Abstract
This paper describes an efficient implementation of Bayesian hierarchical model for space time variability of latent heat flux. Model parameters are estimated using Gibbs sampler. Many computations in the Gibbs sampling scheme are time intensive. Some time intensive computations in the model are matrix operations such as matrix multiplication, matrix inverse, matrix LU decomposition. We have used graphical processing unit (GPU) to run time intensive matrix operations. Some time intensive operations are transformed to matrix operations to take advantage of GPU. To run the model in GPU model is implemented in Compute Unified Device Architecture (CUDA). Two GPUs are used to run the model one is NVIDIA Graphics card Tesla C2075 with 448 cores and other is NVIDIA Graphics card GT 520 with 48 cores. To study the gain in speedup on the GPU we have implemented the model using single threaded C to run on CPU. A comparative study of implementation on CPU and the two GPUs is carried out for 100 iterations of the Gibbs sampler. We found 30-130 fold speedup on Tesla GPU as compared to single threaded CPU code.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Berliner, L.M.: Hierarchical Bayesian time-series models. Fundamental Theories of Physics 79, 15–22 (1996)
Cocchi, D., Greco, F., Trivisano, C.: Hierarchical space-time modelling of pm10 pollution. Atmospheric Environment 41, 532–542 (2007)
Friedrichs, M.S., Eastman, P., Vaidyanathan, V., Houston, M., Legrand, S., Beberg, A.L., Ensign, D.L., Bruns, C.M., Pande, V.S.: Accelerating molecular dynamic simulation on graphics processing units. Journal of Computational Chemistry 30, 864–872 (2009)
Gamerman, D., Lopes, H.F.: Markov chain Monte Carlo: stochastic simulation for Bayesian inference 68. Chapman & Hall/CRC (2006)
Gelfand, A.E., Smith, A.F.M.: Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85, 398–409 (1990)
Gelman, A., Rubin, D.B.: A single series from the gibbs sampler provides a false sense of security. Bayesian Statistics 4, 625–631 (1992)
Geyer, C.J.: Practical markov chain monte carlo. Statistical Science 7, 473–483 (1992)
Lee, A., Yau, C., Giles, M.B., Doucet, A., Holmes, C.C.: On the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods. Journal of Computational and Graphical Statistics 19, 769–789 (2010)
Natvig, B., Tvete, I.: Bayesian hierarchical space–time modeling of earthquake data. Methodology and Computing in Applied Probability 9, 89–114 (2007)
Raftery, A.E., Lewis, S., et al.: How many iterations in the gibbs sampler. Bayesian Statistics 4, 763–773 (1992)
Sahu, S.: Hierarchical bayesian models for space-time air pollution data. In: Handbook of Statistics-Time Series Analysis, Methods and Applications: Handbook of Statistics, vol. 30 (2011)
Sahu, S.K., Challenor, P.: A space-time model for joint modeling of ocean temperature and salinity levels as measured by argo floats (October 2007)
Pinedo, J.S., et al.: Matrix inversion speed up with cuda (2011)
Suchard, M.A., Wang, Q., Chan, C., Frelinger, J., Cron, A., West, M.: Understanding gpu programming for statistical computation. Studies in massively parallel massive mixtures. Journal of Computational and Graphical Statistics 19, 419–438 (2010)
Suchard, M.A., Rambaut, A.: Many-core algorithms for statistical phylogenetics. Bioinformatics 25, 1370–1376 (2009)
Vanem, E., Huseby, A., Natvig, B.: Modelling ocean wave climate with a bayesian hierarchical space–time model and a log-transform of the data. Ocean Dynamics 62, 355–375 (2012)
Wikle, C.K., Berliner, L.M., Cressie, N.: Hierarchical bayesian space-time models. Environmental and Ecological Statistics 5, 117–154 (1998)
Wikle, C.K., Milliff, R.F., Nychka, D., Berliner, L.M.: Spatiotemporal hierarchical bayesian modeling. Tropical ocean surface winds. Journal of the American Statistical Association 96, 382–397 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Singh, M.K., Venkatachalam, P. (2013). Efficient Implementation of Bayesian Hierarchical Model to Study Space Time Variability of Latent Heat Flux. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2013. ICCSA 2013. Lecture Notes in Computer Science, vol 7974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39649-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-39649-6_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39648-9
Online ISBN: 978-3-642-39649-6
eBook Packages: Computer ScienceComputer Science (R0)