How high should we build a dyke today, knowing that it will serve for more than 50 years? This depends on the unconditional probability distribution of future temperatures. We review the literature on estimates of future emissions for current policy scenarios and current pledge scenarios....

Researchers frequently test and improve model fit by holding a sample constant and varying the model. We propose methods to test and improve sample fit by holding a model constant and varying the sample. Much as the bootstrap is a well-known method to re-sample data and estimate the uncertainty...

We show that Kolmogorov's classical strong law of large numbers applies to all expectiles uniformly. The expectiles of a random sample converge almost surely (uniformly) to the true expectiles if and only if the true data generating process has a finite first moment. The result holds for...

We propose a nonparametric Bayesian approach for conducting inference on probabilistic surveys. We use this approach to study whether U.S. Survey of Professional Forecasters density projections for output growth and inflation are consistent with the noisy rational expectations hypothesis. We...

This paper presents the summations of binomial expansions with the optimized binomial coefficients and also the sum of multiple summations of the binomial coefficients. This combinatorial result is useful for researchers who are working in computing, science, engineering, and management

This paper examines the effects of automation on the number of transactions, sales, and cost in the foodservice industry. First, a big data tool is applied to distinguish distributions of transactions during different times of the day. Then the automation impacts on transactions are studied...

The transformation of credit scores into probabilities of default plays an important role in credit risk estimation. The linear logistic regression has developed into a standard calibration approach in the banking sector. With the advent of machine learning techniques in the discriminatory phase...

Anscombe & Aumann (1963) offer a definition of subjective probability in terms of comparisons with objective probabilities. That definition - which has provided the basis for much of the succeeding work on subjective probability - presumes that the subjective probability of an event is...