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The paper makes a case that the current discussions on replicability and the abuse of significance testing have overlooked a more general contributor to the untrustworthiness of published empirical evidence, which is the uninformed and recipe-like implementation of statistical modeling and inference. It is argued that this contributes to the untrustworthiness problem in several different ways, including [a] statistical misspecification, [b] unwarranted evidential interpretations of frequentist inference results, and [c] questionable modeling strategies that rely on curve-fitting. What is more, the alternative proposals to replace or modify frequentist testing, including [i] replacing p-values with observed confidence intervals and effects sizes, and [ii] redefining statistical significance, will not address the untrustworthiness of evidence problem since they are equally vulnerable to [a]–[c]. The paper calls for distinguishing between unduly data-dependant 'statistical results', such as a point estimate, a p-value, and accept/reject H 0 , from 'evidence for or against inferential claims'. The post-data severity (SEV) evaluation of the accept/reject H 0 results, converts them into evidence for or against germane inferential claims. These claims can be used to address/elucidate several foundational issues, including (i) statistical vs. substantive significance, (ii) the large n problem, and (iii) the replicability of evidence. Also, the SEV perspective sheds light on the impertinence of the proposed alternatives [i]–[iii], and oppugns [iii] the alleged arbitrariness of framing H 0 and H 1 which is often exploited to undermine the credibility of frequentist testing. [ABSTRACT FROM AUTHOR]

The full Bayesian significance test (FBST) for precise hypotheses is a Bayesian alternative to the traditional significance tests based on p-values. The FBST is characterized by the e-value as an evidence index in favor of the null hypothesis (H). An important practical issue for the implementation of the FBST is to establish how small the evidence against H must be in order to decide for its rejection. In this work, we present a method to find a cutoff value for the e-value in the FBST by minimizing the linear combination of the averaged type-I and type-II error probabilities for a given sample size and also for a given dimensionality of the parameter space. Furthermore, we compare our methodology with the results obtained from the test with adaptive significance level, which presents the capital-P P-value as a decision-making evidence measure. For this purpose, the scenario of linear regression models with unknown variance under the Bayesian approach is considered. [ABSTRACT FROM AUTHOR]

The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for bounding the Bayes error in statistical hypothesis testing, the divergence found many other applications due to its empirical robustness property found in applications ranging from information fusion to quantum information. From the viewpoint of information theory, the Chernoff information can also be interpreted as a minmax symmetrization of the Kullback–Leibler divergence. In this paper, we first revisit the Chernoff information between two densities of a measurable Lebesgue space by considering the exponential families induced by their geometric mixtures: The so-called likelihood ratio exponential families. Second, we show how to (i) solve exactly the Chernoff information between any two univariate Gaussian distributions or get a closed-form formula using symbolic computing, (ii) report a closed-form formula of the Chernoff information of centered Gaussians with scaled covariance matrices and (iii) use a fast numerical scheme to approximate the Chernoff information between any two multivariate Gaussian distributions. [ABSTRACT FROM AUTHOR]

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam's razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey's prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks' theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than 10 7 . We show that our analytic expressions reproduce the p-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the p-value and Bayes factor can be expressed as an energy versus entropy competition. [ABSTRACT FROM AUTHOR]

Measurement-device-independent quantum key distribution (MDI-QKD) is innately immune to all detection-side attacks. Due to the limitations of technology, most MDI-QKD protocols use weak coherent photon sources (WCPs), which may suffer from a photon-number splitting (PNS) attack from eavesdroppers. Therefore, the existing MDI-QKD protocols also need the decoy-state method, which can resist PNS attacks very well. However, the existing decoy-state methods do not attend to the existence of PNS attacks, and the secure keys are only generated by single-photon components. In fact, multiphoton pulses can also form secure keys if we can confirm that there is no PNS attack. For simplicity, we only analyze the weaker version of a PNS attack in which a legitimate user's pulse count rate changes significantly after the attack. In this paper, under the null hypothesis of no PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state MDI-QKD protocols via statistical hypothesis testing, extract a normal distribution statistic, and provide a detection method and the corresponding Type I error probability. If the result is judged to be an attack, we use the existing decoy-state method to estimate the secure key rate. Otherwise, all pulses with the same basis leading to successful Bell state measurement (BSM) events including both single-photon pulses and multiphoton pulses can be used to generate secure keys, and we give the formula of the secure key rate in this case. Finally, based on actual experimental data from other literature, the associated experimental results (e.g., the significance level is 5%) show the correctness of our method. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to find the relation between the adaptive significance level presented here and the sample size. We statisticians know of the inconsistency, or paradox, in the current classical tests of significance that are based on p-value statistics that are compared to the canonical significance levels (10%, 5%, and 1%): "Raise the sample to reject the null hypothesis" is the recommendation of some ill-advised scientists! This paper will show that it is possible to eliminate this problem of significance tests. We present here the beginning of a larger research project. The intention is to extend its use to more complex applications such as survival analysis, reliability tests, and other areas. The main tools used here are the Bayes factor and the extended Neyman-Pearson Lemma. [ABSTRACT FROM AUTHOR]

In this paper, the noise-enhanced detection problem is investigated for the binary hypothesis-testing. The optimal additive noise is determined according to a criterion proposed by DeGroot and Schervish (2011), which aims to minimize the weighted sum of type I and II error probabilities under constraints on type I and II error probabilities. Based on a generic composite hypothesis-testing formulation, the optimal additive noise is obtained. The sufficient conditions are also deduced to verify whether the usage of the additive noise can or cannot improve the detectability of a given detector. In addition, some additional results are obtained according to the specificity of the binary hypothesis-testing, and an algorithm is developed for finding the corresponding optimal noise. Finally, numerical examples are given to verify the theoretical results and proofs of the main theorems are presented in the Appendix. [ABSTRACT FROM AUTHOR]

The problem of hypothesis testing in the Neyman-Pearson formulation is considered from a geometric viewpoint. In particular, a concise geometric interpretation of deterministic and random signal detection in the philosophy of information geometry is presented. In such a framework, both hypotheses and detectors can be treated as geometrical objects on the statistical manifold of a parameterized family of probability distributions. Both the detector and detection performance are geometrically elucidated in terms of the Kullback-Leibler divergence. Compared to the likelihood ratio test, the geometric interpretation provides a consistent but more comprehensive means to understand and deal with signal detection problems in a rather convenient manner. Example of the geometry based detector in radar constant false alarm rate (CFAR) detection is presented, which shows its advantage over the classical processing method. [ABSTRACT FROM AUTHOR]

Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Based on this inconvenience, one might want to use tests that satisfy logical requirements. However, Izbicki and Esteves shows that the only tests that are in accordance with three logical requirements (monotonicity, invertibility and consonance) are trivial tests based on point estimation, which generally lack statistical optimality. As a possible solution to this dilemma, this paper adapts the above logical requirements to agnostic tests, in which one can accept, reject or remain agnostic with respect to a given hypothesis. Each of the logical requirements is characterized in terms of a Bayesian decision theoretic perspective. Contrary to the results obtained for regular hypothesis tests, there exist agnostic tests that satisfy all logical requirements and also perform well statistically. In particular, agnostic tests that fulfill all logical requirements are characterized as region estimator-based tests. Examples of such tests are provided. [ABSTRACT FROM AUTHOR]

The extraordinary success of physicists to find simple laws that explain many phenomena is beguiling. With the exception of quantum mechanics, it suggests a deterministic world in which theories are right or wrong, and the world is simple. However, attempts to apply such thinking to other phenomena have not been so successful. Individually and collectively we face many situations dominated by uncertainty, about weather and climate, about how wisely to raise children, and how the economy should be managed. The controversy about hypothesis testing is dominated by the tension between simple explanations and the complexity of the world we live in. [ABSTRACT FROM AUTHOR]

This work addresses an important issue regarding the performance of simultaneous test procedures: the construction of multiple tests that at the same time are optimal from a statistical perspective and that also yield logically-consistent results that are easy to communicate to practitioners of statistical methods. For instance, if hypothesis A implies hypothesis B, is it possible to create optimal testing procedures that reject A whenever they reject B Unfortunately, several standard testing procedures fail in having such logical consistency. Although this has been deeply investigated under a frequentist perspective, the literature lacks analyses under a Bayesian paradigm. In this work, we contribute to the discussion by investigating three rational relationships under a Bayesian decision-theoretic standpoint: coherence, invertibility and union consonance. We characterize and illustrate through simple examples optimal Bayes tests that fulfill each of these requisites separately. We also explore how far one can go by putting these requirements together. We show that although fairly intuitive tests satisfy both coherence and invertibility, no Bayesian testing scheme meets the desiderata as a whole, strengthening the understanding that logical consistency cannot be combined with statistical optimality in general. Finally, we associate Bayesian hypothesis testing with Bayes point estimation procedures. We prove the performance of logically-consistent hypothesis testing by means of a Bayes point estimator to be optimal only under very restrictive conditions. [ABSTRACT FROM AUTHOR]

This paper develops a class of density regression models based on proportional hazards family, namely, Gamma transformation proportional hazard (Gt-PH) model. Exact inference for the regression parameters and hazard ratio is derived. These estimators enjoy some good properties such as unbiased estimation, which may not be shared by other inference methods such as maximum likelihood estimate (MLE). Generalised confidence interval and hypothesis testing for regression parameters are also provided. The method itself is easy to implement in practice. The regression method is also extended to Lasso-based variable selection. [ABSTRACT FROM AUTHOR]

Conditional independence tests have received special attention lately in machine learning and computational intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of probabilistic graphical models, which includes Bayesian network models, conditional independence tests are especially important for the task of learning the probabilistic graphical model structure from data. In this paper, we propose the full Bayesian significance test for tests of conditional independence for discrete datasets. The full Bayesian significance test is a powerful Bayesian test for precise hypothesis, as an alternative to the frequentist's significance tests (characterized by the calculation of the p-value). [ABSTRACT FROM AUTHOR]

A generalized maximum entropy estimator is developed for the linear simultaneous equations model. Monte Carlo sampling experiments are used to evaluate the estimator's performance in small and medium sized samples, suggesting contexts in which the current generalized maximum entropy estimator is superior in mean square error to two and three stage least squares. Analytical results are provided relating to asymptotic properties of the estimator and associated hypothesis testing statistics. Monte Carlo experiments are also used to provide evidence on the power and size of test statistics. An empirical application is included to demonstrate the practical implementation of the estimator. [ABSTRACT FROM AUTHOR]

Bayesian testing of a point null hypothesis is considered. The null hypothesisis that an observation, x, is distributed according to the normal distribution with a mean of zero and known variance σ². The alternative hypothesis is that x is distributed accordingto a normal distribution with an unknown nonzero mean, µ, and variance σ². The testingproblem is formulated as a prediction problem. Bayesian testing based on priors constructedby using conditional mutual information is investigated. [ABSTRACT FROM AUTHOR]

We discuss hypothesis testing and compare different theories in light of observed or experimental data as fundamental endeavors in the sciences. Issues associated with the p-value approach and null hypothesis significance testing are reviewed, and the Bayesian alternative based on the Bayes factor is introduced, along with a review of computational methods and sensitivity related to prior distributions. We demonstrate how Bayesian testing can be practically implemented in several examples, such as the t-test, two-sample comparisons, linear mixed models, and Poisson mixed models by using existing software. Caveats and potential problems associated with Bayesian testing are also discussed. We aim to inform researchers in the many fields where Bayesian testing is not in common use of a well-developed alternative to null hypothesis significance testing and to demonstrate its standard implementation. [ABSTRACT FROM AUTHOR]

Minimum Renyi's pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests. [ABSTRACT FROM AUTHOR]

This paper presents, first, a formal exploration of the relationships between information (statistically defined), statistical hypothesis testing, the use of hypothesis testing in reverse as an investigative tool, channel capacity in a communication system, uncertainty, the concept of entropy in thermodynamics, and Bayes' theorem. This exercise brings out the close mathematical interrelationships between different applications of these ideas in diverse areas of psychology. Subsequent illustrative examples are grouped under (a) the human operator as an ideal communications channel, (b) the human operator as a purely physical system, and (c) Bayes' theorem as an algorithm for combining information from different sources. Some tentative conclusions are drawn about the usefulness of information theory within these different categories. (a) The idea of the human operator as an ideal communications channel has long been abandoned, though it provides some lessons that still need to be absorbed today. (b) Treating the human operator as a purely physical system provides a platform for the quantitative exploration of many aspects of human performance by analogy with the analysis of other physical systems. (c) The use of Bayes' theorem to calculate the effects of prior probabilities and stimulus frequencies on human performance is probably misconceived, but it is difficult to obtain results precise enough to resolve this question. [ABSTRACT FROM AUTHOR]

In-vehicle electronic control unit (ECU) communications generally count on private protocols (defined by the manufacturers) under controller area network (CAN) specifications. Parsing the private protocols for a particular vehicle model would be of great significance in testing the vehicle's resistance to various attacks, as well as in designing efficient intrusion detection and prevention systems (IDPS) for the vehicle. This paper proposes a suite of methods for parsing ECU private protocols on in-vehicle CAN network. These methods include an algorithm for parsing discrete variables (encoded in a discrete manner, e.g., gear state), an algorithm for parsing continuous variables (encoded in a continuous manner, e.g., vehicle speed), and a parsing method based on upper-layer protocols (e.g., OBD and UDS). Extensive verifications have been performed on five different brands of automobiles (including an electric vehicle) to demonstrate the universality and the correctness of these parsing algorithms. Some parsing tips and experiences are also presented. Our continuous-variables parsing algorithm could run in a semi-automatic manner and the parsing algorithm from upper-layer protocols could execute in a completely automatic manner. One might view the results obtained by our parsing algorithms as an important indicator of penetration testing on in-vehicle CAN network. [ABSTRACT FROM AUTHOR]

In this work, a Korean peninsula earthquake network, constructed via event-sequential linking known as the Abe–Suzuki method, was investigated in terms of network properties. A significance test for these network properties was performed via comparisons with those of two random networks, constructed from two approaches, that is, EVENT (SEQUENCE) SHUFFLING and NETWORK (MATRIX) SHUFFLING. The Abe–Suzuki earthquake network has a clear difference from the two random networks. However, the two shuffled networks exhibited completely different functions, and even some network properties for one shuffled datum are significantly high and those of the other shuffled data are low compared to actual data. For most cases, the event-shuffled network showed a functional similarity to the real network, but with different exponents/parameters. This result strongly claims that the Korean peninsula earthquake network has a spatiotemporal causal relation. Additionally, the Korean peninsula network properties are mostly similar to those found in previous studies on the US and Japan. Further, the Korean earthquake network showed strong linearity in a specific range of spatial resolution, that is, 0.20°~0.80°, implying that macroscopic properties of the Korean earthquake network are highly regular in this range of resolution. [ABSTRACT FROM AUTHOR]

In the process of extracting hard coal, extensive databases are created on its quality parameters. A statistical assessment was made of the ash, sulfur, and mercury content of commercial coals produced in the Upper Silesian Coal Basin (USCB). The statistical methods applied: non-parametric tests of compatibility for two populations, parametric significance tests, and non-parametric tests of compatibility for the three populations, showed that the distributions of ash and sulfur content in 2014 and 2015 are comparable and the average values are similar. Statistical tests indicated significant differences in the mercury content distributions and their variances. This demonstrates the need for ongoing monitoring of mercury content in commercial coals, as a prediction of mercury content from historical data is hardly possible. [ABSTRACT FROM AUTHOR]

The Bayes error rate is the expected risk for the Bayes classifier, which assigns a given feature vector HT ht to the class with the highest posterior probability. The so obtained rho function is proportional to one minus a suitably scaled normal density raised to the power HT ht . Hence, the large deviation principle in the weak topology of HT ht can be derived (more easily) using a standard Gartner-Ellis argument and, utilizing this, one can, in principle, repeat all of the arguments above to derive results that are analogous to Theorems 2.2 and 2.3. [Extracted from the article]

To perform statistical inference for time series, one should be able to assess if they present deterministic or stochastic trends. For univariate analysis, one way to detect stochastic trends is to test if the series has unit roots, and for multivariate studies it is often relevant to search for stationary linear relationships between the series, or if they cointegrate. The main goal of this article is to briefly review the shortcomings of unit root and cointegration tests proposed by the Bayesian approach of statistical inference and to show how they can be overcome by the Full Bayesian Significance Test (FBST), a procedure designed to test sharp or precise hypothesis. We will compare its performance with the most used frequentist alternatives, namely, the Augmented Dickey–Fuller for unit roots and the maximum eigenvalue test for cointegration. [ABSTRACT FROM AUTHOR]

Information dynamics and computational mechanics provide a suite of measures for assessing the information- and computation-theoretic properties of complex systems in the absence of mechanistic models. However, both approaches lack a core set of inferential tools needed to make them more broadly useful for analyzing real-world systems, namely reliable methods for constructing confidence sets and hypothesis tests for their underlying measures. We develop the computational mechanics bootstrap, a bootstrap method for constructing confidence sets and significance tests for information-dynamic measures via confidence distributions using estimates of ϵ -machines inferred via the Causal State Splitting Reconstruction (CSSR) algorithm. Via Monte Carlo simulation, we compare the inferential properties of the computational mechanics bootstrap to a Markov model bootstrap. The computational mechanics bootstrap is shown to have desirable inferential properties for a collection of model systems and generally outperforms the Markov model bootstrap. Finally, we perform an in silico experiment to assess the computational mechanics bootstrap's performance on a corpus of ϵ -machines derived from the activity patterns of fifteen-thousand Twitter users. [ABSTRACT FROM AUTHOR]

In recent years, there has been a growing interest in the problem of multi-label streaming feature selection with no prior knowledge of the feature space. However, the algorithms proposed to handle this problem seldom consider the group structure of streaming features. Another shortcoming arises from the fact that few studies have addressed atomic feature models, and particularly, few have measured the attraction and repulsion between features. To remedy these shortcomings, we develop the streaming feature selection algorithm with dynamic sliding windows and feature repulsion loss (SF-DSW-FRL). This algorithm is essentially carried out in three consecutive steps. Firstly, within dynamic sliding windows, candidate streaming features that are strongly related to the labels in different feature groups are selected and stored in a fixed sliding window. Then, the interaction between features is measured by a loss function inspired by the mutual repulsion and attraction between atoms in physics. Specifically, one feature attraction term and two feature repulsion terms are constructed and combined to create the feature repulsion loss function. Finally, for the fixed sliding window, the best feature subset is selected according to this loss function. The effectiveness of the proposed algorithm is demonstrated through experiments on several multi-label datasets, statistical hypothesis testing, and stability analysis. [ABSTRACT FROM AUTHOR]

Just like any physical system, projects have entropy that must be managed by spending energy. The entropy is the project's tendency to move to a state of disorder (schedule delays, cost overruns), and the energy process is an inherent part of any project management methodology. In order to manage the inherent uncertainty of these projects, accurate estimates (for durations, costs, resources, ...) are crucial to make informed decisions. Without these estimates, managers have to fall back to their own intuition and experience, which are undoubtedly crucial for making decisions, but are are often subject to biases and hard to quantify. This paper builds further on two published calibration methods that aim to extract data from real projects and calibrate them to better estimate the parameters for the probability distributions of activity durations. Both methods rely on the lognormal distribution model to estimate uncertainty in activity durations and perform a sequence of statistical hypothesis tests that take the possible presence of two human biases into account. Based on these two existing methods, a new so-called statistical partitioning heuristic is presented that integrates the best elements of the two methods to further improve the accuracy of estimating the distribution of activity duration uncertainty. A computational experiment has been carried out on an empirical database of 83 empirical projects. The experiment shows that the new statistical partitioning method performs at least as good as, and often better than, the two existing calibration methods. The improvement will allow a better quantification of the activity duration uncertainty, which will eventually lead to a better prediction of the project schedule and more realistic expectations about the project outcomes. Consequently, the project manager will be able to better cope with the inherent uncertainty (entropy) of projects with a minimum managerial effort (energy). [ABSTRACT FROM AUTHOR]

This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais. [ABSTRACT FROM AUTHOR]

The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell's seminal work to distinguish, via a Bell test, quantum correlations from the set of correlations allowed by local-hidden-variable theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this paper, we show that the prediction-based-ratio method—initially developed for performing a hypothesis test of local-hidden-variable theories—can equally well be applied to test many other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce any of the outer approximation to the quantum set of correlations due to Navascués-Pironio-Acín. We numerically simulate Bell tests using hypothetical nonlocal sources of correlations to illustrate the applicability of the method in both the independent and identically distributed (i.i.d.) scenario and the non-i.i.d. scenario. As a further application, we demonstrate how this method allows us to unveil an apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. This, in turn, highlights the importance of the randomization of measurement settings, as well as a consistency check of the nonsignaling conditions in a Bell test. [ABSTRACT FROM AUTHOR]

We study a binary hypothesis testing problem in which a defender must decide whether a test sequence has been drawn from a given memoryless source P 0 , while an attacker strives to impede the correct detection. With respect to previous works, the adversarial setup addressed in this paper considers an attacker who is active under both hypotheses, namely, a fully active attacker, as opposed to a partially active attacker who is active under one hypothesis only. In the fully active setup, the attacker distorts sequences drawn both from P 0 and from an alternative memoryless source P 1 , up to a certain distortion level, which is possibly different under the two hypotheses, to maximize the confusion in distinguishing between the two sources, i.e., to induce both false positive and false negative errors at the detector, also referred to as the defender. We model the defender–attacker interaction as a game and study two versions of this game, the Neyman–Pearson game and the Bayesian game. Our main result is in the characterization of an attack strategy that is asymptotically both dominant (i.e., optimal no matter what the defender's strategy is) and universal, i.e., independent of P 0 and P 1 . From the analysis of the equilibrium payoff, we also derive the best achievable performance of the defender, by relaxing the requirement on the exponential decay rate of the false positive error probability in the Neyman–Pearson setup and the tradeoff between the error exponents in the Bayesian setup. Such analysis permits characterizing the conditions for the distinguishability of the two sources given the distortion levels. [ABSTRACT FROM AUTHOR]

A strong earthquake of magnitude M w 6.8 struck Western Greece on 25 October 2018 with an epicenter at 37.515 ∘ N 20.564 ∘ E. It was preceded by an anomalous geolectric signal that was recorded on 2 October 2018 at a measuring station 70 km away from the epicenter. Upon analyzing this signal in natural time, we find that it conforms to the conditions suggested for its identification as precursory Seismic Electric Signal (SES) activity. Notably, the observed lead time of 23 days lies within the range of values that has been very recently identified as being statistically significant for the precursory variations of the electric field of the Earth. Moreover, the analysis in natural time of the seismicity subsequent to the SES activity in the area candidate to suffer this strong earthquake reveals that the criticality conditions were obeyed early in the morning of 18 October 2018, i.e., almost a week before the strong earthquake occurrence, in agreement with earlier findings. Finally, when employing the recent method of nowcasting earthquakes, which is based on natural time, we find an earthquake potential score around 80%. [ABSTRACT FROM AUTHOR]

As previous research indicates, a multiple-scanning methodology for discretization of numerical datasets, based on entropy, is very competitive. Discretization is a process of converting numerical values of the data records into discrete values associated with numerical intervals defined over the domains of the data records. In multiple-scanning discretization, the last step is the merging of neighboring intervals in discretized datasets as a kind of postprocessing. Our objective is to check how the error rate, measured by tenfold cross validation within the C4.5 system, is affected by such merging. We conducted experiments on 17 numerical datasets, using the same setup of multiple scanning, with three different options for merging: no merging at all, merging based on the smallest entropy, and merging based on the biggest entropy. As a result of the Friedman rank sum test (5% significance level) we concluded that the differences between all three approaches are statistically insignificant. There is no universally best approach. Then, we repeated all experiments 30 times, recording averages and standard deviations. The test of the difference between averages shows that, for a comparison of no merging with merging based on the smallest entropy, there are statistically highly significant differences (with a 1% significance level). In some cases, the smaller error rate is associated with no merging, in some cases the smaller error rate is associated with merging based on the smallest entropy. A comparison of no merging with merging based on the biggest entropy showed similar results. So, our final conclusion was that there are highly significant differences between no merging and merging, depending on the dataset. The best approach should be chosen by trying all three approaches. [ABSTRACT FROM AUTHOR]

A method is presented to detect earthquake precursors from time series data on earthquakes in a target region. The Regional Entropy of Seismic Information (RESI) is an index that represents the average influence of an earthquake in a target region on the diversity of clusters to which earthquake foci are distributed. Based on a simple qualitative model of the dynamics of land crust, it is hypothesized that the saturation that occurs after an increase in RESI precedes the activation of earthquakes. This hypothesis is validated by the earthquake catalog. This temporal change was found to correlate with the activation of earthquakes in Japanese regions one to two years ahead of the real activation, more reliably than the compared baseline methods. [ABSTRACT FROM AUTHOR]

Testing of evidence in criminal cases can be limited by temporal or financial constraints or by the fact that certain tests may be mutually exclusive, so choosing the tests that will have maximal impact on the final result is essential. In this paper, we assume that a main hypothesis, evidence for it and possible tests for existence of this evidence are represented in the form of a Bayesian network, and use three different methods to measure the impact of a test on the main hypothesis. We illustrate the methods by applying them to an actual digital crime case provided by the Hong Kong police. We conclude that the Kullback–Leibler divergence is the optimal method for selecting the tests with the highest impact. [ABSTRACT FROM AUTHOR]

In recent years, analytical tools of network theory have provided strong empirical support to the well-known hypothesis that regions develop through the local learning of capabilities (tacit productive knowledge). In this paper, we compare two indexes of competitiveness (or accumulated capabilities) for a subnational database of 32 Mexican states in the period 2004–2014. We find that Endogenous Fitness (i.e., region fitness and product complexity are derived jointly using only a Mexican exports database) has a better performance than Exogenous Fitness (i.e., product complexity comes from a world exports database and fitness is the sum of the complexity scores for the region's competitive products). The performance criterion is established with the indicator's capacity to meet a requirement of growth predictability: the existence of at least one laminar (ordered) regime in the fitness–income plane. In the Mexican data, Endogenous Fitness is a reliable predictor of per capita GDP in two distinct areas of the plane: one of continuous progress and opportunities, and another of stagnation and deteriorating fitness. The predictive capacity of this indicator becomes clear only when the metrics' calculations are filtered by removing raw petroleum or oil-dependent states, while such capacity is robust to the inclusion of tourism—another important industry of the Mexican economy. [ABSTRACT FROM AUTHOR]