A Statistically and Numerically Efficient Independence Test Based on Random Projections and Distance Covariance

Testing for independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation-based hypotheses testing for independence) have many advantages, compared with many other alternatives. A known limitation of the distance-based method is that its computational complexity can be high. In general, when the sample size is n, the order of computational complexity of a distance-based method, which typically requires computing of all pairwise distances, can be O(n2). Recent advances have discovered that in the univariate cases, a fast method with O(n log n) computational complexity and O(n) memory requirement exists. In this paper, we introduce a test of independence method based on random projection and distance correlation, which achieves nearly the same power as the state-of-the-art distance-based approach, works in the multivariate cases, and enjoys the O(nK log n) computational complexity and O( max{n, K}) memory requirement, where K is the number of random projections. Note that saving is achieved when K < n/ log n. We name our method a Randomly Projected Distance Covariance (RPDC). The statistical theoretical analysis takes advantage of some techniques on the random projection which are rooted in contemporary machine learning. Numerical experiments demonstrate the efficiency of the proposed method, relative to numerous competitors.

Independence Test and Plots in Correspondence Analysis to Explore Tracer Study Data

The results of the exploration of tracer study data can be used as information about the career of graduates and the relevance of work to the field of study as well as the competencies obtained before graduation. The question items discussed were a description of the time and process of looking for a job, the length of time to get the first job, the relationship between length of study, gender, field of work, total income, alumni's perception of the closeness of the field of study to work, the suitability of the level of education on the job, and average level of competence. The aim of this study was to analyze the relationship between these variables in the 2020 tracer study data from graduates of all faculties at Sriwijaya University. Respondents studied were 2,669 people. The method used is descriptive statistics, biplot analysis, independence test and plots by simple correspondence analysis. Respondents' perceptions of the suitability of the level of education in employment are related to gender and also with respondents' perceptions of the closeness of the field of study to the field of work. Meanwhile, respondents' perceptions of the closeness of the field of study with work are related to the field of work. The average length of study, the average number of job applications, the number of companies or agencies that responded to applications, and invited interviews for female respondents were lower than male respondents.

The Accuracy of Risk Measurement Models on Bitcoin Market during COVID-19 Pandemic

Since late 2019, during one of the largest pandemics in history, COVID-19, global economic recession has continued. Therefore, investors seek an alternative investment that generates profits during this financially risky situation. Cryptocurrency, such as Bitcoin, has become a new currency tool for speculators and investors, and it is expected to be used in future exchanges. Therefore, this paper uses a Value at Risk (VaR) model to measure the risk of investment in Bitcoin. In this paper, we showed the results of the predicted daily loss of investment by using the historical simulation VaR model, the delta-normal VaR model, and the Monte Carlo simulation VaR model with the confidence levels of 99%, 95%, and 90%. This paper displayed backtesting methods to investigate the accuracy of VaR models, which consisted of the Kupiec’s POF and the Kupiec’s TUFF statistical testing results. Finally, Christoffersen’s independence test and Christoffersen’s interval forecasts evaluation showed effectiveness in the predictions for the robustness of VaR models for each confidence level.

Causal Priority in Metaphysics Θ.8

Aristotle’s Metaphysics Θ.8 argument for the priority of actuality to potentiality poses an immediate interpretive problem: the argument uses two distinct tests for priority, one of which threatens to reverse the results of the other. This paper argues that the standard approach to this passage, according to which one thing is prior to another when it satisfies the ontological independence test from Metaphysics Δ.11, fails to secure the argumentative unity of the passage. It introduces a new, causal account of priority which explains both Aristotle’s claims about priority and the way he argues for them.

Artificial diffusion in the simulation of micromixers: A review

False (artificial) diffusion provides an erroneous estimation of molecular diffusion during the simulation of liquid micromixing. The present review introduces discretization methods, numerical grid types, and numerical errors to address the effect of false diffusion on the prediction of mixing efficiency of microfluidic devices. False diffusivity is characterized by the grid Peclet number, grid type, and discretization scheme. This review demonstrates that most investigators have selected a grid resolution just for the grid independence test. It is revealed that the convergence criterion should not be quantitative values of mixing efficiency even when high-order schemes are employed to discretize the computational grid. Based on the previous publications in this field, a straightforward procedure is recommended to manage false diffusion in the numerical simulation of micromixers.