On the Super-Additivity and Estimation Biases of Quantile Contributions

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A U B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions

The Future Has Thicker Tails than the Past: Model Error As Branching Counterfactuals

Abstract Ex ante forecast outcomes should be interpreted as counterfactuals (potential histories), with errors as the spread between outcomes. We reapply measurements of uncertainty about the estimation errors of the estimation errors of an estimation treated as branching counterfactuals. Such recursions of epistemic uncertainty have markedly different distributial properties from conventional sampling error, and lead to fatter tails in the projections than in past realizations. Counterfactuals of error rates always lead to fat tails, regardless of the probability distribution used. A mere .01% branching error rate about the STD (itself an error rate), and .01% branching error rate about that error rate, etc. (recursing all the way) results in explosive (and infinite) moments higher than 1. Missing any degree of regress leads to the underestimation of small probabilities and concave payoffs (a standard example of which is Fukushima). The paper states the conditions under which higher order rates of uncertainty (expressed in spreads of counterfactuals) alters the shapes the of final distribution and shows which a priori beliefs about conterfactuals are needed to accept the reliability of conventional probabilistic methods (thin tails or mildly fat tails)

Quantitative errors in the Cochrane review on "Physical interventions to interrupt or reduce the spread of respiratory viruses"

The COVID-19 pandemic has heightened the urgency to understand and prevent pathogen transmission, specifically regarding infectious airborne particles. Extensive studies validate the understanding of larger (droplets) and smaller (aerosols) particles in disease transmission. Similarly, N95 respirators, and other forms of respiratory protection, have proven efficacy in reducing the risk of infection across various environments. Even though multiple studies confirm their protective effect when adopted in healthcare and public settings for infection prevention, studies on their adoption over the last several decades in both clinical trials and observational studies have not provided as clear an understanding. Here we show that the standard analytical equations used in the analysis of these studies do not accurately represent the random variables impacting study results. By correcting these equations, it is demonstrated that conclusions drawn from these studies are heavily biased and uncertain, providing little useful information. Despite these limitations, we show that when outcome measures are properly analyzed, existing results consistently point to the benefit of N95 respirators over medical masks, and masking over its absence. Correcting errors in widely reported meta-analyses also yields statistically significant estimates. These findings have important implications for study design and using existing evidence for infection control policy guidelines.Comment: 23 pages, 8 figure