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arXiv2024

Risk management in the use of published statistical results for policy decisions

Statistical inferential results generally come with a measure of reliability for decision-making purposes. For a policy implementer, the value of implementing published policy research depends critically upon this reliability. For a policy researcher, the value of policy implementation may depend weakly or not at all upon the policy's outcome. Some researchers might benefit from overstating the reliability of statistical results. Implementers may find it difficult or impossible to determine whether researchers are overstating reliability. This information asymmetry between researchers and implementers can lead to an adverse selection problem where, at best, the full benefits of a policy are not realized or, at worst, a policy is deemed too risky to implement at any scale. Researchers can remedy this by guaranteeing the policy outcome. Researchers can overcome their own risk aversion and wealth constraints by exchanging risks with other researchers or offering only partial insurance. The problem and remedy are illustrated using a confidence interval for the success probability of a binomial policy outcome.

stat.OT↗
arXiv2023

Axiomatization of Interventional Probability Distributions

Causal intervention is an essential tool in causal inference. It is axiomatized under the rules of do-calculus in the case of structure causal models. We provide simple axiomatizations for families of probability distributions to be different types of interventional distributions. Our axiomatizations neatly lead to a simple and clear theory of causality that has several advantages: it does not need to make use of any modeling assumptions such as those imposed by structural causal models; it only relies on interventions on single variables; it includes most cases with latent variables and causal cycles; and more importantly, it does not assume the existence of an underlying true causal graph as we do not take it as the primitive object--in fact, a causal graph is derived as a by-product of our theory. We show that, under our axiomatizations, the intervened distributions are Markovian to the defined intervened causal graphs, and an observed joint probability distribution is Markovian to the obtained causal graph; these results are consistent with the case of structural causal models, and as a result, the existing theory of causal inference applies. We also show that a large class of natural structural causal models satisfy the theory presented here. We note that the aim of this paper is axiomatization of interventional families, which is subtly different from "causal modeling."

math.ST↗
arXiv2023

Measurable Taylor's Theorem: An Elementary Proof

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only tacitly assumed. In this note, we provide an elementary proof of this measurable Taylor's theorem, which guarantees that the interpolating point in the Lagrange form of the remainder can be chosen to depend measurably on the independent variable.

stat.OT↗
arXiv2023

Over-Measurement Paradox: Suspension of Thermonuclear Research Center and Need to Update Standards

In general, the more measurements we perform, the more information we gain about the system and thus, the more adequate decisions we will be able to make. However, in situations when we perform measurements to check for safety, the situation is sometimes opposite: the more additional measurements we perform beyond what is required, the worse the decisions will be: namely, the higher the chance that a perfectly safe system will be erroneously classified as unsafe and therefore, unnecessary additional features will be added to the system design. This is not just a theoretical possibility: exactly this phenomenon is one of the reasons why the construction of a world-wide thermonuclear research center has been suspended. In this paper, we show that the reason for this paradox is in the way the safety standards are formulated now -- what was a right formulation when sensors were much more expensive is no longer adequate now when sensors and measurements are much cheaper. We also propose how to modify the safety standards so as to avoid this paradox and make sure that additional measurements always lead to better solutions.

stat.OT↗
arXiv2023

The Geometry of Chi-Square Degrees of Freedom

In this paper, we state and prove a simple geometric interpretation of the degrees of freedom of a chi-square distribution. The general geometric idea goes back at least to Fisher in the 1920s, but the exact result does not appear to have been explicitly stated or proved prior to this paper.

stat.OT↗
arXiv2023

Using maximum weighted likelihood to derive Lehmer and Hölder mean families

In this paper, we establish the links between the Lehmer and Hölder mean families and maximum weighted likelihood estimator. Considering the regular one-parameter exponential family of probability density functions, we show that the maximum weighted likelihood of the parameter is a generalized weighted mean family from which Lehmer and Hölder mean families are derived. Some of the outcomes obtained provide a probabilistic interpretation of these mean families and could therefore broaden their uses in various applications.

stat.OT↗
arXiv2023

On the Confidence Intervals in Bioequivalence Studies

A bioequivalence study is a type of clinical trial designed to compare the biological equivalence of two different formulations of a drug. Such studies are typically conducted in controlled clinical settings with human subjects, who are randomly assigned to receive two formulations. The two formulations are then compared with respect to their pharmacokinetic profiles, which encompass the absorption, distribution, metabolism, and elimination of the drug. Under the guidance from Food and Drug Administration (FDA), for a size-$α$ bioequivalence test, the standard approach is to construct a $100(1-2α)\%$ confidence interval and verify if the confidence interval falls with the critical region. In this work, we clarify that $100(1-2α)\%$ confidence interval approach for bioequivalence testing yields a size-$α$ test only when the two one-sided tests in TOST are ``equal-tailed''. Furthermore, a $100(1-α)\%$ confidence interval approach is also discussed in the bioequivalence study.

stat.ME↗
arXiv2023

The role of discretization scales in causal inference with continuous-time treatment

There are well-established methods for identifying the causal effect of a time-varying treatment applied at discrete time points. However, in the real world, many treatments are continuous or have a finer time scale than the one used for measurement or analysis. While researchers have investigated the discrepancies between estimates under varying discretization scales using simulations and empirical data, it is still unclear how the choice of discretization scale affects causal inference. To address this gap, we present a framework to understand how discretization scales impact the properties of causal inferences about the effect of a time-varying treatment. We introduce the concept of "identification bias", which is the difference between the causal estimand for a continuous-time treatment and the purported estimand of a discretized version of the treatment. We show that this bias can persist even with an infinite number of longitudinal treatment-outcome trajectories. We specifically examine the identification problem in a class of linear stochastic continuous-time data-generating processes and demonstrate the identification bias of the g-formula in this context. Our findings indicate that discretization bias can significantly impact empirical analysis, especially when there are limited repeated measurements. Therefore, we recommend that researchers carefully consider the choice of discretization scale and perform sensitivity analysis to address this bias. We also propose a simple and heuristic quantitative measure for sensitivity concerning discretization and suggest that researchers report this measure along with point and interval estimates in their work. By doing so, researchers can better understand and address the potential impact of discretization bias on causal inference.

stat.ME↗
arXiv2026

Index-mixed copulas

The class of index-mixed copulas is introduced and its properties are investigated. Index-mixed copulas are constructed from given base copulas and a random index vector, and show a rather remarkable degree of analytical tractability. The analytical form of the copula and, if it exists, its density are derived. As the construction is based on a stochastic representation, sampling algorithms can be given. Properties investigated include bivariate and trivariate margins, mixtures of index-mixed copulas, symmetries such as radial symmetry and exchangeability, tail dependence, measures of concordance such as Blomqvist's beta, Spearman's rho or Kendall's tau and concordance orderings. Examples and illustrations are provided, and applications to the distribution of sums of dependent random variables as well as the stress testing of general dependence structures are given. A particularly interesting feature of index-mixed copulas is that they allow one to provide a revealing interpretation of the well-known family of Eyraud-Farlie-Gumbel-Morgenstern (EFGM) copulas. Through the lens of index-mixing, one can explain why EFGM copulas can only model a limited range of concordance and are tail independent, for example. Index-mixed copulas do not suffer from such restrictions while remaining analytically tractable.

stat.ME↗
arXiv2023

Statistical thinking in simulation design: a continuing conversation on the balancing intercept problem

Epidemiologists have a growing interest in employing computational approaches to solve analytic problems, with simulation being arguably the most accessible among all approaches. While previous literature discussed the utility of simulation and demonstrated how to carry out them, few have focused on connecting underlying statistical concepts to these simulation approaches, creating gaps between theory and application. Based on the recent series of discussions on the balancing intercept, we explain the growing complexity when generalizing the balancing intercept to a wider class of simulations and revise the closed-form equation for the balancing intercept under assumptions. The discussion can broadly inform the future design of more complex simulations and emphasize the importance of applying statistical thinking in the new era of computational science.

stat.CO↗
arXiv2023

Using R for teaching and research

R is a language and environment for statistical computing and graphics, which provides a wide variety of statistical tools (modeling, statistical testing, time series analysis, classification problems, machine learning, ...), together with amazing graphical techniques and the great advantage that it is highly extensible. Nowadays, there is no doubt that it is the software par excellence in statistical courses for any level, for theoretical and applied subjects alike. Besides, it has become an almost essential tool for every research work that involves any kind of analysis or data visualization. Furthermore, it is one of the most employed programming languages for general purposes. The goal of this work is helping to share ideas and resources to improve teaching and/or research using the statistical software R. We will cover its benefits, show how to get started and where to locate specific resources, and will make interesting recommendations for using R, according to our experience. For the classroom we will develop a curricular and assessment infrastructure to support both dissemination and evaluation, while for research we will offer a broader approach to quantitative studies that provides an excellent support for work in science and technology.

stat.OT↗
arXiv2023

Multivariate Rank-Based Analysis of Multiple Endpoints in Clinical Trials: A Global Test Approach

Clinical trials often involve the assessment of multiple endpoints to comprehensively evaluate the efficacy and safety of interventions. In the work, we consider a global nonparametric testing procedure based on multivariate rank for the analysis of multiple endpoints in clinical trials. Unlike other existing approaches that rely on pairwise comparisons for each individual endpoint, the proposed method directly incorporates the multivariate ranks of the observations. By considering the joint ranking of all endpoints, the proposed approach provides robustness against diverse data distributions and censoring mechanisms commonly encountered in clinical trials. Through extensive simulations, we demonstrate the superior performance of the multivariate rank-based approach in controlling type I error and achieving higher power compared to existing rank-based methods. The simulations illustrate the advantages of leveraging multivariate ranks and highlight the robustness of the approach in various settings. The proposed method offers an effective tool for the analysis of multiple endpoints in clinical trials, enhancing the reliability and efficiency of outcome evaluations.

stat.ME↗
arXiv2023

Spaces of innovation and venture formation: the case of biotech in the United Kingdom

Patents serve as valuable indicators of innovation and provide insights into the spaces of innovation and venture formation within geographic regions. In this study, we utilise patent data to examine the dynamics of innovation and venture formation in the biotech sector across the United Kingdom (UK). By analysing patents, we identify key regions that drive biotech innovation in the UK. Our findings highlight the crucial role of biotech incubators in facilitating knowledge exchange between scientific research and industry. However, we observe that the incubators themselves do not significantly contribute to the diversity of innovations which might be due to the underlying effect of geographic proximity on the influences and impact of the patents. These insights contribute to our understanding of the historical development and future prospects of the biotech sector in the UK, emphasising the importance of promoting innovation diversity and fostering inclusive enterprise for achieving equitable economic growth.

physics.soc-ph↗
arXiv2023

Extending the Bayesian Framework from Information to Action

In this review, we examine an extended Bayesian inference method and its relation to biological information processing. We discuss the idea of combining two modes of Bayesian inference. The first is the standard Bayesian inference, which contracts probability space. The second is its inverse, which extends and enriches the probability space of latent and observable variables. Their combination has been observed that, greatly, facilitates discovery. Moreover, this dual search during the updating process elucidates a crucial difference between biological and artificial information processing. The latter is restricted due to nonlinearities, while the former utilizes it. This duality is ubiquitous in biological information process dynamics (`flee-or-fight', `explore-or-exploit' etc.) as is the role of fractality and chaos in its underlying nonequilibrium, nonlinear dynamics. We also propose a new experimental set up that stems from testing these ideas.

stat.OT↗
arXiv2023

Toward optimal placement of spatial sensors

This paper addresses the challenges of optimally placing a finite number of sensors to detect Poisson-distributed targets in a bounded domain. We seek to rigorously account for uncertainty in the target arrival model throughout the problem. Sensor locations are selected to maximize the probability that no targets are missed. While this objective function is well-suited to applications where failure to detect targets is highly undesirable, it does not lead to a computationally efficient optimization problem. We propose an approximation of the objective function that is non-negative, submodular, and monotone and for which greedy selection of sensor locations works well. We also characterize the gap between the desired objective function and our approximation. For numerical illustrations, we consider the case of the detection of ship traffic using sensors mounted on the seafloor.

cs.RO↗
arXiv2023

Multiple Correspondence and Proportional Analysis of Vaccination Rate Among Healthcare Personnel of MINSA

DataProAnalytica is a powerful application for analyzing vaccination data in health care professionals. Through visualizations and multiple correspondence analysis, it uncovers meaningful relationships between variables and categories. The results provide valuable information for improving vaccination strategies. While there are limitations, the potential of DataProAnalytica to improve accuracy and functionality makes it a promising tool for future research and decision making in any other research topic.

stat.OT↗
arXiv2023

Peru Mining: Analysis and Forecast of Mining Production in Peru Using Time Series and Data Science Techniques

Peruvian mining plays a crucial role in the country's economy, being one of the main producers and exporters of minerals worldwide. In this project, an application was developed in RStudio that utilizes statistical analysis and time series modeling techniques to understand and forecast mineral extraction in different departments of Peru. The application includes an interactive map that allows users to explore Peruvian geography and obtain detailed statistics by clicking on each department. Additionally, bar charts, pie charts, and frequency polygons were implemented to visualize and analyze the data. Using the ARIMA model, predictions were made on the future extraction of minerals, enabling informed decision-making in planning and resource management within the mining sector. The application provides an interactive and accessible tool to explore the Peruvian mining industry, comprehend trends, and make accurate forecasts. These predictions for 2027 in total annual production are as follows: Copper = 2,694,957 MT, Gold = 72,817.47 kg Fine, Zinc = 1,369,649 MT, Silver = 3,083,036 MT, Lead = 255,443 MT, Iron = 15,776,609 MT, Tin = 29,542 MT, Molybdenum = 35,044.66 MT, and Cadmium = 724 MT. These predictions, based on historical data, provide valuable information for strategic decision-making and contribute to the sustainable development of the mining industry in Peru.

stat.OT↗
arXiv2023

Bayesian Analysis of Beta Autoregressive Moving Average Models

This work presents a Bayesian approach for the estimation of Beta Autoregressive Moving Average ($β$ARMA) models. We discuss standard choice for the prior distributions and employ a Hamiltonian Monte Carlo algorithm to sample from the posterior. We propose a method to approach the problem of unit roots in the model's systematic component. We then present a series of Monte Carlo simulations to evaluate the performance of this Bayesian approach. In addition to parameter estimation, we evaluate the proposed approach to verify the presence of unit roots in the model's systematic component and study prior sensitivity. An empirical application is presented to exemplify the usefulness of the method. In the application, we compare the fitted Bayesian and frequentist approaches in terms of their out-of-sample forecasting capabilities.

stat.ME↗