Expected value or expectation of a random variableXis defined, if it exists, in a mathematically precise way with respect to a probability space, typically denoted as(Ω,A,P), whereΩis the universe of possibil
Thus, we can think of g(y)=E[X|Y=y]g(y)=E[X|Y=y] as a function of the value of random variable YY. We then write g(Y)=E[X|Y].g(Y)=E[X|Y]. We use this notation to indicate that E[X|Y]E[X|Y] is a random variable whose value equals g(y)=E[X|Y=y]g(y...
The joint probability over all variables can be expressed as products of some factor functions in which each contains only a subset of all variables as arguments and is represented by a factor node. Each variable node expresses a random variable. EXPLORER requires two phases: initially the ...
We study the (weak) equilibrium problem arising from the problem of optimally stopping a one-dimensional diffusion subject to an expectation constraint on the time until stopping. The weak equilibrium problem is realized with a set of randomized but purely state dependent stopping times as admissible...
conditional expectation(条件期望讲义)A Conditional expectation A.1Review of conditional densities,expectations We start with the continuous case.This is sections6.6and6.8in the book.Let X,Y be continuous random variables.We defined the conditional density of X given Y to be f X,Y(x,y)f ...
Then for “Markov-like” random variables, the G-expectation and conditional expectations are defined through the solution of the above equation with this random variable as its terminal condition at time T=1. A G-martingale is then defined easily as a process which satisfies the martingale prope...
This paper proposes a two-stage approach to parametric nonlinear time series modelling in discrete time with the objective of incorporating uncertainty or
chapter5theexpectationoperator.doc,CHAPTER 5 The Expectation Operator Definition 5.1 Let be an n-D random variable with sample space SX and with pdf . Let be any function of . The expectation operator E(*) is defined as (5.1) The integral (1) is an n-D i
We formulate a robust method using Expectation Maximiza- tion (EM) to address the problem of dense photometric stereo. Previous approaches using Markov Random Fields (MRF) utilized a dense set of noisy photometric images for estimating an initial normal to encode the matching cost at each pixel,...
1.One of the more salient effects of listening to music is to create expectations of what is to come next, which may be fulfilled immediately, after some delay, or not at all as the case may be. Th...