Related papers: Generalizing Jeffrey Conditionalization

Jeffrey's rule of conditioning has been proposed in order to revise a probability measure by another probability function. We generalize it within the framework of the models based on belief functions. We show that several forms of…

Bayes's rule deals with hard evidence, that is, we can calculate the probability of event $A$ occuring given that event $B$ has occurred. Soft evidence, on the other hand, involves a degree of uncertainty about whether event $B$ has…

Jacobi brackets (a generalization of standard Poisson brackets in which Leibniz's rule is replaced by a weaker condition) are extended to brackets involving an arbitrary (even) number of functions. This new structure includes, as a…

The concept of updating a probability distribution in the light of new evidence lies at the heart of statistics and machine learning. Pearl's and Jeffrey's rule are two natural update mechanisms which lead to different outcomes, yet the…

Evidence in probabilistic reasoning may be 'hard' or 'soft', that is, it may be of yes/no form, or it may involve a strength of belief, in the unit interval [0, 1]. Reasoning with soft, [0, 1]-valued evidence is important in many situations…

We extend a lower bound of Munshi on sums over divisors of a number $n$ which are less than a fixed power of $n$ from the squarefree case to the general case. In the process we prove a lower bound on the entropy of a geometric distribution…

We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…

Penalization of the likelihood by Jeffreys' invariant prior, or by a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of…

In this paper, we show a more concise and high level proof than the original one, derived by researcher Bart Jacobs, for the following theorem: in the context of Bayesian update rules for learning or updating internal states that produce…

Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…

As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a ``naive space', which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine…

Dempster-Shafer evidence theory has been widely used in various fields of applications, because of the flexibility and effectiveness in modeling uncertainties without prior information. However, the existing evidence theory is insufficient…

We establish the \emph{inverse conjecture for the Gowers norm over finite fields}, which asserts (roughly speaking) that if a bounded function $f: V \to \C$ on a finite-dimensional vector space $V$ over a finite field $\F$ has large Gowers…

In this paper we show that combination of the minimum description length principle and a exchange-ability condition leads directly to the use of Jeffreys prior. This approach works in most cases even when Jeffreys prior cannot be…

In the present note we prove a conjecture of Demailly for finite sets of sufficiently many very general points in projective spaces. This gives a lower bound on Waldschmidt constants of such sets. Waldschmidt constants are asymptotic…

We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…

An important notion of common information between two random variables is due to Wyner. In this paper, we derive a lower bound on Wyner's common information for continuous random variables. The new bound improves on the only other general…

While Jeffreys priors usually are well-defined for the parameters of mixtures of distributions, they are not available in closed form. Furthermore, they often are improper priors. Hence, they have never been used to draw inference on the…

Classification approaches based on the direct estimation and analysis of posterior probabilities will degrade if the original class priors begin to change. We prove that a unique (up to scale) solution is possible to recover the data…

We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's…