Rutgers, Department of Statistics 
Website :harrycrane.com 

Bio/Interests :
Probability, Statistics, Logic


hcrane@stat.rutgers.edu  
HarryDCrane 
This article describes our motivation behind the development of RESEARCHERS.ONE, our mission, and how the new platform will fulfull this mission. We also compare our approach with other recent reform initiatives such as postpublication peer review and open access publications.
I compare forecasts of the 2018 U.S. midterm elections based on (i) probabilistic predictions posted on the FiveThirtyEight blog and (ii) prediction market prices on PredictIt.com. Based on empirical forecast and price data collected prior to the election, the analysis assesses the calibration and accuracy according to Brier and logarithmic scoring rules. I also analyze the performance of a strategy that invests in PredictIt based on the FiveThirtyEight forecasts.
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 lowquality 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.
The notion of typicality appears in scientific theories, philosophical arguments, math ematical inquiry, and everyday reasoning. Typicality is invoked in statistical mechanics to explain the behavior of gases. It is also invoked in quantum mechanics to explain the appearance of quantum probabilities. Typicality plays an implicit role in nonrigorous mathematical inquiry, as when a mathematician forms a conjecture based on personal experience of what seems typical in a given situation. Less formally, the language of typicality is a staple of the common parlance: we often claim that certain things are, or are not, typical. But despite the prominence of typicality in science, philosophy, mathematics, and everyday discourse, no formal logics for typicality have been proposed. In this paper, we propose two formal systems for reasoning about typicality. One system is based on propositional logic: it can be understood as formalizing objective facts about what is and is not typical. The other system is based on the logic of intuitionistic type theory: it can be understood as formalizing subjective judgments about typicality.
I make the distinction between academic probabilities, which are not rooted in reality and thus have no tangible realworld meaning, and real probabilities, which attain a realworld 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 Pvalues, Bayes factors, confidence intervals, etc., are the result of academic probabilities, which are not useful for making meaningful assertions about the real world.
Publication of scientific research all but requires a supporting statistical analysis, anointing statisticians the de facto gatekeepers of modern scientific discovery. While the potential of statistics for providing scientific insights is undeniable, there is a crisis in the scientific community due to poor statistical practice. Unfortunately, widespread calls to action have not been effective, in part because of statisticians’ tendency to make statistics appear simple. We argue that statistics can meet the needs of science only by empowering scientists to make sound judgments that account for both the nuances of the application and the inherent complexity of funda mental effective statistical practice. In particular, we emphasize a set of statistical principles that scientists can adapt to their everexpanding scope of problems.
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.
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.
I introduce a formalization of probability in intensional MartinLöf type theory (MLTT) and homotopy type theory (HoTT) which takes the concept of ‘evidence’ as primitive in judgments about probability. In parallel to the intuition istic conception of truth, in which ‘proof’ is primitive and an assertion A is judged to be true just in case there is a proof witnessing it, here ‘evidence’ is primitive and A is judged to be probable just in case there is evidence supporting it. To formalize this approach, we regard propositions as types in MLTT and define for any proposi tion A a corresponding probability type Prob(A) whose inhabitants represent pieces of evidence in favor of A. Among several practical motivations for this approach, I focus here on its potential for extending metamathematics to include conjecture, in addition to rigorous proof, by regarding a ‘conjecture in A’ as a judgment that ‘A is probable’ on the basis of evidence. I show that the Giry monad provides a formal semantics for this system.