Statistics

Many classical algorithms output graphical representations of causal structures by testing conditional independence among a set of random variables. In dynamical systems, local independence can be used analogously as a testable implication of the underlying data-generating process. We suggest some inexpensive methods for causal screening which provide output with a sound causal interpretation under the assumption of ancestral faithfulness. The popular model class of linear Hawkes processes is used to provide an example of a dynamical causal model. We argue that for sparse causal graphs the output will often be close to complete. We give examples of this framework and apply it to a challenging biological system.

Bad statistics make research papers unreproducible and misleading. For the most part, the reasons for such misusage of numerical data have been found and addressed years ago by experts and proper practical solutions have been presented instead. Yet, we still see numerous instances of statistical fallacies in modern researches which without a doubt play a significant role in the research reproducibility crisis. In this paper, we review different bad practices that impact the research process from its beginning to its very end. Additionally, we briefly propose open science as a universal methodology that can facilitate the entire research life cycle.

The 175th anniversary of the ASA provides an opportunity to look back into the past and peer into the future. What led our forebears to found the association? What commonalities do we still see? What insights might we glean from their experiences and observations? I will use the anniversary as a chance to reflect on where we are now and where we are headed in terms of statistical education amidst the growth of data science. Statistics is the science of learning from data. By fostering more multivariable thinking, building data-related skills, and developing simulation-based problem solving, we can help to ensure that statisticians are fully engaged in data science and the analysis of the abundance of data now available to us.

The von Mises distribution is one of the most important distribution in statistics to deal with circular data. In this paper we will consider some basic properties and characterizations of the sine skewed von Mises distribution.

The objective of this paper is to examine the assertion that the word "statistics" would have been used for the first time in the 17th century, in a report written by Claude Bouchu, administrator of Bourgogne. A historical and bibliographical analysis is carried out to judge the credibility of this thesis. The physical inspection of the report then makes it possible to bring a final answer.

This book presents our case in defense of a constructivist epistemological framework and the use of compatible statistical theory and inference tools. The basic metaphor of decision theory is the maximization of a gambler's expected fortune, according to his own subjective utility, prior beliefs an learned experiences. This metaphor has proven to be very useful, leading the development of Bayesian statistics since its XX-th century revival, rooted on the work of de Finetti, Savage and others. The basic metaphor presented in this text, as a foundation for cognitive constructivism, is that of an eigen-solution, and the verification of its objective epistemic status. The FBST - Full Bayesian Significance Test - is the cornerstone of a set of statistical tolls conceived to assess the epistemic value of such eigen-solutions, according to their four essential attributes, namely, sharpness, stability, separability and composability. We believe that this alternative perspective, complementary to the one ofered by decision theory, can provide powerful insights and make pertinent contributions in the context of scientific research.

Cognitive transfer is the ability to apply learned skills and knowledge to new applications and contexts. This investigation evaluates cognitive transfer outcomes for a tertiary-level introductory statistics course using the CATALST curriculum, which exclusively used simulation-based methods to develop foundations of statistical inference. A common assessment instrument administered at the end of each course measured learning outcomes for students. CATALST students showed evidence of both near and far transfer outcomes while scoring as high, or higher on the assessed learning objectives, when compared with peers enrolled in similar courses that emphasized parametric inferential methods (e.g. the t-test).

Current decision support systems address domains that are heterogeneous in nature and becoming progressively larger. Such systems often require the input of expert judgement about a variety of different fields and an intensive computational power to produce the scores necessary to rank the available policies. Recently, integrating decision support systems have been introduced to enable a formal Bayesian multi-agent decision analysis to be distributed and consequently efficient. In such systems, where different panels of experts oversee disjoint but correlated vectors of variables, each expert group needs to deliver only certain summaries of the variables under their jurisdiction to properly derive an overall score for the available policies. Here we present an algebraic approach that makes this methodology feasible for a wide range of modelling contexts and that enables us to identify the summaries needed for such a combination of judgements. We are also able to demonstrate that coherence, in a sense we formalize here, is still guaranteed when panels only share a partial specification of their model with other panel members. We illustrate this algebraic approach by applying it to a specific class of Bayesian networks and demonstrate how we can use it to derive closed form formulae for the computations of the joint moments of variables that determine the score of different policies.

The use of simulation-based methods for introducing inference is growing in popularity for the Stat 101 course, due in part to increasing evidence of the methods ability to improve students' statistical thinking. This impact comes from simulation-based methods (a) clearly presenting the overarching logic of inference, (b) strengthening ties between statistics and probability or mathematical concepts, (c) encouraging a focus on the entire research process, (d) facilitating student thinking about advanced statistical concepts, (e) allowing more time to explore, do, and talk about real research and messy data, and (f) acting as a firmer foundation on which to build statistical intuition. Thus, we argue that simulation-based inference should be an entry point to an undergraduate statistics program for all students, and that simulation-based inference should be used throughout all undergraduate statistics courses. In order to achieve this goal and fully recognize the benefits of simulation-based inference on the undergraduate statistics program we will need to break free of historical forces tying undergraduate statistics curricula to mathematics, consider radical and innovative new pedagogical approaches in our courses, fully implement assessment-driven content innovations, and embrace computation throughout the curriculum.

Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional assumptions on error terms. However, these distributional assumptions on the errors may not be appropriate for some data sets. In these case, nonparametric methods may be considered to carry on the regression analysis. Empirical likelihood (EL) method is one of these nonparametric methods. The EL method maximizes a function, which is multiplication of the unknown probabilities corresponding to each observation, under some constraints inherited from the normal equations in OLS estimation method. However, it is well known that the OLS method has poor performance when there are some outliers in the data. In this paper, we consider the EL method with robustifyed constraints. The robustification of the constraints is done by using the robust M estimation methods for regression. We provide a small simulation study and a real data example to demonstrate the capability of the robust EL method to handle unusual observations in the data. The simulation and real data results reveal that robust constraints are needed when heavy tailedness and/or outliers are possible in the data.