Causal independence modelling is a well-known method both for reducing the size of probability tables and for explaining the underlying mechanisms in Bayesian networks. Many Bayesian network models incorporate causal independence assumptions; however, only the noisy OR and noisy AND, two examples of causal independence models, are used in practice. Their underlying assumption that either at lea...

The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but they all demand prohibitive amounts of input data. In this paper we consider real-valued time series and construct conditional distribution estimates that make...

We present a class of graphical models for directly representing the joint cumulative distribution function (CDF) of many random variables, called cumulative distribution networks (CDNs). Unlike graphs for probability density and mass functions, in a CDN, the marginal probabilities for any subset of variables are obtained by computing limits of functions in the model. We will show that the cond...

Although knowing the time of the occurrence of the earthquakes is vital and helpful, unfortunately it is still unpredictable. By the way there is an urgent need to find a method to foresee this catastrophic event. There are a lot of methods for forecasting the time of earthquake occurrence. Another method for predicting that is to know probability density function of time interval between earth...

This paper gives upper and lower bounds on the minimum error probability of Bayesian M -ary hypothesis testing in terms of the Arimoto-Rényi conditional entropy of an arbitrary order α. The improved tightness of these bounds over their specialized versions with the Shannon conditional entropy (α = 1) is demonstrated. In particular, in the case where M is finite, we show how to generalize Fano’s...

Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as product functions copula function, this leads to both an intuitive interpretation conditional distribution convenient estimation procedures. However, is no longer case for models mixed discrete continuous d...