A methodology is introduced for the identification of a multi-modal real-valued random variable from a collection of samples. The random variable is seen as a finite mixture of uni-modal random variables. A functional representation of the random variable is used, which can be interpreted as a mixture of polynomial chaos expansions. After a suitable separation of samples into sets of uni-modal ...

We have seen that if X X1 + · · · + Xn is a sum of independent {0, 1} random variables, then X is tightly concentrated around its expected value …[X]. The fact that the random variables were {0, 1}-valued was not essential; similar concentration results hold if we simply assume that they are in some bounded range [−L, L]. One can also relax the independence assumption, as we will see next. Cons...

Let X be a sum of real valued random variables and have a bounded mean EEX]. The generic Chernoo-Hoeeding estimate for large deviations of X is: PrfX?EEX] ag min 0 e ?(a+EEX]) EEe X ], which applies with a 0 to random variables with very small tails. At issue is how to use this method to attain sharp and useful estimates. We present a number of Chernoo-Hoeeding bounds for sums of random variabl...

We have seen that if X X1 + · · · + Xn is a sum of independent {0, 1} random variables, then X is tightly concentrated around its expected value …[X]. The fact that the random variables were {0, 1}-valued was not essential; similar concentration results hold if we simply assume that they are in some bounded range [−L, L]. One can also relax the independence assumption, as we will see next. Cons...

12:45 pm Lunch 02:30–03:30 pm A. COLUBI: Statistical inference about the means of fuzzy random variables: applications to the analysis of fuzzy-and real-valued data Estimation of a simple linear regression model for fuzzy random variables 04:00 pm Coffee break 04:30–05:00 pm A. WÜNSCHE: Asymptotic tests for the Aumann-expectation of fuzzy random variables 05:00–05:30 pm K. LENDELOVÁ, B. RIEČAN:...

We consider convex stochastic programming problems with probabilistic constraints involving integer valued random variables The concept of a p e cient point of a probability distribution is used to derive various equivalent problem for mulations Next we introduce the concept of r concave discrete probability distri butions and analyse its relevance for problems under consideration These notions...

I describe the basics of probability theory, statistical signal processing and information theory, and how these disciplines inter-relate to form the foundations of a theory of information processing. Examples are drawn from point-process applications. Johnson Basics of Information Processing 1 Probability theory Random variables can be either discrete or continuous valued. Discrete random vari...