Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology

The detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as ‘deterministic components’ or ‘trends’ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures

Tests of fit for the logarithmic distribution

Smooth tests for the logarithmic distribution are compared with three tests: the first is a test due to Epps and is based on a probability generating function, the second is the Anderson-Darling test, and the third is due to Klar and is based on the empirical integrated distribution function. These tests all have substantially better power than the traditional Pearson-Fisher X2 test of fit for the logarithmic. These traditional chi-squared tests are the only logarithmic tests of fit commonly applied by ecologists and other scientists

Bootstrapped Information-Theoretic Model Selection with Error Control (BITSEC)

abstract: Statistical model selection using the Akaike Information Criterion (AIC) and similar criteria is a useful tool for comparing multiple and non-nested models without the specification of a null model, which has made it increasingly popular in the natural and social sciences. De- spite their common usage, model selection methods are not driven by a notion of statistical confidence, so their results entail an unknown de- gree of uncertainty. This paper introduces a general framework which extends notions of Type-I and Type-II error to model selection. A theo- retical method for controlling Type-I error using Difference of Goodness of Fit (DGOF) distributions is given, along with a bootstrap approach that approximates the procedure. Results are presented for simulated experiments using normal distributions, random walk models, nested linear regression, and nonnested regression including nonlinear mod- els. Tests are performed using an R package developed by the author which will be made publicly available on journal publication of research results.Dissertation/ThesisMasters Thesis Statistics 201

The interplay of strategic and internal green marketing orientation on competitive advantage

This paper seeks to clarify and refine the relationship between strategic and internal green marketing and firm competitiveness. Despite the significance of corporate environmental strategy to firms adopting a triple-bottom line performance evaluation, there is insufficient focus on strategic green marketing and its impact on a firm’s competitiveness. This study fills the gap by providing a comprehensive view of strategic green marketing and its impact on competitive advantage. Findings also reveal the moderating role of internal green marketing actions towards the development of a sustained competitive advantage. Specifically, the findings build on contemporary green marketing literature suggesting that a significant interplay between strategy and people exists which enhances the creation of competitive advantage. This in turn increases financial performance. Finally, this research uses an updated approach to build on current literature concerning the drivers and outcomes of strategic green marketing. This provides managers with nuanced insights about environmentally-driven competitive advantage

Heterogeneous Impacts in PROGRESA

The “common effect” model in program evaluation assumes that all treated individuals have the same impact from a program. Our paper contributes to the recent literature that tests and goes beyond the common effect model by investigating impact heterogeneity using data from the experimental evaluation of the Mexican conditional cash transfer program PROGRESA. Our analysis builds upon and extends that in Heckman, Smith and Clements (1997) and more recent studies of quantile treatment effects and random coefficient models. We find strong evidence of systematic (i.e. subgroup) variation in impacts in PROGRESA and modest evidence of heterogeneous impacts conditional on the systematic impacts. We find evidence against the perfect positive dependence assumption that underlies the interpretation of quantile treatment effects as impacts at quantiles of the untreated outcome distribution. Our paper concludes with a discussion of the policy relevance of our findings and of heterogeneous impacts more generally.randomized experiment, quantile treatment effects, heterogeneous impacts

Learning and comparing functional connectomes across subjects

Functional connectomes capture brain interactions via synchronized fluctuations in the functional magnetic resonance imaging signal. If measured during rest, they map the intrinsic functional architecture of the brain. With task-driven experiments they represent integration mechanisms between specialized brain areas. Analyzing their variability across subjects and conditions can reveal markers of brain pathologies and mechanisms underlying cognition. Methods of estimating functional connectomes from the imaging signal have undergone rapid developments and the literature is full of diverse strategies for comparing them. This review aims to clarify links across functional-connectivity methods as well as to expose different steps to perform a group study of functional connectomes

Accounting for variance and hyperparameter optimization in machine learning benchmarks

La récente révolution de l'apprentissage automatique s'est fortement appuyée sur l'utilisation de bancs de test standardisés. Ces derniers sont au centre de la méthodologie scientifique en apprentissage automatique, fournissant des cibles et mesures indéniables des améliorations des algorithmes d'apprentissage. Ils ne garantissent cependant pas la validité des résultats ce qui implique que certaines conclusions scientifiques sur les avancées en intelligence artificielle peuvent s'avérer erronées. Nous abordons cette question dans cette thèse en soulevant d'abord la problématique (Chapitre 5), que nous étudions ensuite plus en profondeur pour apporter des solutions (Chapitre 6) et finalement developpons un nouvel outil afin d'amélioration la méthodologie des chercheurs (Chapitre 7). Dans le premier article, chapitre 5, nous démontrons la problématique de la reproductibilité pour des bancs de test stables et consensuels, impliquant que ces problèmes sont endémiques aussi à de grands ensembles d'applications en apprentissage automatique possiblement moins stable et moins consensuels. Dans cet article, nous mettons en évidence l'impact important de la stochasticité des bancs de test, et ce même pour les plus stables tels que la classification d'images. Nous soutenons d'après ces résultats que les solutions doivent tenir compte de cette stochasticité pour améliorer la reproductibilité des bancs de test. Dans le deuxième article, chapitre 6, nous étudions les différentes sources de variation typiques aux bancs de test en apprentissage automatique, mesurons l'effet de ces variations sur les méthodes de comparaison d'algorithmes et fournissons des recommandations sur la base de nos résultats. Une contribution importante de ce travail est la mesure de la fiabilité d'estimateurs peu coûteux à calculer mais biaisés servant à estimer la performance moyenne des algorithmes. Tel qu'expliqué dans l'article, un estimateur idéal implique plusieurs exécution d'optimisation d'hyperparamètres ce qui le rend trop coûteux à calculer. La plupart des chercheurs doivent donc recourir à l'alternative biaisée, mais nous ne savions pas jusqu'à présent la magnitude de la dégradation de cet estimateur. Sur la base de nos résultats, nous fournissons des recommandations pour la comparison d'algorithmes sur des bancs de test avec des budgets de calculs limités. Premièrement, les sources de variations devraient être randomisé autant que possible. Deuxièmement, la randomization devrait inclure le partitionnement aléatoire des données pour les ensembles d'entraînement, de validation et de test, qui s'avère être la plus importante des sources de variance. Troisièmement, des tests statistiques tel que la version du Mann-Withney U-test présenté dans notre article devrait être utilisé plutôt que des comparisons sur la simple base de moyennes afin de prendre en considération l'incertitude des mesures de performance. Dans le chapitre 7, nous présentons un cadriciel d'optimisation d'hyperparamètres développé avec principal objectif de favoriser les bonnes pratiques d'optimisation des hyperparamètres. Le cadriciel est conçu de façon à privilégier une interface simple et intuitive adaptée aux habitudes de travail des chercheurs en apprentissage automatique. Il inclut un nouveau système de versionnage d'expériences afin d'aider les chercheurs à organiser leurs itérations expérimentales et tirer profit des résultats antérieurs pour augmenter l'efficacité de l'optimisation des hyperparamètres. L'optimisation des hyperparamètres joue un rôle important dans les bancs de test, les hyperparamètres étant un facteur confondant significatif. Fournir aux chercheurs un instrument afin de bien contrôler ces facteurs confondants est complémentaire aux recommandations pour tenir compte des sources de variation dans le chapitre 6. Nos recommendations et l'outil pour l'optimisation d'hyperparametre offre une base solide pour une méthodologie robuste et fiable.The recent revolution in machine learning has been strongly based on the use of standardized benchmarks. Providing clear target metrics and undeniable measures of improvements of learning algorithms, they are at the center of the scientific methodology in machine learning. They do not ensure validity of results however, therefore some scientific conclusions based on flawed methodology may prove to be wrong. In this thesis we address this question by first raising the issue (Chapter 5), then we study it to find solutions and recommendations (Chapter 6) and build tools to help improve the methodology of researchers (Chapter 7). In first article, Chapter 5, we demonstrate the issue of reproducibility in stable and consensual benchmarks, implying that these issues are endemic to a large ensemble of machine learning applications that are possibly less stable or less consensual. We raise awareness of the important impact of stochasticity even in stable image classification tasks and contend that solutions for reproducible benchmarks should account for this stochasticity. In second article, Chapter 6, we study the different sources of variation that are typical in machine learning benchmarks, measure their effect on comparison methods to benchmark algorithms and provide recommendations based on our results. One important contribution of this work is that we measure the reliability of a cheaper but biased estimator for the average performance of algorithms. As explained in the article, an ideal estimator involving multiple rounds of hyperparameter optimization is too computationally expensive. Most researchers must resort to use the biased alternative, but it has been unknown until now how serious a degradation of the quality of estimation this leads to. Our investigations provides guidelines for benchmarks on practical budgets. First, as many sources of variations as possible should be randomized. Second, the partitioning of data in training, validation and test sets should be randomized as well, since this is the most important source of variation. Finally, statistical tests should be used instead of ad-hoc average comparisons so that the uncertainty of performance estimation can be accounted for when comparing machine learning algorithms. In Chapter 7, we present a framework for hyperparameter optimization that has been developed with the main goal of encouraging best practices for hyperparameter optimization. The framework is designed to favor a simple and intuitive interface adapted to the workflow of machine learning researchers. It includes a new version control system for experiments to help researchers organize their rounds of experimentations and leverage prior results for more efficient hyperparameter optimization. Hyperparameter optimization plays an important role in benchmarking, with the effect of hyperparameters being a serious confounding factor. Providing an instrument for researchers to properly control this confounding factor is complementary to our guidelines to account for sources of variation in Chapter 7. Our recommendations together with our tool for hyperparameter optimization provides a solid basis for a reliable methodology in machine learning benchmarks