Clinical trial endpoints are often bounded outcome scores (BOS), which are variables having restricted values within finite intervals. Common analysis approaches may treat the data as continuous, categorical, or a mixture of both. The appearance of BOS data being simultaneously continuous and categorical easily leads to confusions in pharmacometrics regarding the appropriate domain for model evaluation and the circumstances under which data likelihoods can be compared. This commentary aims to clarify these fundamental issues and facilitate appropriate pharmacometric analyses.

Many cold-water dependent aquatic organisms are experiencing habitat and population declines from increasing water temperatures. Identifying mechanisms which drive local and regional stream thermal regimes facilitates restoration at ecologically relevant scales. Stream temperatures vary spatially and temporally both within and among river basins. We developed a modeling process to identify statistical relationships between drivers of stream temperature and covariates representing landscape, climate, and management-related processes. The modeling process was tested in 3 study areas of the Pacific Northwest USA during the growing season (May [start], August [warmest], September [end]). Across all months and study systems, covariates with the highest relative importance represented the physical landscape (elevation [1st], catchment area [3rd], main channel slope [5th]) and climate covariates (mean monthly air temperature [2nd] and discharge [4th]). Two management covariates (ground water use [6th] and riparian shade [7th]) also had high relative importance. Across the growing season (for all basins) local reach slope had high relative importance in May, but transitioned to a regional main channel slope covariate in August and September. This modeling process identified regionally similar and locally unique relationships among drivers of stream temperature. High relative importance of management-related covariates suggested potential restoration actions for each system.

A noise-resistant linearization model that reveals the true nonlinearity of the sensor is essential for retrieving accurate physical displacement from the signals captured by sensing electronics. In this paper, we propose a novel information-driven smoothing spline linearization method, which innovatively integrates one new and three standard information criterions into a smoothing spline for the high-precision displacement sensors\' linearization. Using theoretical analysis and Monte Carlo simulation, the proposed linearization method is demonstrated to outperform traditional polynomial and spline linearization methods for high-precision displacement sensors with a low noise to range ratio in the 10-5 level. Validation experiments were carried out on two different types of displacement sensors to benchmark the performance of the proposed method compared to the polynomial models and the the non-smoothing cubic spline. The results show that the proposed method with the new modified Akaike Information Criterion stands out compared to the other linearization methods and can improve the residual nonlinearity by over 50% compared to the standard polynomial model. After being linearized via the proposed method, the residual nonlinearities reach as low as ±0.0311% F.S. (Full Scale of Range), for the 1.5 mm range chromatic confocal displacement sensor, and ±0.0047% F.S., for the 100 mm range laser triangulation displacement sensor.

During the years, adsorption has garnered considerable attention being one of the most cost-effective and efficient methods for separating contaminants out of liquid phase. A comprehensive understanding of adsorption mechanisms entails several crucial steps, including adsorbent characterization, batch and column adsorption tests, fitting of predefined kinetic and isotherm models, and meticulous thermodynamic analysis. These combined efforts serve to provide clarity and insights into the intricate workings of adsorption phenomena. However, the vast amount of literature published in the field each year is riddled with ill-considered model selections and incorrect parameter analyses. Therefore, the aim of this paper is to establish guidelines for the proper employment of these numerous kinetic, isotherm, and fixed-bed models in various applications. A thorough review has been undertaken, encompassing more than 45 kinetic models, 70 isotherm models, and 45 fixed bed models available hitherto, with their classification determined based on the adsorption mechanisms expounded within each of them. Moreover, five general approaches for modifying fixed-bed models were provided. The physical meanings, assumptions, and interconversion relationships of the models were discussed in detail, along with the information criterion used to evaluate their validity. In addition to commonly used activation energy and Gibbs energy analysis, the methods for calculating site energy distribution were also summarized.

BACKGROUND: Correctly identifying spatial disease cluster is a fundamental concern in public health and epidemiology. The spatial scan statistic is widely used for detecting spatial disease clusters in spatial epidemiology and disease surveillance. Many studies default to a maximum reported cluster size (MRCS) set at 50% of the total population when searching for spatial clusters. However, this default setting can sometimes report clusters larger than true clusters, which include less relevant regions. For the Poisson, Bernoulli, ordinal, normal, and exponential models, a Gini coefficient has been developed to optimize the MRCS. Yet, no measure is available for the multinomial model.
RESULTS: We propose two versions of a spatial cluster information criterion (SCIC) for selecting the optimal MRCS value for the multinomial-based spatial scan statistic. Our simulation study suggests that SCIC improves the accuracy of reporting true clusters. Analysis of the Korea Community Health Survey (KCHS) data further demonstrates that our method identifies more meaningful small clusters compared to the default setting.
CONCLUSIONS: Our method focuses on improving the performance of the spatial scan statistic by optimizing the MRCS value when using the multinomial model. In public health and disease surveillance, the proposed method can be used to provide more accurate and meaningful spatial cluster detection for multinomial data, such as disease subtypes.

The various debates around model selection paradigms are important, but in lieu of a consensus, there is a demonstrable need for a deeper appreciation of existing approaches, at least among the end-users of statistics and model selection tools. In the ecological literature, the Akaike information criterion (AIC) dominates model selection practices, and while it is a relatively straightforward concept, there exists what we perceive to be some common misunderstandings around its application. Two specific questions arise with surprising regularity among colleagues and students when interpreting and reporting AIC model tables. The first is related to the issue of \'pretending\' variables, and specifically a muddled understanding of what this means. The second is related to p-values and what constitutes statistical support when using AIC. There exists a wealth of technical literature describing AIC and the relationship between p-values and AIC differences. Here, we complement this technical treatment and use simulation to develop some intuition around these important concepts. In doing so we aim to promote better statistical practices when it comes to using, interpreting and reporting models selected when using AIC.

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases, statistical measures have been constructed, such as cross validation, information criteria and marginal likelihood; however, their mathematical properties have not yet been completely clarified when statistical models are under- or over-parametrized. We introduce a place of mathematical theory of Bayesian statistics for unknown uncertainty, which clarifies general properties of cross validation, information criteria and marginal likelihood, even if an unknown data-generating process is unrealizable by a model or even if the posterior distribution cannot be approximated by any normal distribution. Hence it gives a helpful standpoint for a person who cannot believe in any specific model and prior. This paper consists of three parts. The first is a new result, whereas the second and third are well-known previous results with new experiments. We show there exists a more precise estimator of the generalization loss than leave-one-out cross validation, there exists a more accurate approximation of marginal likelihood than Bayesian information criterion, and the optimal hyperparameters for generalization loss and marginal likelihood are different. This article is part of the theme issue \'Bayesian inference: challenges, perspectives, and prospects\'.

The aim of the study is to increase the functional efficiency of machine learning decision support system (DSS) for the diagnosis of oncopathology on the basis of tissue morphology. The method of hierarchical information-extreme machine learning of diagnostic DSS is offered. The method is developed within the framework of the functional approach to modeling of natural intelligence cognitive processes at formation and acceptance of classification decisions. This approach, in contrast to neuronal structures, allows diagnostic DSS to adapt to arbitrary conditions of histological imaging and flexibility in retraining the system by expanding the recognition classes alphabet that characterize different structures of tissue morphology. In addition, the decisive rules built within the geometric approach are practically invariant to the multidimensionality of the diagnostic features space. The developed method allows to create information, algorithmic, and software of the automated workplace of the histologist for diagnosing oncopathologies of different genesis. The machine learning method is implemented on the example of diagnosing breast cancer.

Parameter estimation accuracy and average sample number (ASN) reduction are important to improving target detection performance in sequential hypothesis tests. Multiple-input multiple-output (MIMO) radar can balance between parameter estimation accuracy and ASN reduction through waveform diversity. In this study, we propose a waveform design method based on a two-stage information criterion to improve multi-target detection performance. In the first stage, the waveform is designed to estimate the target parameters based on the criterion of single-hypothesis mutual information (MI) maximization under the constraint of the signal-to-noise ratio (SNR). In the second stage, the objective function is designed based on the criterion of MI minimization and Kullback-Leibler divergence (KLD) maximization between multi-hypothesis posterior probabilities, and the waveform is chosen from the waveform library of the first-stage parameter estimation. Furthermore, an adaptive waveform design algorithm framework for multi-target detection is proposed. The simulation results reveal that the waveform design based on the two-stage information criterion can rapidly detect the target direction. In addition, the waveform design based on the criterion of dual-hypothesis MI minimization can improve the parameter estimation performance, whereas the design based on the criterion of dual-hypothesis KLD maximization can improve the target detection performance.

Model selection is often implicit: when performing an ANOVA, one assumes that the normal distribution is a good model of the data; fitting a tuning curve implies that an additive and a multiplicative scaler describes the behavior of the neuron; even calculating an average implicitly assumes that the data were sampled from a distribution that has a finite first statistical moment: the mean. Model selection may be explicit, when the aim is to test whether one model provides a better description of the data than a competing one. As a special case, clustering algorithms identify groups with similar properties within the data. They are widely used from spike sorting to cell type identification to gene expression analysis. We discuss model selection and clustering techniques from a statistician\'s point of view, revealing the assumptions behind, and the logic that governs the various approaches. We also showcase important neuroscience applications and provide suggestions how neuroscientists could put model selection algorithms to best use as well as what mistakes should be avoided.