection to network security. However, real-world scenarios often lack labeled data for training, necessitating unsupervised outlier detection methods. This study centers on Unsupervised Outlier Model Selection (UOMS), with a specific focus on the family of Internal, Relative Evaluation of Outlier Solutions (IREOS) algorithms. IREOS measures outlier candidate separability by evaluating multiple maximum-margin classifiers and, while effective, it is constrained by its high computational demands. We investigate the impact of several different separation methods in UOMS in terms of ranking quality and runtime. Surprisingly, our findings indicate that different separability measures have minimal impact on IREOS' effectiveness. However, using linear separation methods within IREOS significantly reduces its computation time. These insights hold significance for real-world applications where efficient outlier detection is critical. In the context of this work, we provide the code for the IREOS algorithm and our separability techniques. [ABSTRACT FROM AUTHOR]

Hierarchical models are common for ecological analysis, but determining appropriate model selection methods remains an ongoing challenge. To confront this challenge, a suitable method is needed to evaluate and compare available candidate models. We compared performance of conditional WAIC, a joint-likelihood approach to WAIC (WAICj), and posterior-predictive loss for selecting between candidate N-mixture models. We tested these model selection criteria on simulated single-season N-mixture models, simulated multi-season N-mixture models with temporal auto-correlation, and three case studies of single-season N-mixture models based on eBird data. WAICj proved more accurate than the standard conditional formulation or posterior-predictive loss, even when models were temporally correlated, suggesting WAICj is a robust alternative to model selection for N-mixture models. [ABSTRACT FROM AUTHOR]

Polytomous categorical data are frequent in studies, that can be obtained with an individual or grouped structure. In both structures, the generalized logit model is commonly used to relate the covariates on the response variable. After fitting a model, one of the challenges is the definition of an appropriate residual and choosing diagnostic techniques. Since the polytomous variable is multivariate, raw, Pearson, or deviance residuals are vectors and their asymptotic distribution is generally unknown, which leads to difficulties in graphical visualization and interpretation. Therefore, the definition of appropriate residuals and the choice of the correct analysis in diagnostic tools is important, especially for nominal data, where a restriction of methods is observed. This paper proposes the use of randomized quantile residuals associated with individual and grouped nominal data, as well as Euclidean and Mahalanobis distance measures, as an alternative to reduce the dimension of the residuals. We developed simulation studies with both data structures associated. The half-normal plots with simulation envelopes were used to assess model performance. These studies demonstrated a good performance of the quantile residuals, and the distance measurements allowed a better interpretation of the graphical techniques. We illustrate the proposed procedures with two applications to real data. [ABSTRACT FROM AUTHOR]

Most statistical modeling applications involve the consideration of a candidate collection of models based on various sets of explanatory variables. The candidate models may also differ in terms of the structural formulations for the systematic component and the posited probability distributions for the random component. A common practice is to use an information criterion to select a model from the collection that provides an optimal balance between fidelity to the data and parsimony. The analyst then typically proceeds as if the chosen model was the only model ever considered. However, such a practice fails to account for the variability inherent in the model selection process, which can lead to inappropriate inferential results and conclusions. In recent years, inferential methods have been proposed for multimodel frameworks that attempt to provide an appropriate accounting of modeling uncertainty. In the frequentist paradigm, such methods should ideally involve model selection probabilities, i.e., the relative frequencies of selection for each candidate model based on repeated sampling. Model selection probabilities can be conveniently approximated through bootstrapping. When the Akaike information criterion is employed, Akaike weights are also commonly used as a surrogate for selection probabilities. In this work, we show that the conventional bootstrap approach for approximating model selection probabilities is impacted by bias. We propose a simple correction to adjust for this bias. We also argue that Akaike weights do not provide adequate approximations for selection probabilities, although they do provide a crude gauge of model plausibility. [ABSTRACT FROM AUTHOR]

Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier inclusion, outlier trimming, and post hoc outlier identification methods, with the former two often requiring pre-specification of the number of outliers. The fact that sample squared Mahalanobis distance is beta-distributed is used to derive an approximate distribution for the log-likelihoods of subset finite Gaussian mixture models. An algorithm is then proposed that removes the least plausible points according to the subset log-likelihoods, which are deemed outliers, until the subset log-likelihoods adhere to the reference distribution. This results in a trimming method, called OCLUST, that inherently estimates the number of outliers. [ABSTRACT FROM AUTHOR]

Abstract.In this work, we deal with some Bayesian inference problems in the presence of right censored data. First, we propose a dual ϕ−divergence Bayes type estimators for parametric models and we establish their asymptotic normality. To establish this result, we need a uniform strong law of large numbers that we prove as well. Then, we consider the problem of prior distributions construction for model selection using ϕ−divergences. Finally, we consider the problem of the predictive density estimation on the basis of ϕ−divergences. We apply an expansion result of the generalized Bayesian predictive density on two parametric models widely used in survival analysis, namely the Weibull and the inverse Weibull model, under right censoring. We also check the performances of our proposed methods through simulations and real data applications. The results of these studies show that our proposed dual ϕ−divergence Bayes type estimators are more robust than other Bayesian estimators. Moreover, the generalized Bayesian predictive density performs better than the classical estimative density especially for the inverse Weibull model. [ABSTRACT FROM AUTHOR]

Hierarchical models can express ecological dynamics using a combination of fixed and random effects, and measurement of their complexity (effective degrees of freedom, EDF) requires estimating how much random effects are shrunk toward a shared mean. Estimating EDF is helpful to (1) penalize complexity during model selection and (2) to improve understanding of model behavior. I applied the conditional Akaike Information Criterion (cAIC) to estimate EDF from the finite‐difference approximation to the gradient of model predictions with respect to each datum. I confirmed that this has similar behavior to widely used Bayesian criteria, and I illustrated ecological applications using three case studies. The first compared model parsimony with or without time‐varying parameters when predicting density‐dependent survival, where cAIC favors time‐varying demographic parameters more than conventional Akaike Information Criterion. The second estimates EDF in a phylogenetic structural equation model, and identifies a larger EDF when predicting longevity than mortality rates in fishes. The third compares EDF for a species distribution model fitted for 20 bird species and identifies those species requiring more model complexity. These highlight the ecological and statistical insight from comparing EDF among experimental units, models, and data partitions, using an approach that can be broadly adopted for nonlinear ecological models. [ABSTRACT FROM AUTHOR]

Climate change poses a threat to biodiversity, and it is unclear whether species can adapt to or tolerate new conditions, or migrate to areas with suitable habitats. Reconstructions of range shifts that occurred in response to environmental changes since the last glacial maximum (LGM) from species distribution models (SDMs) can provide useful data to inform conservation efforts. However, different SDM algorithms and climate reconstructions often produce contrasting patterns, and validation methods typically focus on accuracy in recreating current distributions, limiting their relevance for assessing predictions to the past or future. We modeled historically suitable habitat for the threatened North American tree green ash Fraxinus pennsylvanica using 24 SDMs built using two climate models, three calibration regions, and four modeling algorithms. We evaluated the SDMs using contemporary data with spatial block cross‐validation and compared the relative support for alternative models using a novel integrative method based on coupled demographic‐genetic simulations. We simulated genomic datasets using habitat suitability of each of the 24 SDMs in a spatially‐explicit model. Approximate Bayesian computation (ABC) was then used to evaluate the support for alternative SDMs through comparisons to an empirical population genomic dataset. Models had very similar performance when assessed with contemporary occurrences using spatial cross‐validation, but ABC model selection analyses consistently supported SDMs based on the CCSM climate model, an intermediate calibration extent, and the generalized linear modeling algorithm. Finally, we projected the future range of green ash under four climate change scenarios. Future projections using the SDMs selected via ABC suggest only minor shifts in suitable habitat for this species, while some of those that were rejected predicted dramatic changes. Our results highlight the different inferences that may result from the application of alternative distribution modeling algorithms and provide a novel approach for selecting among a set of competing SDMs with independent data. [ABSTRACT FROM AUTHOR]

In preparation to the launch of a pharmaceutical product, an estimate of its shelf life via stability testing is required by regulatory agencies. The ICH-Q1E guidance has been the worldwide reference to reach this objective, but in recent years several authors have criticized many of its aspects. To that end we discuss a complete Bayesian transcript of the ICH-Q1E, treating all the apparent shortcomings, while also addressing the presence of multiple batches using a linear mixed model (LMM) for proper shelf life prediction by explicitly modelling the batch-to-batch variability. This comprises a redefinition of the linear models proposed in the ICH-Q1E by suitable LMM counterparts, and a Bayesian analogue for model selection, which is more intuitive and remedies detrimental features of the ICH approach. In that context, a proper mathematical foundation of shelf life is provided that we use to investigate and mathematically compare the two available approaches to shelf life determination via shelf life distribution and batch distribution. The discussed method is then tested and evaluated using real data in comparison with the ICH-Q1E approach demonstrating their approximate equivalency for 6 batches. As a major objective, we extended the LMM with auxiliary fixed effects, here the concentration, which interconnect data sets allowing a prediction of shelf lives for concentrations lacking a sufficient number of batches. This establishes a novel approach to accelerate the speed to submission while retaining the patients' safety. Both case studies underline the inherent superiority of LMMs within a Bayesian framework regarding predictability and interpretability, and we hope that the relevant authorities will accept this approach in the future. [ABSTRACT FROM AUTHOR]

As the pandemic continues to pose challenges to global public health, developing effective predictive models has become an urgent research topic. This study aims to explore the application of multi-objective optimization methods in selecting infectious disease prediction models and evaluate their impact on improving prediction accuracy, generalizability, and computational efficiency. In this study, the NSGA-II algorithm was used to compare models selected by multi-objective optimization with those selected by traditional single-objective optimization. The results indicate that decision tree (DT) and extreme gradient boosting regressor (XGBoost) models selected through multi-objective optimization methods outperform those selected by other methods in terms of accuracy, generalizability, and computational efficiency. Compared to the ridge regression model selected through single-objective optimization methods, the decision tree (DT) and XGBoost models demonstrate significantly lower root mean square error (RMSE) on real datasets. This finding highlights the potential advantages of multi-objective optimization in balancing multiple evaluation metrics. However, this study's limitations suggest future research directions, including algorithm improvements, expanded evaluation metrics, and the use of more diverse datasets. The conclusions of this study emphasize the theoretical and practical significance of multi-objective optimization methods in public health decision support systems, indicating their wide-ranging potential applications in selecting predictive models. [ABSTRACT FROM AUTHOR]

Evaluating policy in imperfectly competitive markets requires understanding firm behavior. While researchers test conduct via model selection and assessment, we present the advantages of Rivers and Vuong (2002) (RV) model selection under misspecification. However, degeneracy of RV invalidates inference. With a novel definition of weak instruments for testing, we connect degeneracy to instrument strength, derive weak instrument properties of RV, and provide a diagnostic for weak instruments by extending the framework of Stock and Yogo (2005) to model selection. We test vertical conduct (Villas‐Boas (2007)) using common instrument sets. Some are weak, providing no power. Strong instruments support manufacturers setting retail prices. [ABSTRACT FROM AUTHOR]

The primary goal of this study is to effectively measure the impact of a severe random shock, such as the COVID-19 pandemic on aggregate economic activity in Greece, seven other euro area economies, three Scandinavian countries, and the United States. The class of linear and quantile predictive regression models is proposed for the analysis of real gross domestic product (GDP) growth, and a Bayesian approach for model selection is developed, by using a computationally flexible Markov chain Monte Carlo stochastic search algorithm that explores the posterior distribution of linear and quantile models, and identifies the relevant predictor variables. Penalized likelihood regression models are also implemented to tackle the issue of model selection. The model confidence set approach is applied and verifies that the selected models identified by the stochastic search algorithm belong to the set of superior models. Our analysis confirms that the outbreak of the pandemic had a profound effect on the economies under study, and reveals that different predictor variables are able to explain different quantiles of the underlying real GDP growth distribution for analyzed countries, suggesting that the quantile modeling approach improves the ability to adequately explain real GDP series compared with the standard conditional mean approach that explains only the average of the relationship between real GDP growth and several predictor variables. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of insolvency prediction in Spanish SMEs from a binary classification perspective. From a dataset containing more than 325 dependent variables of different natures (including demographic and economic-financial) and 17562 SMEs, a decision tree has been fitted that with a 0.93 accuracy predicts the state of a company and allows it to identify the most relevant variables in such prediction. The results obtained indicate that, in general, insolvency can be predicted from very few financial variables and with an anticipation of more than 10 years before the insolvency event. As a result, it is possible to provide early warnings to SMEs based on the indicators identified. [ABSTRACT FROM AUTHOR]

A researcher choosing between models ordered by some criterion may seek the best specification that satisfies a testable assumption. In this scenario, sequential specification tests (SSTs) are hypothesis tests of that assumption for each model in the sequence. We introduce a method using the p-values from SSTs to estimate the point in the sequence where the assumption ceases to hold. Unlike alternative approaches, this method is robust to individual errant p-values and does not require choosing a test level or tuning parameter. We demonstrate the method's properties with a simulation study, and illustrate it by choosing a bandwidth in a regression discontinuity design and a lag order for a time series model. [ABSTRACT FROM AUTHOR]

Abstract.This article proposes a One-Covariate-at-a-time Multiple Testing (OCMT) approach to choose significant variables in high-dimensional nonparametric additive regression models. Similarly to Chudik, Kapetanios, and Pesaran, we consider the statistical significance of individual nonparametric additive components one at a time and take into account the multiple testing nature of the problem. Both one-stage and multiple-stage procedures are considered. The former works well in terms of the true positive rate only if the net effects of all signals are strong enough; the latter helps to pick up hidden signals that have weak net effects. Simulations demonstrate the good finite-sample performance of the proposed procedures. As an empirical illustration, we apply the OCMT procedure to a dataset extracted from the Longitudinal Survey on Rural Urban Migration in China. We find that our procedure works well in terms of out-of-sample root mean square forecast errors, compared with competing methods such as adaptive group Lasso (AGLASSO). [ABSTRACT FROM AUTHOR]

Myeloproliferative neoplasms (MPN) are blood cancers that appear after acquiring a driver mutation in a hematopoietic stem cell. These hematological malignancies result in the overproduction of mature blood cells and, if not treated, induce a risk of cardiovascular events and thrombosis. Pegylated IFN |$\alpha $| is commonly used to treat MPN, but no clear guidelines exist concerning the dose prescribed to patients. We applied a model selection procedure and ran a hierarchical Bayesian inference method to decipher how dose variations impact the response to the therapy. We inferred that IFN |$\alpha $| acts on mutated stem cells by inducing their differentiation into progenitor cells; the higher the dose, the higher the effect. We found that the treatment can induce long-term remission when a sufficient (patient-dependent) dose is reached. We determined this minimal dose for individuals in a cohort of patients and estimated the most suitable starting dose to give to a new patient to increase the chances of being cured. [ABSTRACT FROM AUTHOR]

The road passenger transportation enterprise is a complex system, requiring a clear understanding of their active safety situation (ASS), trends, and influencing factors. This facilitates transportation authorities to promptly receive signals and take effective measures. Through exploratory factor analysis and confirmatory factor analysis, we delved into potential factors for evaluating ASS and extracted an ASS index. To predict obtaining a higher ASS information rate, we compared multiple time series models, including GRU (gated recurrent unit), LSTM (long short-term memory), ARIMA, Prophet, Conv_LSTM, and TCN (temporal convolutional network). This paper proposed the WDA-DBN (water drop algorithm-Deep Belief Network) model and employed DEEPSHAP to identify factors with higher ASS information content. TCN and GRU performed well in the prediction. Compared to the other models, WDA-DBN exhibited the best performance in terms of MSE and MAE. Overall, deep learning models outperform econometric models in terms of information processing. The total time spent processing alarms positively influences ASS, while variables such as fatigue driving occurrences, abnormal driving occurrences, and nighttime driving alarm occurrences have a negative impact on ASS. [ABSTRACT FROM AUTHOR]

Statistical network analysis primarily focuses on inferring the parameters of an observed network. In many applications, especially in the social sciences, the observed data is the groups formed by individual subjects. In these applications, the network is itself a parameter of a statistical model. Zhao and Weko propose a model-based approach, called the hub model, to infer implicit networks from grouping behavior. The hub model assumes that each member of the group is brought together by a member of the group called the hub. The set of members which can serve as a hub is called the hub set. The hub model belongs to the family of Bernoulli mixture models. Identifiability of Bernoulli mixture model parameters is a notoriously difficult problem. This article proves identifiability of the hub model parameters and estimation consistency under mild conditions. Furthermore, this article generalizes the hub model by introducing a model component that allows hubless groups in which individual nodes spontaneously appear independent of any other individual. We refer to this additional component as the null component. The new model bridges the gap between the hub model and the degenerate case of the mixture model—the Bernoulli product. Identifiability and consistency are also proved for the new model. In addition, a penalized likelihood approach is proposed to estimate the hub set when it is unknown. for this article are available online. [ABSTRACT FROM AUTHOR]

Modern statistics provides an ever-expanding toolkit for estimating unknown parameters. Consequently, applied statisticians frequently face a difficult decision: retain a parameter estimate from a familiar method or replace it with an estimate from a newer or more complex one. While it is traditional to compare estimates using risk, such comparisons are rarely conclusive in realistic settings. In response, we propose the "c-value" as a measure of confidence that a new estimate achieves smaller loss than an old estimate on a given dataset. We show that it is unlikely that a large c-value coincides with a larger loss for the new estimate. Therefore, just as a small p-value supports rejecting a null hypothesis, a large c-value supports using a new estimate in place of the old. For a wide class of problems and estimates, we show how to compute a c-value by first constructing a data-dependent high-probability lower bound on the difference in loss. The c-value is frequentist in nature, but we show that it can provide validation of shrinkage estimates derived from Bayesian models in real data applications involving hierarchical models and Gaussian processes. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In supervised learning, feature selection methods identify the most relevant predictors to include in a model. For linear models, the inclusion or exclusion of each variable may be represented as a vector of bits playing the role of the genetic material that defines the model. Genetic algorithms reproduce the strategies of natural selection on a population of models to identify the best. We derive the distribution of the importance scores for parallel genetic algorithms under the null hypothesis that none of the features has predictive power. They, hence, provide an objective threshold for feature selection that does not require the visual inspection of a bubble plot. We also introduce the eradication strategy, akin to forward stepwise selection, where the genes of useful variables are sequentially forced into the models. The method is illustrated on real data, and simulation studies are run to describe its performance. [ABSTRACT FROM AUTHOR]

A Monte Carlo simulation study was conducted to compare fit indices used for detecting the correct latent class in three dichotomous mixture item response theory (IRT) models. Ten indices were considered: Akaike's information criterion (AIC), the corrected AIC (AICc), Bayesian information criterion (BIC), consistent AIC (CAIC), Draper's information criterion (DIC), sample size adjusted BIC (SABIC), relative entropy, the integrated classification likelihood criterion (ICL-BIC), the adjusted Lo–Mendell–Rubin (LMR), and Vuong-Lo–Mendell–Rubin (VLMR). The accuracy of the fit indices was assessed for correct detection of the number of latent classes for different simulation conditions including sample size (2,500 and 5,000), test length (15, 30, and 45), mixture proportions (equal and unequal), number of latent classes (2, 3, and 4), and latent class separation (no-separation and small separation). Simulation study results indicated that as the number of examinees or number of items increased, correct identification rates also increased for most of the indices. Correct identification rates by the different fit indices, however, decreased as the number of estimated latent classes or parameters (i.e., model complexity) increased. Results were good for BIC, CAIC, DIC, SABIC, ICL-BIC, LMR, and VLMR, and the relative entropy index tended to select correct models most of the time. Consistent with previous studies, AIC and AICc showed poor performance. Most of these indices had limited utility for three-class and four-class mixture 3PL model conditions. [ABSTRACT FROM AUTHOR]

While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, selection of possibly high-dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we propose a selective machine learning framework for making inferences about a finite-dimensional functional defined on a semiparametric model, when the latter admits a doubly robust estimating function and several candidate machine learning algorithms are available for estimating the nuisance parameters. We introduce a new selection criterion aimed at bias reduction in estimating the functional of interest based on a novel definition of pseudo risk inspired by the double robustness property. Intuitively, the proposed criterion selects a pair of learners with the smallest pseudo risk, so that the estimated functional is least sensitive to perturbations of a nuisance parameter. We establish an oracle property for a multi-fold cross-validation version of the new selection criterion that states that our empirical criterion performs nearly as well as an oracle with a priori knowledge of the pseudo risk for each pair of candidate learners. Finally, we apply the approach to model selection of a semiparametric estimator of average treatment effect given an ensemble of candidate machine learners to account for confounding in an observational study that we illustrate in simulations and a data application. [ABSTRACT FROM AUTHOR]

This article presents a method within a Bayesian framework for quantifying uncertainty in satellite aerosol remote sensing when retrieving aerosol optical depth (AOD). By using a Bayesian model averaging technique, we take into account uncertainty in aerosol optical model selection and also obtain a shared inference about AOD based on the best-fitting optical models. In particular, uncertainty caused by forward-model approximations has been taken into account in the AOD retrieval process to obtain a more realistic uncertainty estimate. We evaluated a model discrepancy, i.e., forward-model uncertainty, empirically by exploiting the residuals of model fits and using a Gaussian process to characterise the discrepancy. We illustrate the method with examples using observations from the TROPOspheric Monitoring Instrument (TROPOMI) on the Sentinel-5 Precursor satellite. We evaluated the results against ground-based remote sensing aerosol data from the Aerosol Robotic Network (AERONET). [ABSTRACT FROM AUTHOR]

We derive approximations to the bias and squared bias with errors of order o(1/n) where n is the sample size. Our results hold for a large class of estimators, including quantiles, transformations of unbiased estimators, maximum likelihood estimators in (possibly) incorrectly specified models, and functions thereof. Furthermore, we use the approximations to derive estimators of the mean squared error (MSE) which are correct to order o(1/n). Since the variance of many estimators is of order O(1/n), this level of precision is needed for the MSE estimator to properly take the variance into account. We also formulate a new focused information criterion (FIC) for model selection based on the estimators of the squared bias. Lastly, we illustrate the methods on data containing the number of battle deaths in all major inter‐state wars between 1823 and the present day. The application illustrates the potentially large impact of using a less‐accurate estimator of the squared bias. [ABSTRACT FROM AUTHOR]

With linear dependency between the explanatory variables, partial least squares (PLS) regression is commonly used for regression analysis. If the response variable correlates to a high degree with the explanatory variables, a model with excellent predictive ability can usually be obtained. Ranking of variable importance is commonly used to interpret the model and sometimes this interpretation guides further experimentation. For instance, when analyzing natural product extracts for bioactivity, an underlying assumption is that the highest ranked compounds represent the best candidates for isolation and further testing. A problem with this approach is that in most cases, the number of compounds is larger than the number of samples (and usually much larger) and that the concentrations of the compounds correlate. Furthermore, compounds may interact as synergists or as antagonists. If the modeling process does not account for this possibility, the interpretation can be thoroughly wrong because unmodeled variables that strongly influence the response will give rise to confounding of a first‐order PLS model and send the experimenter on a wrong track. We show the consequences of this by a practical example from natural product research. Furthermore, we show that by including the possibility of interactions between explanatory variables, visualization using a selectivity ratio plot may provide model interpretation that can be used to make inferences. [ABSTRACT FROM AUTHOR]

Pakistan is situated in an earthquake-prone area, and in the past, many destructive earthquakes have occurred including the most destructive 1935 Quetta, and 2005 Kashmir, earthquakes. Therefore, it is of vital importance to investigate the statistical properties of the earthquake temporal data of Pakistan. The present study brings novelty through the vast extension of the linear and nonlinear autoregressive conditional duration models in the field of seismology. A simple duration model capable of describing and forecasting the earthquake elapsed times data has been developed. Different specifications of the duration models were considered to completely extract the time-dependent structure in earthquake data. This study aims to identify the most suitable in-sample fitted and out-of-sample forecasting models for the earthquake elapsed times data of Pakistan. A variety of autoregressive conditional duration models were applied to the complete and updated earthquake catalog of Pakistan. The most suitable model was chosen through statistical model evaluation techniques. The method of maximum likelihood was used to estimate the model parameters. The adequacy of fitted models is assessed through residual analysis. The obtained results suggest that the Logarithmic Autoregressive Conditional Duration model of type 2 (LACD2) appeared as the most suitable in-sample fitted model for describing the earthquake temporal data of the different zones of Pakistan. Further, the simple autoregressive conditional duration (ACD) model outperforms the remaining considered models regarding 1-through-4 steps-ahead out-of-sample forecasting performance for both India–Eurasia collision (IEC) and Makran subduction (MS) zones. Autoregressive models with Burr and exponential distributions as assumed error distributions have appeared as the most suitable fitted models for IEC and MS zones, respectively. The residuals analysis results show that the most suitable fitted models are correctly identified. The results show that the earthquake short-term (h = 1) forecasting with duration models is more accurate in comparison with earthquake long-term (h = 1 , 2 , 3) forecasting. The forecasted elapsed times for IEC and MS zones are 0.60 and 2.94 years, respectively. The obtained results show that the autoregressive conditional models are a more useful tool for forecasting the earthquake elapsed times for short term in comparison with the long-term forecasting. Hence, autoregressive conditional models are capable of modeling and forecasting the earthquake temporal data of the different regions of Pakistan. Among the competing models, the best fit model can serve the purpose of data description, missing value estimation in earthquake catalogs and uncertainty quantification in the earthquake occurrence process. The most suitable forecasted model yields the future earthquake occurrence trend in the study region. [ABSTRACT FROM AUTHOR]

Inverse Weibull, lognormal, and inverse Gaussian are some commonly used statistical distributions for modeling positively skewed failure lifetime data. These distributions share some interesting properties among themselves like they all have uni‐modal hazard rates. In this paper, we address the problem of discriminating among these statistical distributions to consider a more appropriate lifetime model. We first consider the complete samples and make use of the maximized log‐likelihood approach for choosing the correct model. We also obtain the expressions for logarithmic of defined test statistics, and associated asymptotic distributions. We then extend our discussion based on the observed sample in the presence of some censoring. We perform a simulation study in both cases to compare the probabilities of correct selection. Furthermore, for a given probability of correct selection and user‐specified protection level, we present a discussion to determine the minimum sample size required to discriminate among the three lifetime models. Finally, two real data sets are analyzed to illustrate the proposed methodology. In our findings, we observed that model parameters and methods of estimating unknown parameters play very important roles in the discrimination process, and sample size and the proportion of censoring become key factors to ensure a high probability of selecting a correct model. [ABSTRACT FROM AUTHOR]

As data and computing power have surged in recent decades, statistical modeling has become an important tool for understanding ecological patterns and processes. Statistical modeling in ecology faces two major challenges. First, ecological data may not conform to traditional methods, and second, professional ecologists often do not receive extensive statistical training. In response to these challenges, the journal Ecology has published many innovative statistical ecology papers that introduced novel modeling methods and provided accessible guides to statistical best practices. In this paper, we reflect on Ecology's history and its role in the emergence of the subdiscipline of statistical ecology, which we define as the study of ecological systems using mathematical equations, probability, and empirical data. We showcase 36 influential statistical ecology papers that have been published in Ecology over the last century and, in so doing, comment on the evolution of the field. As data and computing power continue to increase, we anticipate continued growth in statistical ecology to tackle complex analyses and an expanding role for Ecology to publish innovative and influential papers, advancing the discipline and guiding practicing ecologists. [ABSTRACT FROM AUTHOR]

We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the induced posterior distribution on model space is derived in terms of a simple branching process, and several consequences of this are explored in theory and in practice. First, it is shown that the branching process representation leads to a simple variable-dimensional Monte Carlo sampler for the joint posterior distribution on models and parameters, which can efficiently produce independent samples. This sampler is found to be more efficient than earlier MCMC samplers for the same tasks. Then, the branching process representation is used to establish the asymptotic consistency of the BCT posterior, including the derivation of an almost-sure convergence rate. Finally, an extensive study is carried out on the performance of the induced Bayesian entropy estimator. Its utility is illustrated through both simulation experiments and real-world applications, where it is found to outperform several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Purpose: Personalized treatment planning in Molecular Radiotherapy (MRT) with accurately determining the absorbed dose is highly desirable. The absorbed dose is calculated based on the Time-Integrated Activity (TIA) and the dose conversion factor. A crucial unresolved issue in MRT dosimetry is which fit function to use for the TIA calculation. A data-driven population-based fitting function selection could help solve this problem. Therefore, this project aims to develop and evaluate a method for accurately determining TIAs in MRT, which performs a Population-Based Model Selection within the framework of the Non-Linear Mixed-Effects (NLME-PBMS) model. Methods: Biokinetic data of a radioligand for the Prostate-Specific Membrane Antigen (PSMA) for cancer treatment were used. Eleven fit functions were derived from various parameterisations of mono-, bi-, and tri-exponential functions. The functions' fixed and random effects parameters were fitted (in the NLME framework) to the biokinetic data of all patients. The goodness of fit was assumed acceptable based on the visual inspection of the fitted curves and the coefficients of variation of the fitted fixed effects. The Akaike weight, the probability that the model is the best among the whole set of considered models, was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit. NLME-PBMS Model Averaging (MA) was performed with all functions having acceptable goodness of fit. The Root-Mean-Square Error (RMSE) of the calculated TIAs from individual-based model selection (IBMS), a shared-parameter population-based model selection (SP-PBMS) reported in the literature, and the functions from NLME-PBMS method to the TIAs from MA were calculated and analysed. The NLME-PBMS (MA) model was used as the reference as this model considers all relevant functions with corresponding Akaike weights. Results: The function f3a=A1e-λ1+λphyst+A2e-λphyst was selected as the function most supported by the data with an Akaike weight of (54 ± 11) %. Visual inspection of the fitted graphs and the RMSE values show that the NLME model selection method has a relatively better or equivalent performance than the IBMS or SP-PBMS methods. The RMSEs of the IBMS, SP-PBMS, and NLME-PBMS (f3a) methods are 7.4%, 8.8%, and 2.4%, respectively. Conclusion: A procedure including fitting function selection in a population-based method was developed to determine the best fit function for calculating TIAs in MRT for a given radiopharmaceutical, organ and set of biokinetic data. The technique combines standard practice approaches in pharmacokinetics, i.e. an Akaike-weight-based model selection and the NLME model framework.

Abstract In this work, we explore the extent to which the spectrum of the graph Laplacian can characterize the probability distribution of random graphs for the purpose of model evaluation and model selection for network data applications. Network data, often represented as a graph, consist of a set of pairwise observations between elements of a population of interests. The statistical network analysis literature has developed many different classes of network data models, with notable model classes including stochastic block models, latent node position models, and exponential families of random graph models. We develop a novel methodology which exploits the information contained in the spectrum of the graph Laplacian to predict the data-generating model from a set of candidate models. Through simulation studies, we explore the extent to which network data models can be differentiated by the spectrum of the graph Laplacian. We demonstrate the potential of our method through two applications to well-studied network data sets and validate our findings against existing analyses in the statistical network analysis literature.

Abstract Hierarchical models are common for ecological analysis, but determining appropriate model selection methods remains an ongoing challenge. To confront this challenge, a suitable method is needed to evaluate and compare available candidate models. We compared performance of conditional WAIC, a joint-likelihood approach to WAIC (WAICj), and posterior-predictive loss for selecting between candidate N-mixture models. We tested these model selection criteria on simulated single-season N-mixture models, simulated multi-season N-mixture models with temporal auto-correlation, and three case studies of single-season N-mixture models based on eBird data. WAICj proved more accurate than the standard conditional formulation or posterior-predictive loss, even when models were temporally correlated, suggesting WAICj is a robust alternative to model selection for N-mixture models.