Related papers: The Art of Probability Assignment

This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…

Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…

The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…

We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference…

How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…

We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…

A very simple example demonstrates that Fisher's application of the conditionality principle to regression ("fixed-$x$ regression"), endorsed by Sprott and many other followers, makes prediction impossible in the context of statistical…

Estimating prevalence, the fraction of a population with a certain medical condition, is fundamental to epidemiology. Traditional methods rely on classification of test samples taken at random from a population. Such approaches to…

Uncertainty associated with statistical problems arises due to what has not been seen as opposed to what has been seen. Using probability to quantify the uncertainty the task is to construct a probability model for what has not been seen…

Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…

Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…

Employing a generalized definition of Pratt (1964) and Arrow's (1965, 1971) probability premium, we introduce a new concept of attitude towards probability. We illustrate in a problem of risk sharing that whether attitude towards…

Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…

Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…

The following zero-sum game between nature and a statistician blends Bayesian methods with frequentist methods such as p-values and confidence intervals. Nature chooses a posterior distribution consistent with a set of possible priors. At…

Behavioural economics provides labels for patterns in human economic behaviour. Probability weighting is one such label. It expresses a mismatch between probabilities used in a formal model of a decision (i.e. model parameters) and…

Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…

We consider the problem of assessing whether, in an individual case, there is a causal relationship between an observed exposure and a response variable. When data are available on similar individuals we may be able to estimate prospective…

Is it a good idea to use the frequency of events in the past, as a guide to their frequency in the future (as we all do anyway)? In this paper the question is attacked from the perspective of universal prediction of individual sequences. It…

Randomized experiments have long been the gold standard for scientists seeking to learn about cause and effect. When randomized experiments are infeasible, scientists often resort to observational studies, which are widely available and…