We present an algorithm for learning the intersection of half-spaces in n dimensions. Over nearly-uniform distributions, it runs in polynomial time for up to O(log n= log log n) half-spaces or, more generally , for any number of half-spaces whose normal vectors lie in an O(log n= log log n) dimensional subspace. Over less restricted \non-concentrated" distributions it runs in polynomial time fo...

In this paper, we explore a sequential Bayesian bound for state-space models focusing on hybrid continuous and discrete random states. We provide an analytic recursion for the sequential Weiss–Weinstein (SWW) bound for linear state-space models with solutions for Gaussian, uniform, and exponential distributions as derived, as well as for a combination of these. We compare the SWW bound for disc...

In some fields of biometrical research joint modelling of longitudinal measures and event time data has become very popular. This article reviews the work in that area of recent fruitful research by classifying approaches on joint models in three categories: approaches with focus on serial trends, approaches with focus on event time data and approaches with equal focus on both outcomes. Typical...

In many practical situations, the Maximum Entropy (MaxEnt) approach leads to reasonable distributions. However, in an important case when all we know is that the value of a random variable is somewhere within the interval, this approach leads to a uniform distribution on this interval – while our intuition says that we should have a distribution whose probability density tends to 0 when we appr...

The series solutions of the random nonlinear partial differential equations have been examined by a hybrid method. are studied both normal and uniform distributions. Two initial-value problems indicated to exemplify influence acquired Also, functions for first second moments approximate in MAPLE software. method is implemented analyze equations. software used find solutions. Besides, drawing fi...

Contents 1. Introduction. 2. The distribution function of a random variable. 3. Classification of random variables. 4. Some special discrete probability distributions. 5. Some special continuous probability distributions. 6. Location characteristics of a real-valued random variable. 7. Dispersion characteristics of a real-valued random variable. 8. Joint distribution functions. 9. Independence ...