The Geometry of Uncertainty: The Geometry of Imprecise Probabilities

Introduction.- Part I: Theories of Uncertainty.- Belief Functions.- Understanding Belief Functions.- Reasoning with Belief Functions.- A Toolbox for the Working Scientist.- The Bigger Picture.- Part II: The Geometry of Uncertainty.- The Geometry of Belief Functions.- Geometry of Dempster's Rule.- Three Equivalent Models.- The Geometry of Possibility.- Part III: Geometry Interplays.- Probability Transforms: The Affine Family.- Probability Transforms: The Epistemic Family.- Consonant Approximation.- Consistent Approximation.- Part IV: Geometric Reasoning.- Geometric Conditioning.- Decision Making with Epistemic Transforms.- Part V The Future of Uncertainty.- An Agenda for the Future.- References.