Related papers: Data analysis recipes: Probability calculus for in…
We take some first steps in providing a synthetic theory of distributions. In particular, we are interested in the use of distribution theory as foundation, not just as tool, in the study of the wave equation.
In many applications (in particular information systems, such as pattern recognition, machine learning, cheminformatics, bioinformatics to name but a few) the assessment of uncertainty is essential - i.e., the estimation of the underlying…
The theory of belief functions manages uncertainty and also proposes a set of combination rules to aggregate opinions of several sources. Some combination rules mix evidential information where sources are independent; other rules are…
Statistical science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators - even for purely descriptive goals. Statistical decision theory requires more…
We extend the synthetic theories of discrete and Gaussian categorical probability by introducing a diagrammatic calculus for reasoning about hybrid probabilistic models in which continuous random variables, conditioned on discrete ones,…
There has been an ever-increasing interest in multidisciplinary research on representing and reasoning with imperfect data. Possibilistic networks present one of the powerful frameworks of interest for representing uncertain and imprecise…
Probabilistic techniques are central to data analysis, but different approaches can be difficult to apply, combine, and compare. This paper introduces composable generative population models (CGPMs), a computational abstraction that extends…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
We present probabilistic neural programs, a framework for program induction that permits flexible specification of both a computational model and inference algorithm while simultaneously enabling the use of deep neural networks.…
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
In Official Statistics, interest for data integration has been increasingly growing, due to the need of extracting information from different sources. However, the effects of these procedures on the validity of the resulting statistical…
We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
One way to investigate the precision of estimates likely to result from planned experiments and planned epidemiological studies is to simulate a large number of possible outcomes and analyse the sets of possible results. This appears to be…
Drawing on the Data and Predictions strand of the Indicazioni Nazionali per il curricolo 2012, this study proposes a problem based instructional approach to the teaching of probability. More specifically, the study adopts a design based…
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…
The roles played by decision factors in making complex subject are decisions are characterized by how these factors affect the overall decision. Evidence that partially matches a factor is evaluated, and then effective computational rules…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…