Related papers: Minimum scoring rule inference
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
We revisit the mathematical foundations of proper scoring rules (PSRs) and Bregman divergences and present their characteristic properties in a unified theoretical framework. In many situations it is preferable not to generate a PSR…
Quadrature rules estimate the value of an integral when the function is given by a table of values. Every binary string defines a quadrature rule by choosing which endpoint of each interval represents the interval. The standard rules, such…
We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…
In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate…
Many proper scoring rules such as the Brier and log scoring rules implicitly reward a probability forecaster relative to a uniform baseline distribution. Recent work has motivated weighted proper scoring rules, which have an additional…
We study the problem of deriving policies, or rules, that when enacted on a complex system, cause a desired outcome. Absent the ability to perform controlled experiments, such rules have to be inferred from past observations of the system's…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
Rule models are often preferred in prediction tasks with tabular inputs as they can be easily interpreted using natural language and provide predictive performance on par with more complex models. However, most rule models' predictions are…
Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate…
With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
Probabilistic forecasting relies on past observations to provide a probability distribution for a future outcome, which is often evaluated against the realization using a scoring rule. Here, we perform probabilistic forecasting with…
Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…
We discuss weighted scoring rules for forecast evaluation and their connection to hypothesis testing. First, a general construction principle for strictly locally proper weighted scoring rules based on conditional densities and scoring…