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A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…
The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and…
Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities.…
Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
When there exists uncertainty, AI machines are designed to make decisions so as to reach the best expected outcomes. Expectations are based on true facts about the objective environment the machines interact with, and those facts can be…
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
The predictability of errors in deterministic temperature forecasts is investigated. More precisely, the aim is to issue warnings whenever the differences between forecast and verification exceed a given threshold. The warnings are…
This paper defines theoretical lower bounds of uncertainty of observations of macroeconomic variables that depend on statistical moments and correlations of random values and volumes of market trades. Any econometric assessments of…
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
To many statisticians and citizens, the outcome of the most recent U.S. presidential election represents a failure of data-driven methods on the grandest scale. This impression has led to much debate and discussion about how the election…
Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to…
We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate…
What does it mean to say that, for example, the probability for rain tomorrow is between 20% and 30%? The theory for the evaluation of precise probabilistic forecasts is well-developed and is grounded in the key concepts of proper scoring…
Increasingly high-stakes decisions are made using neural networks in order to make predictions. Specifically, meteorologists and hedge funds apply these techniques to time series data. When it comes to prediction, there are certain…
The quality of probabilistic forecasts is crucial for decision-making under uncertainty. While proper scoring rules incentivize truthful reporting of precise forecasts, they fall short when forecasters face epistemic uncertainty about their…
We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…
Non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain-but-bounded parameters, which is very effective for structural uncertainty analysis with limited or poor-quality experimental data. To…
The paper studies one-shot two-player games with non-Bayesian uncertainty. The players have an attitude that ranges from optimism to pessimism in the face of uncertainty. Given the attitudes, each player forms a belief about the set of…