The most common bets in 19th-century casinos were even-money bets on red or black in Roulette or Trente et Quarante. Many casino gamblers allowed themselves to be persuaded that they could make money for sure in these games by following betting systems such as the d'Alembert. What made these systems so seductive? Part of the answer is that some of the systems, including the d'Alembert, can give bettors a very high probability of winning a small or moderate amount. But there is also a more subtle aspect of the seduction. When the systems do win, their return on investment --- the gain relative to the amount of money the bettor has to take out of their pocket and put on the table to cover their bets --- can be astonishingly high. Systems such as le tiers et le tout, which offer a large gain when they do win rather than a high probability of winning, also typically have a high upside return on investment. In order to understand these high returns on investment, we need to recognize that the denominator --- the amount invested --- is random, as it depends on how successive bets come out.

In this article, we compare some systems on their return on investment and their success in hiding their pitfalls. Systems that provide a moderate gain with a very high probability seem to accomplish this by stopping when they are ahead and more generally by betting less when they are ahead or at least have just won, while betting more when they are behind or have just lost. For historical reasons, we call this martingaling. Among martingales, the d'Alembert seems especially good at making an impressive return on investment quickly, encouraging gamblers' hope that they can use it so gingerly as to avoid the possible large losses, and this may explain why its popularity was so durable.

We also discuss the lessons that this aspect of gambling can have for evaluating success in business and finance and for evaluating the results of statistical testing.

The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains important information such as thesource of the infection. We consider the problem of statistical inference on aspects of the latent history using only a single snapshot of the final tree. Our approach is to apply random labels to the observed unlabeled tree and analyze the resulting distribution of the growth process, conditional on the final outcome. We show that this conditional distribution is tractable under a shape-exchangeability condition, which we introduce here, and that this condition is satisfied for many popular models for randomly growing trees such as uniform attachment, linear preferential attachment and uniform attachment on a D-regular tree. For inference of the rootunder shape-exchangeability, we propose computationally scalable algorithms for constructing confidence sets with valid frequentist coverage as well as bounds on the expected size of the confidence sets. We also provide efficient sampling algorithms which extend our methods to a wide class of inference problems.

When gambling, think probability.

When hedging, think plausibility.

When preparing, think possibility.

When this fails, stop thinking. Just survive.

Naive probabilism is the (naive) view, held by many technocrats and academics, that all rational thought boils down to probability calculations. This viewpoint is behind the obsession with `data-driven methods' that has overtaken the hard sciences, soft sciences, pseudosciences and non-sciences. It has infiltrated politics, society and business. It's the workhorse of formal epistemology, decision theory and behavioral economics. Because it is mostly applied in low or no-stakes academic investigations and philosophical meandering, few have noticed its many flaws. Real world applications of naive probabilism, however, pose disproportionate risks which scale exponentially with the stakes, ranging from harmless (and also helpless) in many academic contexts to destructive in the most extreme events (war, pandemic). The 2019--2020 coronavirus outbreak (COVID-19) is a living example of the dire consequences of such probabilistic naivet\'e. As I write this on March 13, 2020, we are in the midst of a 6 continent pandemic, the world economy is collapsing and our future is bound to look very different from the recent past. The major damage caused by the spread of COVID-19 is attributable to a failure to act and a refusal to acknowledge what was in plain sight. This shared negligence stems from a blind reliance on naive probabilism and the denial of basic common sense by global and local leaders, and many in the general public.

Submitted on 2020-03-09

This introductory chapter of *Probabilistic Foundations of Statistical Network Analysis* explains the major shortcomings of prevailing efforts in statistical analysis of networks and other kinds of complex data, and why there is a need for a new way to conceive of and understand data arising from complex systems.

Submitted on 2019-10-18

Submitted on 2019-09-30

Whether the predictions put forth prior to the 2016 U.S. presidential election were right or wrong is a question that led to much debate. But rather than focusing on right or wrong, we analyze the 2016 predictions with respect to a core set of {\em effectiveness principles}, and conclude that they were ineffective in conveying the uncertainty behind their assessments. Along the way, we extract key insights that will help to avoid, in future elections, the systematic errors that lead to overly precise and overconfident predictions in 2016. Specifically, we highlight shortcomings of the classical interpretations of probability and its communication in the form of predictions, and present an alternative approach with two important features. First, our recommended predictions are safer in that they come with certain guarantees on the probability of an erroneous prediction; second, our approach easily and naturally reflects the (possibly substantial) uncertainty about the model by outputting *plausibilities* instead of *probabilities*.

Submitted on 2018-11-06

This article describes how the filtering role played by peer review may actually be harmful rather than helpful to the quality of the scientific literature. We argue that, instead of trying to filter out the low-quality research, as is done by traditional journals, a better strategy is to let everything through but with an acknowledgment of the uncertain quality of what is published, as is done on the RESEARCHERS.ONE platform. We refer to this as "scholarly mithridatism." When researchers approach what they read with doubt rather than blind trust, they are more likely to identify errors, which protects the scientific community from the dangerous effects of error propagation, making the literature stronger rather than more fragile.

Submitted on 2018-08-30

I make the distinction between *academic* probabilities, which are not rooted in reality and thus have no tangible real-world meaning, and *real* probabilities, which attain a real-world meaning as the odds that the subject asserting the probabilities is forced to accept for a bet against the stated outcome. With this I discuss how the replication crisis can be resolved easily by requiring that probabilities published in the scientific literature are real, instead of academic. At present, all probabilities and derivatives that appear in published work, such as P-values, Bayes factors, confidence intervals, etc., are the result of academic probabilities, which are not useful for making meaningful assertions about the real world.

Submitted on 2018-08-30

Submitted on 2018-08-21

I prove a connection between the logical framework for intuitive probabilistic reasoning (IPR) introduced by Crane (2017) and sets of imprecise probabilities. More specifically, this connection provides a straightforward interpretation to sets of imprecise probabilities as subjective credal states, giving a formal semantics for Crane's formal system of IPR. The main theorem establishes the IPR framework as a potential logical foundation for imprecise probability that is independent of the traditional probability calculus.

Irune Orinuela's Spanish translation of https://www.researchers.one/article/2020-03-10

© 2018-2020 Researchers.One