Related papers: Reality and Probability: Introducing a New Type of…
We describe a method for estimation of the discovery potential on new physics in planned experiments. The effective significance of signal for given probability of observation is proposed for planned experiments instead of the usual…
Randomness is a crucial resource for a broad range of important applications, such as Monte Carlo simulation and computation, generative artificial intelligence and cryptography. But what is randomness? A widely accepted definition has…
Practical problems with missing data are common, and statistical methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism…
Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
The problem of interpreting quantum theory on a large (e.g. cosmological) scale has been commonly conceived as a search for objective reality in a framework that is fundamentally probabilistic. The Everett programme attempts to evade the…
We define a generalized likelihood function based on uncertainty measures and show that maximizing such a likelihood function for different measures induces different types of classifiers. In the probabilistic framework, we obtain…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
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…
Recently, Halpern and Leung suggested representing uncertainty by a weighted set of probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not…
This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…
In this paper, we take a fresh look at three Popperian concepts: riskiness, falsifiability, and truthlikeness (or verisimilitude) of scientific hypotheses or theories. First, we make explicit the dimensions that underlie the notion of…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
The superstatistics approach recently introduced by Beck [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism that aims to deal in a unifying way with a large variety of complex nonequilibrium systems, for which…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…
Interpretation of the nonclassical total probability formula arising in some quantum experiments is provided based on stochastic models described by means of a sequence of random vectors changing in the measurement procedures.
Cosmological fine-tuning has traditionally been associated with the narrowness of the intervals in which the parameters of the physical models must be located to make life possible. A more thorough approach focuses on the probability of the…
I start from the fundamental principles of non-relativistic quantum mechanics, without probability, and interpret them using the notion of coexistence: a quantum state can be read, not uniquely, as a coexistence of other quantum states,…
Realism -- the idea that the concepts in physical theories refer to 'things' existing in the real world -- is introduced as a tool to analyze the status of the wave-function. Although the physical entities are recognized by the existence of…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…