相关论文: Updating Probabilities
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…
This paper discusses an alternative to conditioning that may be used when the probability distribution is not fully specified. It does not require any assumptions (such as CAR: coarsening at random) on the unknown distribution. The…
Conditioning is the generally agreed-upon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of cross-entropy minimization,…
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…
In recent years a popular nonparametric model for coarsened data is an assumption on the coarsening mechanism called coarsening at random (CAR). It has been conjectured in several papers that this assumption cannot be tested by the data,…
The concept of updating (or conditioning or revising) a probability distribution is fundamental in (machine) learning and in predictive coding theory. The two main approaches for doing so are called Pearl's rule and Jeffrey's rule. Here we…
In probabilistic updating one transforms a prior distribution in the light of given evidence into a posterior distribution, via what is called conditioning, updating, belief revision or inference. This is the essence of learning, as…
The study of question answering has received increasing attention in recent years. This work focuses on providing an answer that compatible with both user intent and conditioning information corresponding to the question, such as delivery…
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…
This paper discusses how a measure of uncertainty representing a state of knowledge can be updated when a new information, which may be pervaded with uncertainty, becomes available. This problem is considered in various framework, namely:…
Jeffrey's rule has been generalized by Wagner to the case in which new evidence bounds the possible revisions of a prior probability below by a Dempsterian lower probability. Classical probability kinematics arises within this…
Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or set-valued). This is a fundamental problem, and of particular interest for Bayesian networks.…
Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming…
Traditional credibility analysis of risks in insurance is based on the random effects model, where the heterogeneity across the policyholders is assumed to be time-invariant. One popular extension is the dynamic random effects (or…
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…
Models of updating a set of priors either do not allow a decision maker to make inference about her priors (full bayesian updating or FB) or require an extreme degree of selection (maximum likelihood updating or ML). I characterize a…
The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the…
We consider how an agent should update her uncertainty when it is represented by a set $\P$ of probability distributions and the agent observes that a random variable $X$ takes on value $x$, given that the agent makes decisions using the…