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APPLD STOCHASTC PROCESSE

by: Helga Torp Sr.

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APPLD STOCHASTC PROCESSE STA 624

Marketplace > University of Kentucky > Statistics > STA 624 > APPLD STOCHASTC PROCESSE
Helga Torp Sr.
UK
GPA 3.87

Staff

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Staff
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This 2 page Class Notes was uploaded by Helga Torp Sr. on Friday October 23, 2015. The Class Notes belongs to STA 624 at University of Kentucky taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/228278/sta-624-university-of-kentucky in Statistics at University of Kentucky.

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Date Created: 10/23/15
Notes7 April 187 Sta624 Spring 2006 Example of MC for continuous state space cont random variables But still discrete time 1 Transition probability matrix needs to be replaced by a transition probability kernel pzly which is a density for any given y value 2 in the following example is taken to be Uniform 17y7 1 State space is the interval 07 1 Example of a MC X0 N any number between 0 and 1 or could be from any distribution on 01 interval X1 Unif 17 X071 X2 Unif 17 X171 Xn Unif17 Xn17 1 This is a MC 1f the distribution of Xn is convergent at all here it does7 the stationary distribution must satisfy the following integral equation pltziygtfltygtdy 7 M We may check that distribution fz 2x solves the above equation Therefore Xn7 as n large7 will have a distribution approximately equal tofz2zfor0ltmlt1 Remark this is the cont version of the equation 7r0P 7r0 for discrete MC Since 17yltzlt1 39 MW We compute7 using fy 2y 1 1 0 pzlyfydy 7 I1yltmlt12dy 7 2 1 dy 7 2x 7w 1 Notice here we only used the random variables from uniform distributions and end up with a random variable with density x 2x The idea of MCMC is to use an easy in the iteration but end up with a random variable with complicated x that we desire Suppose X0 N any number between 0 and 1 X1 Unif 017 X0 X2 Unif 017 X1 Xn Unif017 Xn17 Find the stationary distribution x of this MC This will also be the approx distribution of Xn for large n

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