Abstract
In this paper, we propose a Bayesian Graphical Lasso for correlated countable data and apply it to spatial crime data. In the proposed model, we assume a Gaussian Graphical Model for the latent variables which dominate the potential risks of crimes. To evaluate the proposed model, we determine optimal hyperparameters which represent samples better. We apply the proposed model for estimation of the sparse inverse covariance of the latent variable and evaluate the partial correlation coefficients. Finally, we illustrate the results on crime spots data and consider the estimated latent variables and the partial correlation coefficients of the sparse inverse covariance.
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References
S. Chib, I. Jeliazkov, Marginal likelihood from the metropolis–hastings output. J. Am. Stat. Assoc. 96(453), 270–281 (2001)
J. Friedman, T. Hastie, R. Tibshirani, Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9, 432–441 (2008)
N. Homepage, Real-time crime forecasting challenge. https://nij.ojp.gov/funding/real-time-crime-forecasting-challenge. Last accessed 18 May 2020
Y. Igarashi, K. Nagata, T. Kuwatani, T. Omori, Y. Nakanishi-Ohno, M. Okada, Three levels of data-driven science. J. Phys. Conf. Ser. 699, 012001 (2016). https://doi.org/10.1088/1742-6596/699/1/012001
A. Ihler, J. Hutchins, P. Smyth, Adaptive event detection with time-varying poisson processes, in Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2006), pp. 207–216
D.W. Osgood, Poisson-based regression analysis of aggregate crime rates. J. Quant. Criminol. 16(1), 21–43 (2000)
A. Sitek, A.M. Celler, Limitations of poisson statistics in describing radioactive decay. Phys. Med. 31(8), 1105–1107 (2015)
R. Tibshirani, Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B (Methodological) 58(1), 267–288 (1996). http://www.jstor.org/stable/2346178
H. Wang et al., Bayesian graphical lasso models and efficient posterior computation. Bayesian Anal. 7(4), 867–886 (2012)
J. Weinberg, L.D. Brown, J.R. Stroud, Bayesian forecasting of an inhomogeneous poisson process with applications to call center data. J. Am. Stat. Assoc. 102(480), 1185–1198 (2007)
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Ichigozaki, S., Kawashima, T., Shouno, H. (2021). Bayesian Sparse Covariance Structure Analysis for Correlated Count Data. In: Arabnia, H.R., et al. Advances in Parallel & Distributed Processing, and Applications. Transactions on Computational Science and Computational Intelligence. Springer, Cham. https://doi.org/10.1007/978-3-030-69984-0_57
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DOI: https://doi.org/10.1007/978-3-030-69984-0_57
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