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The usual way of testing probability forecasts in game-theoretic probability is via construction of test martingales. The standard assumption is that all forecasts are output by the same forecaster. In this paper I will discuss possible…

Modelling football outcomes has gained increasing attention, in large part due to the potential for making substantial profits. Despite the strong connection existing between football models and the bookmakers' betting odds, no authors have…

We have developed a frequentist approach for model selection which determines the consistency between any cosmological model and the data using the distribution of likelihoods from the iterative smoothing method. Using this approach, we…

This study investigates differential games with motion-payoff uncertainty in continuous-time settings. We propose a framework where players update their beliefs about uncertain parameters using continuous Bayesian updating. Theoretical…

This note proposes a procedure for enhancing the quality of probabilistic prediction algorithms via betting against their predictions. It is inspired by the success of the conformal test martingales that have been developed recently.

Probability predictions are essential to inform decision making across many fields. Ideally, probability predictions are (i) well calibrated, (ii) accurate, and (iii) bold, i.e., spread out enough to be informative for decision making.…

The method of model averaging has become an important tool to deal with model uncertainty, for example in situations where a large amount of different theories exist, as are common in economics. Model averaging is a natural and formal…

The inability to correctly resolve rumours circulating online can have harmful real-world consequences. We present a method for incorporating model and data uncertainty estimates into natural language processing models for automatic rumour…

This paper defines systematic value investing as an empirical optimization problem. Predictive modeling is introduced as a systematic value investing methodology with dynamic and optimization features. A predictive modeling process is…

This paper proposed a methodology to forecast electoral outcomes using the result of the combination of a fundamental model and a model-based aggregation of polls. We propose a Bayesian hierarchical structure for the fundamental model that…

Large-scale prediction models using tools from artificial intelligence (AI) or machine learning (ML) are increasingly common across a variety of industries and scientific domains. Despite their effectiveness, training AI and ML tools at…

As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…

Traditional interpretations of probability, whether frequentist or subjective, make no reference to the concept of energy. In this paper, we propose that assigning hypothetical energy levels to the outcomes of a random variable can yield…

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…

Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than…

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…

Forecasting and forecast evaluation are inherently sequential tasks. Predictions are often issued on a regular basis, such as every hour, day, or month, and their quality is monitored continuously. However, the classical statistical tools…

Prediction markets are useful for estimating probabilities of claims whose truth will be revealed at some fixed time -- this includes questions about the values of real-world events (i.e. statistical uncertainty), and questions about the…

Decision-guided perspectives on model uncertainty expand traditional statistical thinking about managing, comparing and combining inferences from sets of models. Bayesian predictive decision synthesis (BPDS) advances conceptual and…

It is a common misconception that in order to make consistent profits as a trader, one needs to posses some extra information leading to an asset value estimation more accurate than that reflected by the current market price. While the idea…