1,593 research outputs found
The CONEstrip algorithm
Uncertainty models such as sets of desirable gambles and (conditional) lower previsions can be represented as convex cones. Checking the consistency of and drawing inferences from such models requires solving feasibility and optimization problems. We consider finitely generated such models. For closed cones, we can use linear programming; for conditional lower prevision-based cones, there is an efficient algorithm using an iteration of linear programs. We present an efficient algorithm for general cones that also uses an iteration of linear programs
A new method for learning imprecise hidden Markov models
We present a method for learning imprecise local uncertainty models in stationary hidden Markov models. If there is enough data to justify precise local uncertainty models, then existing learning algorithms, such as the Baum–Welch algorithm, can be used. When there is not enough evidence to justify precise models, the method we suggest here has a number of interesting features
Sets of Priors Reflecting Prior-Data Conflict and Agreement
In Bayesian statistics, the choice of prior distribution is often debatable,
especially if prior knowledge is limited or data are scarce. In imprecise
probability, sets of priors are used to accurately model and reflect prior
knowledge. This has the advantage that prior-data conflict sensitivity can be
modelled: Ranges of posterior inferences should be larger when prior and data
are in conflict. We propose a new method for generating prior sets which, in
addition to prior-data conflict sensitivity, allows to reflect strong
prior-data agreement by decreased posterior imprecision.Comment: 12 pages, 6 figures, In: Paulo Joao Carvalho et al. (eds.), IPMU
2016: Proceedings of the 16th International Conference on Information
Processing and Management of Uncertainty in Knowledge-Based Systems,
Eindhoven, The Netherland
Factorisation properties of the strong product
We investigate a number of factorisation conditions in the frame- work of sets of probability measures, or coherent lower previsions, with finite referential spaces. We show that the so-called strong product constitutes one way to combine a number of marginal coherent lower previsions into an independent joint lower prevision, and we prove that under some conditions it is the only independent product that satisfies the factorisation conditions
Soil origin and land use history determine C cycling in transplanted soils after 21 years
Non-Peer Reviewe
Response of transplanted Chernozems towards C addition after 21 years of identical climatic, topographic, and management practices
Non-Peer Reviewe
Maximin and maximal solutions for linear programming problems with possibilistic uncertainty
We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possi-bility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-probabilistic uncer-tainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them
Robust Inference of Trees
This paper is concerned with the reliable inference of optimal
tree-approximations to the dependency structure of an unknown distribution
generating data. The traditional approach to the problem measures the
dependency strength between random variables by the index called mutual
information. In this paper reliability is achieved by Walley's imprecise
Dirichlet model, which generalizes Bayesian learning with Dirichlet priors.
Adopting the imprecise Dirichlet model results in posterior interval
expectation for mutual information, and in a set of plausible trees consistent
with the data. Reliable inference about the actual tree is achieved by focusing
on the substructure common to all the plausible trees. We develop an exact
algorithm that infers the substructure in time O(m^4), m being the number of
random variables. The new algorithm is applied to a set of data sampled from a
known distribution. The method is shown to reliably infer edges of the actual
tree even when the data are very scarce, unlike the traditional approach.
Finally, we provide lower and upper credibility limits for mutual information
under the imprecise Dirichlet model. These enable the previous developments to
be extended to a full inferential method for trees.Comment: 26 pages, 7 figure
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