Spatial Modeling of Precipitation Based on Data-Driven Warping of Gaussian Processes.

Modeling and forecasting spatiotemporal patterns of precipitation is crucial for managing water resources and mitigating water-related hazards. Globally valid spatiotemporal models of precipitation are not available. This is due to the intermittent nature, non-Gaussian distribution, and complex geographical dependence of precipitation processes. Herein we propose a data-driven model of precipitation amount which employs a novel, data-driven (non-parametric) implementation of warped Gaussian processes. We investigate the proposed warped Gaussian process regression (wGPR) using (i) a synthetic test function contaminated with non-Gaussian noise and (ii) a reanalysis dataset of monthly precipitation from the Mediterranean island of Crete. Cross-validation analysis is used to establish the advantages of non-parametric warping for the interpolation of incomplete data. We conclude that wGPR equipped with the proposed data-driven warping provides enhanced flexibility and-at least for the cases studied- improved predictive accuracy for non-Gaussian data.

Towards Generalizing the Information Theory for Neural Communication.

Neuroscience extensively uses the information theory to describe neural communication, among others, to calculate the amount of information transferred in neural communication and to attempt the cracking of its coding. There are fierce debates on how information is represented in the brain and during transmission inside the brain. The neural information theory attempts to use the assumptions of electronic communication; despite the experimental evidence that the neural spikes carry information on non-discrete states, they have shallow communication speed, and the spikes' timing precision matters. Furthermore, in biology, the communication channel is active, which enforces an additional power bandwidth limitation to the neural information transfer. The paper revises the notions needed to describe information transfer in technical and biological communication systems. It argues that biology uses Shannon's idea outside of its range of validity and introduces an adequate interpretation of information. In addition, the presented time-aware approach to the information theory reveals pieces of evidence for the role of processes (as opposed to states) in neural operations. The generalized information theory describes both kinds of communication, and the classic theory is the particular case of the generalized theory.

Bayesian quantile regression-based nonlinear mixed-effects joint models for time-to-event and longitudinal data with multiple features.

This article explores Bayesian joint models for a quantile of longitudinal response, mismeasured covariate and event time outcome with an attempt to (i) characterize the entire conditional distribution of the response variable based on quantile regression that may be more robust to outliers and misspecification of error distribution; (ii) tailor accuracy from measurement error, evaluate non-ignorable missing observations, and adjust departures from normality in covariate; and (iii) overcome shortages of confidence in specifying a time-to-event model. When statistical inference is carried out for a longitudinal data set with non-central location, non-linearity, non-normality, measurement error, and missing values as well as event time with being interval censored, it is important to account for the simultaneous treatment of these data features in order to obtain more reliable and robust inferential results. Toward this end, we develop Bayesian joint modeling approach to simultaneously estimating all parameters in the three models: quantile regression-based nonlinear mixed-effects model for response using asymmetric Laplace distribution, linear mixed-effects model with skew-t distribution for mismeasured covariate in the presence of informative missingness and accelerated failure time model with unspecified nonparametric distribution for event time. We apply the proposed modeling approach to analyzing an AIDS clinical data set and conduct simulation studies to assess the performance of the proposed joint models and method. Copyright © 2016 John Wiley & Sons, Ltd.

An Updated Guide to Robust Statistical Methods in Neuroscience.

There is a vast array of new and improved methods for comparing groups and studying associations that offer the potential for substantially increasing power, providing improved control over the probability of false positives, and yielding a deeper and more nuanced understanding of data. These new techniques effectively deal with four insights into when and why conventional methods can be unsatisfactory. But for the non-statistician, this vast array of techniques for comparing groups and studying associations can seem daunting. This article briefly reviews when and why conventional methods can have relatively low power and yield misleading results. The main goal is to suggest guidelines regarding the use of modern techniques that improve upon classic approaches such as Pearson's correlation, ordinary linear regression, ANOVA, and ANCOVA. This updated version includes recent advances dealing with effect sizes, including situations where there is a covariate. The R code, figures, and accompanying notebooks have been updated as well. © 2023 The Authors. Current Protocols published by Wiley Periodicals LLC.

Trend analysis and outlier distribution of CO2 and CH4: A case study at a rural site in northern Spain.

CO2 and CH4 outliers may have a noticeable impact on the trend of both gases. Nine years of measurements since 2010 recorded at a rural site in northern Spain were used to investigate these outliers. Their influence on the trend was presented and two limits were established. No more than 23.5% of outliers should be excluded from the measurement series in order to obtain representative trends, which were 2.349 ± 0.012 ppm year-1 for CO2 and 0.00879 ± 0.00004 ppm year-1 for CH4. Two types of outliers were distinguished. Those above the trend line and the rest below the trend line. Outliers were described by skewed distributions where the Weibull distribution figures prominently in most cases. A qualitative procedure was presented to exclude the worst fits, although five statistics were considered to select the best fit. In this case, the modified Nash-Sutcliffe efficiency is prominent. Finally, three symmetrical distributions were added to fit the observations when outliers are excluded, with the Gaussian and beta distributions providing the best fits. As a result, certain skewed functions, such as the lognormal distribution, whose use is frequent for air pollutants, could be questioned in certain applications.

Influence of Wind Speed on CO2 and CH4 Concentrations at a Rural Site.

Meteorological variables have a noticeable impact on pollutant concentrations. Among these variables, wind speed is typically measured, although research into how pollutants respond to it can be improved. This study considers nine years of hourly CO2 and CH4 measurements at a rural site, where wind speed values were calculated by the METEX model. Nine wind speed intervals are proposed where concentrations, distribution functions, and daily as well as annual cycles are calculated. Contrasts between local and transported concentrations are around 5 and 0.03 ppm for CO2 and CH4, respectively. Seven skewed distributions are applied, and five efficiency criteria are considered to test the goodness of fit, with the modified Nash-Sutcliffe efficiency proving to be the most sensitive statistic. The Gumbel distribution is seen to be the most suitable for CO2, whereas the Weibull distribution is chosen for CH4, with the exponential function being the worst. Finally, daily and annual cycles are analysed, where a gradual decrease in amplitude is observed, particularly for the daily cycle. Parametric and nonparametric procedures are used to fit both cycles. The latter gave the best fits, with the agreement being higher for the daily cycle, where evolution is smoother than for the annual cycle.

A Guide to Robust Statistical Methods in Neuroscience.

There is a vast array of new and improved methods for comparing groups and studying associations that offer the potential for substantially increasing power, providing improved control over the probability of a Type I error, and yielding a deeper and more nuanced understanding of data. These new techniques effectively deal with four insights into when and why conventional methods can be unsatisfactory. But for the non-statistician, the vast array of new and improved techniques for comparing groups and studying associations can seem daunting, simply because there are so many new methods that are now available. This unit briefly reviews when and why conventional methods can have relatively low power and yield misleading results. The main goal is to suggest some general guidelines regarding when, how, and why certain modern techniques might be used. © 2018 by John Wiley & Sons, Inc.

Regression away from the mean: Theory and examples.

Using a standard repeated measures model with arbitrary true score distribution and normal error variables, we present some fundamental closed-form results which explicitly indicate the conditions under which regression effects towards (RTM) and away from the mean are expected. Specifically, we show that for skewed and bimodal distributions many or even most cases will show a regression effect that is in expectation away from the mean, or that is not just towards but actually beyond the mean. We illustrate our results in quantitative detail with typical examples from experimental and biometric applications, which exhibit a clear regression away from the mean ('egression from the mean') signature. We aim not to repeal cautionary advice against potential RTM effects, but to present a balanced view of regression effects, based on a clear identification of the conditions governing the form that regression effects take in repeated measures designs.

Hypothesis Testing, p Values, Confidence Intervals, Measures of Effect Size, and Bayesian Methods in Light of Modern Robust Techniques.

The article provides perspectives on p values, null hypothesis testing, and alternative techniques in light of modern robust statistical methods. Null hypothesis testing and p values can provide useful information provided they are interpreted in a sound manner, which includes taking into account insights and advances that have occurred during the past 50 years. There are, of course, limitations to what null hypothesis testing and p values reveal about data. But modern advances make it clear that there are serious limitations and concerns associated with conventional confidence intervals, standard Bayesian methods, and commonly used measures of effect size. Many of these concerns can be addressed using modern robust methods.

A Dynamic Network Model to Explain the Development of Excellent Human Performance.

Across different domains, from sports to science, some individuals accomplish excellent levels of performance. For over 150 years, researchers have debated the roles of specific nature and nurture components to develop excellence. In this article, we argue that the key to excellence does not reside in specific underlying components, but rather in the ongoing interactions among the components. We propose that excellence emerges out of dynamic networks consisting of idiosyncratic mixtures of interacting components such as genetic endowment, motivation, practice, and coaching. Using computer simulations we demonstrate that the dynamic network model accurately predicts typical properties of excellence reported in the literature, such as the idiosyncratic developmental trajectories leading to excellence and the highly skewed distributions of productivity present in virtually any achievement domain. Based on this novel theoretical perspective on excellent human performance, this article concludes by suggesting policy implications and directions for future research.