Approximate methods in Bayesian point process spatial models. (English) Zbl 1453.62113
Summary: A range of point process models which are commonly used in spatial epidemiology applications for the increased incidence of disease are compared. The models considered vary from approximate methods to an exact method. The approximate methods include the Poisson process model and methods that are based on discretization of the study window. The exact method includes a marked point process model, i.e., the conditional logistic model. Apart from analyzing a real dataset (Lancashire larynx cancer data), a small simulation study is also carried out to examine the ability of these methods to recover known parameter values. The main results are as follows. In estimating the distance effect of larynx cancer incidences from the incinerator, the conditional logistic model and the binomial model for the discretized window perform relatively well. In explaining the spatial heterogeneity, the Poisson model (or the log Gaussian Cox process model) for the discretized window produces the best estimate.
MSC:
| 62-08 | Computational methods for problems pertaining to statistics |
| 62F15 | Bayesian inference |
| 62J12 | Generalized linear models (logistic models) |
| 60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |
| 62M30 | Inference from spatial processes |
References:
| [1] | Agarwal, D. K.; Gelfand, A. E.; Citron-Pousty, S., Zero-inflated models with application to spatial count data, Environmental and Ecological Statistics, 9, 341-355 (2002) |
| [2] | Baddeley, A.; Turner, R., Spatstat: An R package for analyzing spatial point patterns, Journal of Statistical Software, 12, 1-42 (2005) |
| [3] | Banerjee, S., Gelfand, A.E., Finley, A.O., Sang, H., 2008. Gaussian predictive process models for large spatial datasets. Journal of the Royal Statistical Society, Series B (in press); Banerjee, S., Gelfand, A.E., Finley, A.O., Sang, H., 2008. Gaussian predictive process models for large spatial datasets. Journal of the Royal Statistical Society, Series B (in press) · Zbl 1533.62065 |
| [4] | Berman, M.; Turner, R., Approximating point process likelihoods with GLIM, Applied Statistics, 41, 31-38 (1992) · Zbl 0825.62614 |
| [5] | Besag, J.; York, J.; Mollie, A., Bayesian image restoration with two applications in spatial statistics (with discussion), Annals of the Institute of Statistical Mathematics, 43, 1-59 (1991) · Zbl 0760.62029 |
| [6] | Congdon, P., Applied Bayesian Models (2003), John Wiley · Zbl 1023.62026 |
| [7] | Diggle, P., Overview of statistical methods for disease mapping and its relationship to cluster detection, (Elliott, P.; Wakefield, J.; Best, N.; Briggs, D. J., Spatial Epidemiology: Methods and Applications (2000), Oxford University Press) |
| [8] | Diggle, P. J., A point process modelling approach to raised incidence of a rare phenomenon in the vicinity of a prespecified point, Journal of the Royal Statistical Society, Series A, 153, 349-362 (1990) |
| [9] | Diggle, P. J.; Morris, S. N.; Elliott, P.; Shaddick, G., Regression modelling of disease risk in relation to point sources, Journal of the Royal Statistical Society, Series A, 160, 491-505 (1997) |
| [10] | Diggle, P. J.; Rowlingson, B., A conditional approach to point process modelling of elevated risk, Journal of the Royal Statistical Society, Series A, 157, 433-440 (1994) |
| [11] | Fuentes, M., Approximate likelihood for large irregularly spaced spatial data, Journal of the American Statistical Association, 102, 321-331 (2007) · Zbl 1284.62589 |
| [12] | Gómez-Rubio, V., Ferrándiz, J., López, A., 2004. In Functions for the detection of spatial clusters of diseases. http://matheron.uv.es/ virgil/Rpackages/DCluster; Gómez-Rubio, V., Ferrándiz, J., López, A., 2004. In Functions for the detection of spatial clusters of diseases. http://matheron.uv.es/ virgil/Rpackages/DCluster |
| [13] | Kammann, E. E.; Wand, M. P., Geoadditive models, Applied Statistics, 52, 1-18 (2003) · Zbl 1111.62346 |
| [14] | Lawson, A. B., GLIM and normalising constant models in spatial and directional data analysis, Computational Statistics & Data Analysis, 13, 331-348 (1992) · Zbl 0800.62008 |
| [15] | Lawson, A. B.; Browne, W. J.; Vidal-Rodiero, C. L., Disease Mapping with WinBUGS and MLwiN (2003), Wiley: Wiley New York |
| [16] | Ma, B.; Lawson, A. B.; Liu, Y., Evaluation of Bayesian models for focused clustering in health data, Environmetrics, 18, 1-16 (2007) |
| [17] | Moller, J.; Syversveen, A. N.; Waagepetersen, R. P., Log Gaussian Cox processes, Scandinavian Journal of Statistics, 25, 451-482 (1998) · Zbl 0931.60038 |
| [18] | Okabe, A.; Boots, B.; Sugihara, K.; Chiu, S. N., Spatial Tessellations: Concepts and Applications of Voronoi Diagrams (2000), Wiley · Zbl 0946.68144 |
| [19] | R Development Core Team, 2004. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria; R Development Core Team, 2004. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria |
| [20] | Rowlingson, B.; Diggle, P., Splancs: Spatial point pattern analysis code in S-Plus, Computers and Geosciences, 19, 627-655 (1993) |
| [21] | Rue, H., Martino, S., Chopin, N., 2007. Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (submitted for publication); Rue, H., Martino, S., Chopin, N., 2007. Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (submitted for publication) · Zbl 1248.62156 |
| [22] | Spiegelhalter, D.; Best, N.; Carlin, B.; Linde, A., Bayesian measures of model complexity and fit (with discussion), Journal of the Royal Statistical Society, Series B, 64, 583-639 (2002) · Zbl 1067.62010 |
| [23] | Spiegelhalter, D., Thomas, A., Best, N., Lunn, D., 2003. WinBUGS User Manual. MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK; Spiegelhalter, D., Thomas, A., Best, N., Lunn, D., 2003. WinBUGS User Manual. MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK |
| [24] | Waagepetersen, R., Convergence of posteriors for discretized log Gaussian Cox processes, Statistics & Probability Letters, 66, 229-235 (2003) · Zbl 1102.60045 |
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