Gibbs sampling block updating

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The root node was responsible for generating and partitioning the matrix , transmitting the submatrices, updating and broadcasting item parameters, and recording execution time, in addition to assuming the same duties as the slave nodes.Each node on the cluster has an Intel Xeon dual CPU quad-core processor clocked at 2.3 GHz, 8 GB of RAM, 90 TB storage, and Linux 64 bit operating system.The results suggest that the proposed approach increased the speedup and the efficiency for each implementation while minimizing the cost and the total overhead.This further sheds light on developing high performance Gibbs samplers for more complicated IRT models.Given that the fully Bayesian estimation of IRT models requires a minimum of 20 or 30 times more subjects than test items, which typically occurs in a test situation, it is believed that one can reduce the communication overhead if item parameters are communicated instead of person parameters.Hence, an alternative approach is to decompose data matrices and person parameters into rows.In spite of the many advantages, the fully Bayesian estimation is computationally expensive, which further limits its actual applications.

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In addition to educational and psychological measurement, IRT models have been used in other areas of applied mathematics and statistical research, including US Supreme Court decision-making processes [5], alcohol disorder analysis [6–9], nicotine dependency [10–12], multiple-recapture population estimation [13], and psychiatric epidemiology [14–16], to name a few.IRT has the advantage of allowing the inference of what the items and persons have on the responses to be modeled by distinct sets of parameters.As a result, a primary concern associated with IRT research has been on parameter estimation, which offers the basis for the theoretical advantages of IRT.Specifically, of concern are the statistical complexities that can often arise when item and person parameters are simultaneously estimated (see [1, 17–19]).More recent attention has focused on the fully Bayesian estimation where Markov chain Monte Carlo (MCMC, [20, 21]) simulation techniques are used.

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