Bayesian network (BN) A directed graph whose nodes represent variables, and edges represent influences. Together with conditional probability distributions, a Bayesian network represents the joint probability distribution of its variables. Conditional probability distribution Assignment of probabilities to all instances of a set of variables when the value of one or more variables is known. Con...

We introduce a new theory of belief revision under ambiguity. It is recursive (random variables are evaluated by backward induction) and consequentialist (the conditional expectation of any random variable depends only on the values the random variable attains on the conditioning event). Agents experience no change in preferences but may not be indifferent to the timing of resolution of uncerta...

The concept of Conditional Value-at-Risk (CVaR) is used in various applications in uncertain environment. This paper introduces CVaR norm for a random variable, which is by de nition CVaR of absolute value of this random variable. It is proved that CVaR norm is indeed a norm in the space of random variables. CVaR norm is de ned in two variations: scaled and non-scaled. L-1 and L-in nity norms a...

Knowledge about complex events is usually incomplete in practice. Zeros can be utilized to capture such events within probability models. In this article, Geiger and Pearl’s conditional probabilistic independence statements are investigated in the presence of zeros. Random variables can be specified to be zero-free, i.e., to disallow zeros in their domains. Zero-free random variables provide an...

The concept of Conditional Value-at-Risk (CVaR) is used in various applications in uncertain environment. This paper introduces CVaR (superquantile) norm for a random variable, which is by de nition CVaR of absolute value of this random variable. It is proved that CVaR norm is indeed a norm in the space of random variables. CVaR norm is de ned in two variations: scaled and non-scaled. L-1 and L...

We use the conditional distribution and conditional expectation of one random variable given the other one being large to capture the strength of dependence in the tails of a bivariate random vector. We study the tail behavior of the boundary conditional cumulative distribution function (cdf) and two forms of conditional tail expectation (CTE) for various bivariate copula families. In general, ...

Density regression provides a flexible strategy for modeling the distribution of a response variable Y given predictors X = (X1, . . . ,Xp) by letting that the conditional density of Y given X as a completely unknown function and allowing its shape to change with the value of X. The number of predictors p may be very large, possibly much larger than the number of observations n, but the conditi...

In this paper a new nonparametric functional method is introduced for predicting a scalar random variable Y from a functional random variable X. The resulting prediction has the form of a weighted average of the training data set, where the weights are determined by the conditional probability density of X given Y , which is assumed to be Gaussian. In this way such a conditional probability den...

researchers of language teaching believe that teaching method has a lot of impact on the speed and depth of learning. the importance of this is so obvious on teaching some persian language structures which are syntactically and semantically complicated. one of these structures is conditional sentences which has been considered in this study. here we tried to teach conditional sentences via both...