135,735 research outputs found
Nonparametric predictive inference and interval probability
This paper presents the unique position of A(n)-based nonparametric predictive inference within the theory of interval probability. It provides a completely new understanding, leading to powerful new results and a well-founded justification of such inferences by proving strong internal consistency results
Combining Non-probability and Probability Survey Samples Through Mass Imputation
This paper presents theoretical results on combining non-probability and
probability survey samples through mass imputation, an approach originally
proposed by Rivers (2007) as sample matching without rigorous theoretical
justification. Under suitable regularity conditions, we establish the
consistency of the mass imputation estimator and derive its asymptotic variance
formula. Variance estimators are developed using either linearization or
bootstrap. Finite sample performances of the mass imputation estimator are
investigated through simulation studies and an application to analyzing a
non-probability sample collected by the Pew Research Centre.Comment: Submitted to Journal of the Royal Statistical Society: Series
Merging the local and global approaches to probabilistic satisfiability
AbstractThe probabilistic satisfiability problem is to verify the consistency of a set of probability values or intervals for logical propositions. The (tight) probabilistic entailment problem is to find best bounds on the probability of an additional proposition. The local approach to these problems applies rules on small sets of logical sentences and probabilities to tighten given probability intervals. The global approach uses linear programming to find best bounds. We show that merging these approaches is profitable to both: local solutions can be used to find global solutions more quickly through stabilized column generation, and global solutions can be used to confirm or refute the optimality of the local solutions found. As a result, best bounds are found, together with their step-by-step justification
Subset models for justification logic
We introduce a new semantics for justification logic based on subset
relations. Instead of using the established and more symbolic interpretation of
justifications, we model justifications as sets of possible worlds. We
introduce a new justification logic that is sound and complete with respect to
our semantics. Moreover, we present another variant of our semantics that
corresponds to traditional justification logic.
These types of models offer us a versatile tool to work with justifications,
e.g.~by extending them with a probability measure to capture uncertain
justifications. Following this strategy we will show that they subsume
Artemov's approach to aggregating probabilistic evidence
Epistemic Akrasia and Epistemic Reasons
It seems that epistemically rational agents should avoid incoherent combinations of beliefs and should respond correctly to their epistemic reasons. However, some situations seem to indicate that such requirements cannot be simultaneously satisfied. In such contexts, assuming that there is no unsolvable dilemma of epistemic rationality, either (i) it could be rational that one’s higher-order attitudes do not align with one’s first-order attitudes or (ii) requirements such as responding correctly to epistemic reasons that agents have are not genuine rationality requirements. This result doesn’t square well with plausible theoretical assumptions concerning epistemic rationality. So, how do we solve this puzzle? In this paper, I will suggest that an agent can always reason from infallible higher-order reasons. This provides a partial solution to the above puzzle
Bayesian Probabilities and the Histories Algebra
We attempt a justification of a generalisation of the consistent histories
programme using a notion of probability that is valid for all complete sets of
history propositions. This consists of introducing Cox's axioms of probability
theory and showing that our candidate notion of probability obeys them. We also
give a generalisation of Bayes' theorem and comment upon how Bayesianism should
be useful for the quantum gravity/cosmology programmes.Comment: 10 pages, accepted by Int. J. Theo. Phys. Feb 200
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