The authors introduce new approaches for the combinational circuit design based on Estimation of Distribution Algorithms. In this paradigm, the structure and data dependencies embedded in the data (population of candidate circuits) are modeled by a conditional probability distribution function. The new population is simulated from the probability model thus inheriting the dependencies. The auth...

One of the conventional methods for temporary support of tunnels is to use steel sets with shotcrete. The nature of a temporary support system demands a quick installation of its structures. As a result, the spacing between steel sets is not a fixed amount and it can be considered as a random variable. Hence, in the reliability analysis of these types of structures, the selection of an appropri...

The most common approach to estimating conditional quantile curves is to fit a curve, typically linear, pointwise for each quantile. Linear functional forms, coupled with pointwise fitting, are used for a number of reasons including parsimony of the resulting approximations and good computational properties. The resulting fits, however, may not respect a logical monotonicity requirement – that ...

The most common approach to estimating conditional quantile curves is to fit a curve, typically linear, pointwise for each quantile. Linear functional forms, coupled with pointwise fitting, are used for a number of reasons including parsimony of the resulting approximations and good computational properties. The resulting fits, however, may not respect a logical monotonicity requirement – that ...

Two real-valued or vector-valued random variables X, Y are independent for probability measure P (written: X ⊥ Y [P ]) if for all sets A and B, P[X ∈ A, Y ∈ B] = P[X ∈ A] · P[Y ∈ B]. For jointly discrete or jointly continuous random variables this is equivalent to factoring of the joint probability mass function or probability density function, respectively. The variables X and Y are conditiona...

We introduce the Multiple Quantile Graphical Model (MQGM), which extends the neighborhood selection approach of Meinshausen and Bühlmann for learning sparse graphical models. The latter is defined by the basic subproblem of modeling the conditional mean of one variable as a sparse function of all others. Our approach models a set of conditional quantiles of one variable as a sparse function of ...

1 Last two lectures ¯ probability spaces ¯ probability measure ¯ random variables and stochastic processes ¯ distribution functions ¯ independence ¯ conditional probability ¯ memoriless property of geometric and exponential distributions ¯ expectation ¯ conditional expectation (double expectation) ¯ mean-square estimation 1

Conditional distribution reflects the dependency link among random variables, but two-dimensional random variables Conditional Distribution has some limitations. In order to rich the content of conditional distribution this paper gives the extension of conditional distribution and examples in the case of continuous random variables. For the given definition of conditional distribution of three-...

We show how to extend any finite probability space into another one which satisfies the conditional construal of for original propositions, given some maximal allowed degree nesting conditional. This mitigates force well-known triviality results.

This paper studies the consequences of alternative ways of representing uncertainty about a law of motion in a version of a classic macroeconomic targetting problem of Milton Friedman (1953). We study both “unstructured uncertainty” – ignorance of the conditional distribution of the target next period as a function of states and controls – and more “structured uncertainty” – ignorance of the pr...