Nassim Nicholas Taleb’s research while affiliated with American University of Beirut and other places

Principal Component Analysis (PCA) is a powerful multivariate tool allowing the projection of data in low-dimensional representations. Nevertheless, datapoint distances on these low-dimensional projections are challenging to interpret. Here, we propose a computationally simple heuristic to transform a map based on standard PCA (when the variables are asymptotically Gaussian) into an entropy-based map where distances are based on mutual information (MI). Moreover, we show that in certain instances our proposed scaled PCA can improve cluster identification. Rescaling principal component-based distances using MI results in a representation of relative statistical associations when, as in genetics, it is applied on bit measurements between individuals' genomic mutual information. This entropy-rescaled PCA, while preserving order relationships (along a dimension), quantifies relative distances into information units, such as “bits”. We illustrate the effect of this rescaling using genomics data derived from world populations and describe how the interpretation of results is impacted.

Lebanon’s rich history as a cultural crossroad spanning millennia has significantly impacted the genetic composition of its population through successive waves of migration and conquests from surrounding regions. Within modern-day Lebanon, the Koura district stands out with its unique cultural foundations, primarily characterized by a notably high concentration of Greek Orthodox Christians compared to the rest of the country. This study investigates whether the prevalence of Greek Orthodoxy in Koura can be attributed to modern Greek heritage or continuous blending resulting from the ongoing influx of refugees and trade interactions with Greece and Anatolia. We analyzed both ancient and modern DNA data from various populations in the region which could have played a role in shaping the current population of Koura using our own and published data. Our findings indicate that the genetic influence stemming directly from modern Greek immigration into the area appears to be limited. While the historical presence of Greek colonies has left its mark on the region’s past, the distinctive character of Koura seems to have been primarily shaped by cultural and political factors, displaying a stronger genetic connection mostly with Anatolia, with affinity to ancient but not modern Greeks.

The COVID-19 pandemic has brought a heightened sense of urgency in the scientific community regarding the need to advance understanding and prevention of pathogen transmission, particularly concerning infectious airborne particles and the utility of various preventive strategies in reducing the risk of infection. There are extensive studies validating scientific understanding about the behavior of larger (droplets) and smaller (aerosols) particles in disease transmission and the dosimetry of particles in the respiratory track. Similarly, modalities for respiratory protection against particles in the size range spanned by infectious particles, such as N95 respirators, are available and known to be efficacious with tested standards for harm reduction across environments including physical, chemical and biological hazards. Even though multiple studies also confirm their protective effect when adopted in healthcare and public settings for infection prevention, overall, studies of protocols of their adoption over the last several decades in both clinical trials and observational studies have not provided as clear an understanding. Here we demonstrate that these studies are strongly biased towards the null by infections resulting from transmission outside of the investigated environments and study participants. Such study limitations are frequently mis-stated as not influencing the conclusions of research on respiratory protection. The reason for the failure to properly analyze the studies is that the standard analytical equations used do not correctly represent the random variables that play a role in the study results. By correcting the mathematical representation and the equations that result from them, we demonstrate that conclusions drawn from these studies are strongly biased and much more uncertain than is acknowledged, providing almost no useful information. Even with all these limitations, we show that existing results, when outcome measures are properly analyzed, consistently point to the benefit of precautionary measures such as N95 respirators over medical masks, and masking over its absence. We also show that correcting manifest errors of widely reported meta-analyses also leads to statistically significant estimates. Our results have implications for the design of studies and analyses on the effectiveness of respiratory protection and on using existing evidence for policy guidelines for infection control.

We discuss the inadequacy of covariances/correlations and other measures in L2 as relative distance metrics under some conditions. We propose a computationally simple heuristic to transform a map based on standard principal component analysis (PCA) (when the variables are asymptotically Gaussian) into an entropy-based map where distances are based on mutual information (MI). Rescaling Principal Component based distances using MI allows a representation of relative statistical associations when, as in genetics, it is applied on bit measurements between individuals' genomic mutual information. This entropy rescaled PCA, while preserving order relationships (along a dimension), changes the relative distances to make them linear to information. We show the effect on the entire world population and some subsamples, which leads to significant differences with the results of current research.

We extend techniques and learnings about the stochastic properties of nonlinear responses from finance to medicine, particularly oncology, where it can inform dosing and intervention. We define antifragility. We propose uses of risk analysis for medical problems, through the properties of nonlinear responses (convex or concave). We (1) link the convexity/concavity of the dose-response function to the statistical properties of the results; (2) define “antifragility” as a mathematical property for local beneficial convex responses and the generalization of “fragility” as its opposite, locally concave in the tails of the statistical distribution; (3) propose mathematically tractable relations between dosage, severity of conditions, and iatrogenics. In short, we propose a framework to integrate the necessary consequences of nonlinearities in evidence-based oncology and more general clinical risk management.

We respond to Tetlock et al. (2022) showing 1) how expert judgment fails to reflect tail risk, 2) the lack of compatibility between forecasting tournaments and tail risk assessment methods (such as extreme value theory). More importantly, we communicate a new result showing a greater gap between the properties of tail expectation and those of the corresponding probability.

We extend techniques and learnings about the stochastic properties of nonlinear responses from finance to medicine, particularly oncology where it can inform dosing and intervention. We define antifragility. We propose uses of risk analysis to medical problems, through the properties of nonlinear responses (convex or concave). We 1) link the convexity/concavity of the dose-response function to the statistical properties of the results; 2) define "antifragility" as a mathematical property for local beneficial convex responses and the generalization of "fragility" as its opposite, locally concave in the tails of the statistical distribution; 3) propose mathematically tractable relations between dosage, severity of conditions, and iatrogenics. In short we propose a framework to integrate the necessary consequences of nonlinearities in evidence-based oncology and more general clinical risk management.

Background: Pre-pandemic empirical studies have produced mixed statistical results on the effectiveness of masks against respiratory viruses, leading to confusion that may have contributed to organizations such as the WHO and CDC initially not recommending that the general public wear masks during the COVID-19 pandemic. Methods: A threshold-based dose–response curve framework is used to analyse the effects of interventions on infection probabilities for both single and repeated exposure events. Empirical studies on mask effectiveness are evaluated with a statistical power analysis that includes the effect of adherence to mask usage protocols. Results: When the adherence to mask-usage guidelines is taken into account, the empirical evidence indicates that masks prevent disease transmission: all studies we analysed that did not find surgical masks to be effective were under-powered to such an extent that even if masks were 100% effective, the studies in question would still have been unlikely to find a statistically significant effect. We also provide a framework for understanding the effect of masks on the probability of infection for single and repeated exposures. The framework demonstrates that masks can have a disproportionately large protective effect and that more frequently wearing a mask provides super-linearly compounding protection. Conclusions: This work shows (1) that both theoretical and empirical evidence is consistent with masks protecting against respiratory infections and (2) that nonlinear effects and statistical considerations regarding the percentage of exposures for which masks are worn must be taken into account when designing empirical studies and interpreting their results.