Spectroscopy meets modern statistics: International workshop in April 2024

Problem. The statistical analysis of the changing and uncertain information is an increasingly important component of decision making in the modern world. Therefore, the necessity to develop statistical thinking of students of all levels of education has grown significantly. The "statistical literacy" of students is a relatively new term in statistics education research which needs special attention. Goal. The purpose of this article is to attract attention to the problems of teaching modern statistics to university students which is necessary to meet the requirements of statistics knowledge in today’s information world, and to comprehend the matter of the term "statistical literacy" of students in modern understanding of these words, to understand what should be considered as the desired outcomes of the statistic education. Methodology. The results presented in this paper were obtained by the analysis of the existing methodological investigations in the modern statistics education with the emphasis on the development of the students’ statistical thinking and reasoning, and on the ability to apply their knowledge in statistics in fulfilling the professional tasks. Results. Application of new pedagogical techniques in the statistics education is of paramount importance for the development of students' statistical thinking and reasoning. It is important for students to develop statistical thinking by combining abstract conceptions of statistics with the actual content of information to which statistical analysis is applied. The statistical reasoning of the students can best be assessed through oral discussions or detailed student work with professional content. For deeper understanding of statistical concepts, it is important to simplify learning rather than extending the educational program. Students should be encouraged to explain their reasoning, to mutually criticize arguments and to find new ways of solving problems. They should be encouraged to ask «why» rather than «how», and pushed to substantiate their thinking process and, by this means, modern understanding of statistics will be provided. Originality. Training engineers as sufficiently informed workers capable of making correct decisions requires educations in the area of methods of modern statistics in close connection with professional education. Practical value. Summing up, it has been proved that one of the most important tasks of the students’ education in statistics is, first of all, to develop their understanding of the practical necessity and economic feasibility of using statistics in their future professional activities, to develop their statistical thinking, and to learn how to use the methods of mathematical statistics for analyzing professional information.

Chapter 13 - Empirical Methods

1.06 - Resampling and Testing in Regression Models with Environmetrical Applications

Asymptotic theory plays a fundamental role in the developments of modern statistics, especially in the theoretical analysis of new methodologies. Some asymptotic results may borrow directly from the limit theory in probability, but many need deep insights of statistical contents and more accurate approximations, which have in turn fostered further developments of limit theory in probability. Peter Bickel has made far-reaching and wide-ranging contributions to modern statistics. He is a giant in theoretical statistics. In asymptotic theory, besides his contributions to bootstrap and high-dimensional statistical inference, in this paper I shall focus on four of his seminal papers on asymptotic expansions and Bartlett correction for Bayes solutions, likelihood ratio statistics and maximum-likelihood estimator for general hidden Markov models. The papers will be reviewed in chronological order.KeywordsHide Markov ModelAsymptotic DistributionAsymptotic TheoryAsymptotic NormalityLikelihood Ratio StatisticThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The ongoing climate change requires a quantitative assessment of the impact of weather conditions on the nature and livelihoods of the population. However, to date, the concept of “climate risk” has not been finally defined, and the corresponding terminology is not universally recognized. One manifestation of climate change is an increase in climate variability and extremeness in many regions. At the same time, modern statistics indicate growing worldwide damage from dangerous weather and climate events. The most widely used in climate services is the concept of “Vulnerability index”, which reflects a combination (with or without weighing) of several indicators that indicate the potential damage that climate change can cause to a particular sector of the economy. development of adaptation measures to ensure sustainable development of territories. The main criterion for the vulnerability of the territory from the point of view of meteorological parameters is the extremeness of the basic values: daily air temperature, daily precipitation, maximum wind speed. To fully take into account the possible impacts of extreme climatic conditions on the region’s economy, it is necessary to detail the weather and climate risks taking into account the entire observation network, since significant differences in quantitative assessment are possible. The obtained average regional values of the climate vulnerability indices for the Belgorod Region of the Russian Federation provide 150 points for the winter period, 330 points for the summer season, which indicates the prevalence of extreme weather conditions in the warm season. Most of the territory has a relative influence on climatic phenomena, with the exception of the East and the Southeast Region. Moreover, the eastern part of the region is the most vulnerable in climatic terms.

This innovative textbook presents material for a course on modern statistics that incorporates Python as a pedagogical and practical resource.

Reliability of dielectric composite materials (DCMs) is a multifaceted problem. Both high voltage and dimensional miniaturization decrease the path length for charge dissipation in the DCMs. This results in short life due to charge entrapment and uncontrolled release. The source of trapped charges in the DCM arises due to the intrinsic interfacial polarization in the filled system. From the compound perspective, at least four interacting variables are involved in determining relative reliability of DCMs: filler size, curing time, thickness, and polarization voltage magnitude. Experimental and data analysis of all four variables, with uncertainty propagated for each factor, is paramount to understanding behavior of each property and its interactions, shaping DCMs characteristics. Combining views from The Design of Experiments (Fisher, 1935), modern statistics (Hand, 2008), and analytical computer software (NIST Dataplot 2015) yields a free graphic user interface tool to optimize the design of compound mixtures to minimize the polarization for increased reliability.

In this overview, we summarise key findings from our systematic review on the aetiology of ADHD. The efforts to identify the causes of ADHD have been extensive and the findings may be useful for developing treatments and reducing its incidence. Over the past few decades, modern statistics have been applied to data sets of twin and family studies that can discern the extent to which variation in symptoms is attributable to the social, rearing or familial environment, to unique events that befall only one family member, or to genetics. These studies consistently support the strong level of genetics contributing to this disorder (70-80%) with the residual variation accounted for by unique, non-shared events. Advances in molecular genetics have established the disorder as polygenic and thus dimensional in nature. Additionally, epidemiological and naturalistic research designs have identified two independent, environmental causes of ADHD; occurring rarely. We discuss the numerous implications of these results for the categorisation of ADHD, clinical practice, theoretical conceptualisations of executive functioning, and usefulness in rebutting misinformation propagated by the trade media.

Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are a popular class of models used for this purpose. Gaussian DAG models introduce sparsity in the Cholesky factor of the inverse covariance matrix, and the sparsity pattern in turn corresponds to specific conditional independence assumptions on the underlying variables. A variety of priors have been developed in recent years for Bayesian inference in DAG models, yet crucial convergence and sparsity selection properties for these models have not been thoroughly investigated. Most of these priors are adaptations/generalizations of the Wishart distribution in the DAG context. In this paper, we consider a flexible and general class of these “DAG-Wishart” priors with multiple shape parameters. Under mild regularity assumptions, we establish strong graph selection consistency and establish posterior convergence rates for estimation when the number of variables $p$ is allowed to grow at an appropriate subexponential rate with the sample size $n$.

Optimal randomized classification trees

Human biometeorology is quite an old science: during the times of Hippokrates in ancient Greece the influence of weather changes on physiological processes in the human body were considered to exist. However, not until the progress in modern statistics, physics and physiology in the course of this century provided quantitative methods did human-biometeorology become an acknowledged natural science. In the first half of this century primarily the explanation of the phenomena of reactions of the body to weather changes was the general objective. In the second half of this century quantitative descriptions of thermal interchanges between the human body and the environment by means of energy balance models of the human body have gained increasing importance. The methods of modern human biometeorology increasingly are acknowledged by workers in disciplines of potential application, such as urban or regional planners or air conditioning engineers. Human biometeorology tries to assess all atmospheric influences in its entirety, including the air pollution pattern. The discipline considers itself as branch of science which is tied closely to environmental meteorology and environmental medicine.

Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in other words, performing "least squares under a convex constraint." Many problems in modern statistics and statistical signal processing theory are special cases of this general situation. Examples include the lasso and other high-dimensional regression techniques, function estimation problems, matrix estimation and completion, shape-restricted regression, constrained denoising, linear inverse problems, etc. This paper presents three general results about this problem, namely, (a) an exact computation of the main term in the estimation error by relating it to expected maxima of Gaussian processes (existing results only give upper bounds), (b) a theorem showing that the least squares estimator is always admissible up to a universal constant in any problem of the above kind and (c) a counterexample showing that least squares estimator may not always be minimax rate-optimal. The result from part (a) is then used to compute the error of the least squares estimator in two examples of contemporary interest.

Hunting for significance: Bayesian classifiers under a mixture loss function

During the current COVID-19 pandemic, the number of infected people in the world exceeded 56 million, and the number of deaths from this infection was more than 1.3 million cases. Such figures can undoubtedly cause alarm and concern for everyone, since these indicators are the fate of people, and the current situation suggests that in the case of a particular person's illness, the outcome cannot be predicted. For a complete picture of current events, it is interesting to look at similar statistics just over 10 years ago, when bacterial forms of acute pneumonia (AP) clearly prevailed, and viral diseases were rare. The total number of cases of AP (not infected, as it is now) in the world has reached 450 million cases and 4 million deaths annually (1,2). The figures presented which are many times higher than the current ones, have not been replicated and are not even familiar to all specialists. It is not difficult to understand that, despite such a dramatic difference in indicators, modern statistics, due to their wide distribution, undoubtedly have a greater psychological impact on public opinion. However, in this context, it is not so much the informative role of statistics as the additional characteristics of the pandemic hidden in statistical figures. Analysis of the statistics of the current COVID-19 pandemic allows us to expand the understanding of this infectious invasion in a completely unexpected perspective, which goes beyond the generally accepted opinion about the nature of this phenomenon. According to statistics, most people infected with coronavirus tolerate this contact without any consequences. So, according to statistics, most infected people do without the help of medicine at all, resorting to its services only for diagnostic procedures. The total established number of coronavirus carriers is approximate and depends on the breadth of diagnostic tests, while the actual number of infected is unknown and may be significantly higher.

Markov Chain Monte Carlo (MCMC) based methods have been the main tool for Bayesian Inference for some years now, and recently they find increasing applications in modern statistics and machine learning. Nevertheless, with the availability of large datasets and increasing complexity of Bayesian models, MCMC methods are becoming prohibitively expensive for real-world problems. At the heart of these methods, lies the computation of likelihood functions that requires access to all input data points in each iteration of the method. Current approaches, based on data subsampling, aim to accelerate these algorithms by reducing the number of the data points for likelihood evaluations at each MCMC iteration. However the existing work doesn't consider the properties of modern memory hierarchies, but treats the memory as one monolithic storage space. This paper proposes a communication-aware MCMC framework that takes into account the underlying performance of the memory subsystem. The framework is based on a novel subsampling algorithm that utilises an unbiased likelihood estimator based on Probability Proportional-to-Size (PPS) sampling, allowing information on the performance of the memory system to be taken into account during the sampling stage. The proposed MCMC sampler is mapped to an FPGA device and its performance is evaluated using the Bayesian logistic regression model on MNIST dataset. The proposed system achieves a 3.37x speed up over a highly optimised traditional FPGA design, therefore the risk in the estimates based on the generated samples is largely decreased.