Nonlinear and Non-Gaussian State-Space Modeling with Monte by Tanizaki H.

By Tanizaki H.

Show description

Read Online or Download Nonlinear and Non-Gaussian State-Space Modeling with Monte Carlo Techniques: A Survey and Comparative Study PDF

Best aerospace equipment books

A to Z of Scientists in Space and Astronomy (2005)(en)(336s)

This reference for basic readers and scholars in highschool and up compiles biographies of approximately a hundred thirty scientists in house and astronomy, from antiquity to the current. each one access presents start and demise dates and knowledge on fields of specialization, and examines the scientist's paintings and contributions to the sphere, in addition to relations and academic heritage.

Time-Saver Standards for Interior Design and Space

At Last-A Time-Saver typical for inside layout. release time for creativity with this all-in-one advisor to hour- and money-saving inside layout shortcuts,plus millions of items of well-organized info to make your task more straightforward. Time-Saver criteria for inside layout and area making plans makes decision-making simple-and implementation even more uncomplicated.

Extra info for Nonlinear and Non-Gaussian State-Space Modeling with Monte Carlo Techniques: A Survey and Comparative Study

Example text

T and ηt are assumed to be mutually independent. We compare the extended Kalman filter and smoother16 and the nonlinear and nonGaussian filters and smoothers introduced in Section 3. The simulation procedure is as follows: (i) generating random numbers of t and ηt for t = 1, 2, · · · , T , we obtain a set of data yt and αt , t = 1, 2, · · · , T , from equations (1) and (2), where T = 20, 40, 100 is taken, (ii) given YT , perform each estimator, (iii) repeat (i) and (ii) G times and compare the root mean 1/2 square error (RMSE) for each estimator.

Let P∗ (z|x) be the proposal density, which is the conditional distribution of z given x. We should choose the proposal density P∗ (z|x) such that random draws can be easily and quickly generated. Define the acceptance probability ω(x, z) as follows:     min     ω(x, z) =        1, P (z|Ai,t−1 , A∗i−1,t+1 , YT )P∗ (x|z) ,1 , P (x|Ai,t−1 , A∗i−1,t+1 , YT )P∗ (z|x) if P (x|Ai,t−1 , A∗i−1,t+1 , YT )P∗ (z|x) > 0, otherwise. To generate random draws from P (AT |YT ), the following procedure is taken: (i) pick up appropriate values for α1,0 and α0,t , t = 1, 2, · · · , T , (ii) generate a random draw z from P∗ (·|αi−1,t ) and a uniform random draw u from the uniform distribution between zero and one, (iii) set αi,t = z if u ≤ ω(αi−1,t , z) and set αi,t = αi−1,t otherwise, (iv) repeat (ii) and (iii) for t = 1, 2, · · · , T , and (v) repeat (ii) – (iv) for i = 1, 2, · · · , N .

However, the disadvantages of rejection sampling are: (i) we need to compute a, which sometimes does not exist and (ii) it takes a long time when the acceptance probability ω(·) is close to zero. See, for example, Knuth (1981), Boswell, Gore, Patil and Taillie (1993), O’Hagan (1994) and Geweke (1996) for rejection sampling. Gibbs Sampling: Geman and Geman (1984), Tanner and Wong (1987), Gelfand and Smith (1990), Gelfand, Hills, Racine-Poon and Smith (1990) and so on developed the Gibbs sampling theory, which is concisely described as follows (also see Geweke (1996, 1997)).

Download PDF sample

Rated 4.28 of 5 – based on 8 votes