By Geweke J., Tanizaki H.

During this paper, an try is made to teach a basic approach to nonlinear and/or non-Gaussian state-space modeling in a Bayesian framework, which corresponds to an extension of Carlin et al. (J. Amer. Statist. Assoc. 87(418} (1992) 493-500) and Carter and Kohn (Biometrika 81(3} (1994) 541-553; Biometrika 83(3) (1996) 589-601). utilizing the Gibbs sampler and the Metropolis-Hastings set of rules, an asymptotically certain estimate of the smoothing suggest is bought from any nonlinear and/or non-Gaussian version. furthermore, taking numerous applicants of the thought density functionality, we study precision of the proposed Bayes estimator.

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5. 6. Some simple computations Some simple architectures Algorithms for a linear array Algorithms for a binary tree Algorithms for a 2D mesh Algorithms with shared variables 25 This page intentionally left blank. 1. SOME SIMPLE COMPUTATIONS In this section, we define five fundamental building-block computations: 1. 2. 3. 4. 5. Semigroup (reduction, fan-in) computation Parallel prefix computation Packet routing Broadcasting, and its more general version, multicasting Sorting records in ascending/descending order of their keys Semigroup Computation.

For example, if P 0 is holding (1, 3, 7, 8) and P 1 has (2, 4, 5, 9), a merge–split step will turn the lists into (1, 2, 3, 4) and (5, 7, 8, 9), respectively. Because the sublists are sorted, the merge–split step requires n/p compare–exchange steps. Thus, the total time of the algorithm is (n/p)log2 (n /p ) + n . Note that the first term (local sorting) will be dominant if p < log 2 n, while the second term (array merging) is dominant for p > log2 n . For p ≥ log 2 n, the time complexity of the algorithm is linear in n; hence, the algorithm is more efficient than the one-key-per-processor version.

For p ≥ log 2 n, the time complexity of the algorithm is linear in n; hence, the algorithm is more efficient than the one-key-per-processor version. One final observation about sorting: Sorting is important in its own right, but occasionally it also helps us in data routing. Suppose data values being held by the p processors of a linear array are to be routed to other processors, such that the destination of each value is different from all others. This is known as a permutation routing problem.