77 citations · 225 across the 13 of their papers we have counts for
11 papers · 1 filter
Randomness and imprecision: from supermartingales to randomness tests
Gert de Cooman, Floris Persiau, Jasper De Bock
We generalise the randomness test definitions in the literature for both the Martin-Löf and Schnorr randomness of a series of binary outcomes, in order to allow for interval-valued…
Imprecision in Martingale-Theoretic Prequential Randomness
Floris Persiau, Gert de Cooman
In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast `on the fly' without the need for fully specifying a probability measure on…
On the (dis)similarities between stationary imprecise and non-stationary precise uncertainty models in algorithmic randomness
Floris Persiau, Jasper De Bock, Gert de Cooman
The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, martingale-theoretic notions of…
Randomness is inherently imprecise
Gert de Cooman, Jasper De Bock
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define several notions of randomne…
Game-Theoretic Upper Expectations for Discrete-Time Finite-State Uncertain Processes
Natan T'Joens, Jasper De Bock, Gert de Cooman
Game-theoretic upper expectations are joint (global) probability models that mathematically describe the behaviour of uncertain processes in terms of supermartingales; capital proc…
Computable Randomness is Inherently Imprecise
Gert de Cooman, Jasper De Bock
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable rand…
A study of imprecise Markov chains: joint lower expectations and point-wise ergodic theorems
Gert de Cooman, Jasper De Bock, Stavros Lopatatzidis
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such…
Continuity of imprecise stochastic processes with respect to the pointwise convergence of monotone sequences
Jasper De Bock, Gert de Cooman
We consider the joint lower expectation of a finite-state imprecise stochastic process, defined using either the Ville-Vovk-Shafer natural extension or the Williams natural extensi…
Accept & Reject Statement-Based Uncertainty Models
Erik Quaeghebeur, Gert de Cooman, Filip Hermans
We develop a framework for modelling and reasoning with uncertainty based on accept and reject statements about gambles. It generalises the frameworks found in the literature based…
Exchangeability and sets of desirable gambles
Gert de Cooman, Erik Quaeghebeur
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their…
Imprecise Markov chains and their limit behaviour
Gert de Cooman, Filip Hermans, Erik Quaeghebeur
When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This can be done by considerin…