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In the present paper we construct plans orthogonal through the block factor (POTBs). We describe procedures for adding blocks as well as factors to an initial plan and thus generate a bigger plan. Using these procedures we construct POTBs for symmetrical experiments with factors having three or more levels. We also construct a series of plans inter-class orthogonal through the block factor for two-level factors.
We propose a simple model selection approach for algorithms in stochastic bandit and reinforcement learning problems. As opposed to prior work that (implicitly) assumes knowledge of the optimal regret, we only require that each base algorithm comes with a candidate regret bound that may or may not hold during all rounds. In each round, our approach plays a base algorithm to keep the candidate regret bounds of all remaining base algorithms balanced, and eliminates algorithms that violate their candidate bound. We prove that the total regret of this approach is bounded by the best valid candidate regret bound times a multiplicative factor. This factor is reasonably small in several applications, including linear bandits and MDPs with nested function classes, linear bandits with unknown misspecification, and LinUCB applied to linear bandits with different confidence parameters. We further show that, under a suitable gap-assumption, this factor only scales with the number of base algorithms and not their complexity when the number of rounds is large enough. Finally, unlike recent efforts in model selection for linear stochastic bandits, our approach is versatile enough to also cover cases where the context information is generated by an adversarial environment, rather than a stochastic one.
Reproducibility has been consistently identified as an important component of scientific research. Although there is a general consensus on the importance of reproducibility along with the other commonly used 'R' terminology (i.e., Replicability, Repeatability etc.), there is some disagreement on the usage of these terms, including conflicting definitions used by different parts of the research community. In this encyclopedia article, we explore the different definitions used in scientific literature (specifically pertaining to computational research), whether there is a need for a single standardized definition and provide an alternative based on non-functional requirements. We also describe the role of reproducibility (and other R's) in scientific workflows.
Our introductory classes in statistics and data science use too much mathematics. The key causal effect which our students want our classes to have is to improve their future performance and opportunities. The more professional their computing skills (in the context of data analysis), the greater their likely success. Introductory courses should feature almost no mathematical/statistical formulas beyond simple algebra.
Understanding the microeconomic details of technological catch-up processes offers great potential for informing both innovation economics and development policy. We study the economic transition of the PR China from an agrarian country to a high-tech economy as one example for such a case. It is clear from past literature that rapidly rising productivity levels played a crucial role. However, the distribution of labor productivity in Chinese firms has not been comprehensively investigated and it remains an open question if this can be used to guide economic development. We analyze labor productivity and the dynamic change of labor productivity in firm-level data for the years 1998-2013 from the Chinese Industrial Enterprise Database. We demonstrate that both variables are conveniently modeled as Lévy alpha-stable distributions, provide parameter estimates and analyze dynamic changes to this distribution. We find that the productivity gains were not due to super-star firms, but due to a systematic shift of the entire distribution with otherwise mostly unchanged characteristics. We also found an emerging right-skew in the distribution of labor productivity change. While there are significant differences between the 31 provinces and autonomous regions of the P.R. China, we also show that there are systematic relations between micro-level and province-level variables. We conclude with some implications of these findings for development policy.
The wealth of nations and the health of populations are intimately strongly associated, yet the extent to which economic prosperity (GDP per capita) causes improved health remains disputed. The purpose of this article is to analyze the impact of sovereign debt crises (SDC) on child mortality, using a sample of 57 low- and middle-income countries surveyed by the Demographic and Health Survey between the years 1990 and 2015. These surveys supply 229 household data and containing about 3 million childbirth history records. This focus on SDC instead of GDP provides a quasi-experimental moment in which the influence of unobserved confounding is less than a moment analyzing the normal fluctuations of GDP. This study measures child mortality at six thresholds: neonatal, under-one (infant), under-two, under-three, under-four, and under-five mortality. Using a machine-learning (ML) model for causal inference, this study finds that while an SDC causes an adverse yet statistically insignificant effect on neonatal mortality, all other child mortality group samples are adversely affected between a probability of 0.12 to 0.14 (all statistically significant at the 95-percent threshold). Through this ML, this study also finds that the most important treatment heterogeneity moderator, in the entire adjustment set, is whether a child is born in a low-income country.
Multivariate hypergeometric distribution arises frequently in elementary statistics and probability courses, for simultaneously studying the occurence law of specified events, when sampling without replacement from a finite population with fixed number of classification. Covariance matrix of this distribution is well known to be identical to its multinomial counterpart multiplied by 1-(n-1)/(N-1), with N and n being population and sample sizes, respectively. It appears to however, have been less discussed in the literature about the meaning of this relationship, especially regarding the specific form of the multiplier. Based on an augmenting argument together with probabilistic symmetry, we present a more transparent understanding for the covariance structure of the multivariate hypergeometric distribution. We discuss implications of these combined techniques and provide a unified description about the relative efficiency for estimating population mean based on simple random sampling, probability proportional-to-size sampling and adaptive cluster sampling, with versus without replacement. We also provide insight into the classic random group method for variance estimation.
Motivated by the complexity of network data, we propose a directed hybrid random network that mixes preferential attachment (PA) rules with uniform attachment (UA) rules. When a new edge is created, with probability $p\in [0,1]$, it follows the PA rule. Otherwise, this new edge is added between two uniformly chosen nodes. Such mixture makes the in- and out-degrees of a fixed node grow at a slower rate, compared to the pure PA case, thus leading to lighter distributional tails. Useful inference methods for the proposed hybrid model are then provided and applied to both synthetic and real datasets. We see that with extra flexibility given by the parameter $p$, the hybrid random network provides a better fit to real-world scenarios, where lighter tails from in- and out-degrees are observed.
The latest Industrial revolution has helped industries in achieving very high rates of productivity and efficiency. It has introduced data aggregation and cyber-physical systems to optimize planning and scheduling. Although, uncertainty in the environment and the imprecise nature of human operators are not accurately considered for into the decision making process. This leads to delays in consignments and imprecise budget estimations. This widespread practice in the industrial models is flawed and requires rectification. Various other articles have approached to solve this problem through stochastic or fuzzy set model methods. This paper presents a comprehensive method to logically and realistically quantify the non-deterministic uncertainty through probabilistic uncertainty modelling. This method is applicable on virtually all Industrial data sets, as the model is self adjusting and uses epsilon-contamination to cater to limited or incomplete data sets. The results are numerically validated through an Industrial data set in Flanders, Belgium. The data driven results achieved through this robust scheduling method illustrate the improvement in performance.
Quantum computers use quantum resources to carry out computational tasks and may outperform classical computers in solving certain computational problems. Special-purpose quantum computers such as quantum annealers employ quantum adiabatic theorem to solve combinatorial optimization problems. In this paper, we compare classical annealings such as simulated annealing and quantum annealings that are done by the D-Wave machines both theoretically and numerically. We show that if the classical and quantum annealing are characterized by equivalent Ising models, then solving an optimization problem, i.e., finding the minimal energy of each Ising model, by the two annealing procedures, are mathematically identical. For quantum annealing, we also derive the probability lower-bound on successfully solving an optimization problem by measuring the system at the end of the annealing procedure. Moreover, we present the Markov chain Monte Carlo (MCMC) method to realize quantum annealing by classical computers and investigate its statistical properties. In the numerical section, we discuss the discrepancies between the MCMC based annealing approaches and the quantum annealing approach in solving optimization problems.
Objective: In some situations that exist both scalar and functional data, called mixed and hybrid data, the hybrid PCA (HPCA) was introduced. Among the regression models for the hybrid data, we can count covariate-adjusted HPCA, the Semi-functional partial linear regression, function-on-function (FOF) regression with signal compression, and functional additive regression, models. In this article, we study the effects of HPCA decomposition of hybrid data on the prediction accuracy of the FOF regression with signal compressions. Method: We stated a two-step procedure for incorporating the HPCA in the functional regressions. The first step is reconstructing the data based on the HPCAs and the second step is merging data on the other dimensions and calculate the point-wise average of the desired functional dimension. We also choose the number of HPCA based on Mean Squared Perdition Error (MSPE). Result: In the two simulations, we show that the regression models with the first HPCA have the best accuracy prediction and model fit summaries among no HPCA and all HPCAs with a training/testing approach. Finally, we applied our methodology to the EEG-fMRI dataset. Conclusions: We conclude that our methodology improves the prediction of the experiments with the EEG datasets. And we recommend that instead of using the functional PCA on the desired dimension, reconstruct the data with HPCA and average it on the other two dimensions for functional regression models.
During World War II the German army used tanks to devastating advantage. The Allies needed accurate estimates of their tank production and deployment. They used two approaches to find these values: spies, and statistics. This note describes the statistical approach. Assuming the tanks are labeled consecutively starting at 1, if we observe $k$ serial numbers from an unknown number $N$ of tanks, with the maximum observed value $m$, then the best estimate for $N$ is $m(1 + 1/k) - 1$. This is now known as the German Tank Problem, and is a terrific example of the applicability of mathematics and statistics in the real world. The first part of the paper reproduces known results, specifically deriving this estimate and comparing its effectiveness to that of the spies. The second part presents a result we have not found in print elsewhere, the generalization to the case where the smallest value is not necessarily 1. We emphasize in detail why we are able to obtain such clean, closed-form expressions for the estimates, and conclude with an appendix highlighting how to use this problem to teach regression and how statistics can help us find functional relationships.
We consider the properties of listwise deletion when both $n$ and the number of variables grow large. We show that when (i) all data has some idiosyncratic missingness and (ii) the number of variables grows superlogarithmically in $n$, then, for large $n$, listwise deletion will drop all rows with probability 1. Using two canonical datasets from the study of comparative politics and international relations, we provide numerical illustration that these problems may emerge in real world settings. These results suggest, in practice, using listwise deletion may mean using few of the variables available to the researcher.
The world is becoming increasingly complex, both in terms of the rich sources of data we have access to as well as in terms of the statistical and computational methods we can use on those data. These factors create an ever-increasing risk for errors in our code and sensitivity in our findings to data preparation and execution of complex statistical and computing methods. The consequences of coding and data mistakes can be substantial. Openness (e.g., providing others with data code) and transparency (e.g., requiring that data processing and code follow standards) are two key solutions to help alleviate concerns about replicability and errors. In this paper, we describe the key steps for implementing a code quality assurance (QA) process for researchers to follow to improve their coding practices throughout a project to assure the quality of the final data, code, analyses and ultimately the results. These steps include: (i) adherence to principles for code writing and style that follow best practices, (ii) clear written documentation that describes code, workflow and key analytic decisions; (iii) careful version control, (iv) good data management; and (iv) regular testing and review. Following all these steps will greatly improve the ability of a study to assure results are accurate and reproducible. The responsibility for code QA falls not only on individual researchers but institutions, journals, and funding agencies as well.
In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science, mathematical methods are not selected because of any relevance for a problem at hand; mathematical methods are applied to a specific problem only by 'forcing', i.e. on the basis of their ability to reorganize the data for further analysis and the intrinsic richness of their mathematical structure. In particular, we argue that deep learning neural networks are best understood within the context of forcing optimization methods. We finally explore the broader question of the appropriateness of data science methods in solving problems. We argue that this question should not be interpreted as a search for a correspondence between phenomena and specific solutions found by data science methods; rather, it is the internal structure of data science methods that is open to precise forms of understanding.
Human population is at the centre of research on global environmental change. On the one hand, population dynamics influence the environment and the global climate system through consumption-based carbon emissions. On the other hand, health and wellbeing of the population is already being affected by climate change. The knowledge on population dynamics and population heterogeneity thus is fundamental in improving our understanding of how population size, composition and distribution influence global environmental change and how these changes affect subgroups of population differentially by demographic characteristics and spatial distribution. Existing theoretical concepts and methodological tools in demography can be readily applied to the study of population and global environmental change. In the past couple of decades, demographic research has enriched climate change research both in the analysis of the impact of population dynamics on the global climate system as well as the impact of climate change on human population. What is missing in the literature is the study that investigates how global environmental change affect current and future demographic processes and consequently population trends. If global environmental change does influence fertility, mortality and migration, the three key demographic components underlying population change, population estimates and forecast need to adjust from the climate feedback in population projections. Indisputably, this is the new area of research that directly requires expertise in population science and contribution from demographers.
This paper demonstrates the predictive superiority of discrete wavelet transform (DWT) over previously used methods of feature extraction in the diagnosis of epileptic seizures from EEG data. Classification accuracy, specificity, and sensitivity are used as evaluation metrics. We specifically show the immense potential of 2 combinations (DWT-db4 combined with SVM and DWT-db2 combined with RF) as compared to others when it comes to diagnosing epileptic seizures either in the balanced or the imbalanced dataset. The results also highlight that MFCC performs less than all the DWT used in this study and that, The mean-differences are statistically significant respectively in the imbalanced and balanced dataset. Finally, either in the balanced or the imbalanced dataset, the feature extraction techniques, the models, and the interaction between them have a statistically significant effect on the classification accuracy.
In any other circumstance, it might make sense to define the extent of the terrain (Data Science) first, and then locate and describe the landmarks (Principles). But this data revolution we are experiencing defies a cadastral survey. Areas are continually being annexed into Data Science. For example, biometrics was traditionally statistics for agriculture in all its forms but now, in Data Science, it means the study of characteristics that can be used to identify an individual. Examples of non-intrusive measurements include height, weight, fingerprints, retina scan, voice, photograph/video (facial landmarks and facial expressions), and gait. A multivariate analysis of such data would be a complex project for a statistician, but a software engineer might appear to have no trouble with it at all. In any applied-statistics project, the statistician worries about uncertainty and quantifies it by modelling data as realisations generated from a probability space. Another approach to uncertainty quantification is to find similar data sets, and then use the variability of results between these data sets to capture the uncertainty. Both approaches allow 'error bars' to be put on estimates obtained from the original data set, although the interpretations are different. A third approach, that concentrates on giving a single answer and gives up on uncertainty quantification, could be considered as Data Engineering, although it has staked a claim in the Data Science terrain. This article presents a few (actually nine) statistical principles for data scientists that have helped me, and continue to help me, when I work on complex interdisciplinary projects.