Abstract
This is an invited discussion of review paper “Nonparametric Bayesian Inference in Applications” by Peter Müller, Fernando A. Quintana and Garritt L. Page.
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References
Banerjee S, Carlin BP, Gelfand AE (2015) Hierarchical modeling and analysis for spatial data, 2nd edn. Chapman & Hall/CRC, London
Best NG, Ickstadt K, Wolpert RL (2000) Spatial Poisson regression for health and exposure data measured at disparate resolutions. J Am Stat Assoc 95:1076–1088
Brix A, Diggle PJ (2001) Spatiotemporal prediction for log-Gaussian Cox processes. J R Stat Soc B 63:823–841
Brix A, Møller J (2001) Space-time multi type log Gaussian Cox processes with a view to modeling weeds. Scand J Stat 28:471–488
Brown PE, Roberts GO, Kåresen KF, Tonellato S (2000) Blur-generated non-separable space-time models. J R Stat Soc B 62:847–860
Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, New York
Gelfand AE, Kottas A, MacEachern S (2005) Bayesian nonparametric spatial modeling with Dirichlet process mixing. J Am Stat Assoc 100:1021–1035
Heikkinen J, Arjas E (1998) Non-parametric Bayesian estimation of a spatial poisson intensity. Scand J Stat 25:435–450
Heikkinen J, Arjas E (1999) Modeling a poisson forest in variable elevations: a nonparametric Bayesian approach. Biometrics 55:738–745
Higdon D (1998) A process-convolution approach to modelling temperatures in the North Atlantic Ocean. Environ Ecol Stat 5:173–190
Ickstadt K, Wolpert RL (1999) Spatial regression for marked point processes. In: Bernardo JM, Berger JO, Dawid P, Smith AFM (eds) Bayesian statistics, vol 6. Oxford University Press, Oxford, pp 323–341
Ishwaran H, James LF (2004) Computational methods for multiplicative intensity models using weighted gamma processes: proportional hazards, marked point processes, and panel count data. J Am Stat Assoc 99:175–190
Ji C, Merl D, Kepler TB, West M (2009) Spatial mixture modelling for unobserved point processes: examples in immunofluorescence histology. Bayesian Anal 4:297–315
Kang J, Nichols TE, Wager TD, Johnson TD (2014) A Bayesian hierarchical spatial point process model for multi-type neuroimaging meta-analysis. Ann Appl Stat 8:1800–1824
Kottas A (2016) Bayesian nonparametric modeling for disease incidence data. In: Lawson AB, Banerjee S, Haining RP, Ugarte MD (eds) Handbook of spatial epidemiology. Chapman and Hall/CRC, London, pp 363–374
Kottas A, Behseta S (2010) Bayesian nonparametric modeling for comparison of single-neuron firing intensities. Biometrics 66:277–286
Kottas A, Sansó B (2007) Bayesian mixture modeling for spatial Poisson process intensities, with applications to extreme value analysis. J Stat Plan Inference 137:3151–3163
Kottas A, Duan J, Gelfand AE (2008) Modeling disease incidence data with spatial and spatio-temporal dirichlet process mixtures. Biomet J 50:29–42
Liang S, Carlin BP, Gelfand AE (2009) Analysis of Minnesota colon and rectum cancer point patterns with spatial and nonspatial covariate information. Ann Appl Stat 3:943–962
MacEachern S (2000) Dependent dirichlet processes. Technical report. Department of Statistics, Ohio State University
Mena RH, Ruggiero M, Walker SG (2011) Geometric stick-breaking processes for continuous-time Bayesian nonparametric modeling. J Stat Plan Inference 141:3217–3230
Møller J, Waagepetersen RP (2004) Statistical inference and simulation for spatial point processes. Chapman & Hall/CRC, London
Møller J, Syversveen AR, Waagepetersen RP (1998) Log Gaussian Cox processes. Scand J Stat 25:451–482
Petrone S (1999) Bayesian density estimation using Bernstein polynomials. Can J Stat 27:105–126
Richardson R, Kottas A, Sansó B (2016) Bayesian non-parametric modeling for integro-difference equations. Stat Comput. doi:10.1007/s11222-016-9719-1
Richardson R, Kottas A, Sansó B (2017a) Flexible integro-difference equation modeling for spatio-temporal data. Comput Stat Data Anal 109:182–198
Richardson R, Kottas A, Sansó B (2017b) Spatio-temporal modelling using integro-difference equations with bivariate stable kernels. Technical report, Baskin School of Engineering, University of California, Santa Cruz
Storvik G, Frigessi A, Hirst D (2002) Stationary space-time gaussian fields and their time autoregressive representation. Stat Model 2:139–161
Taddy M (2010) Autoregressive mixture models for dynamic spatial Poisson processes: application to tracking the intensity of violent crime. J Am Stat Assoc 105:1403–1417
Taddy MA, Kottas A (2012) Mixture modeling for marked Poisson processes. Bayesian Anal 7:335–362
Wikle CK (2002) A kernel-based spectral model for non-Gaussian spatio-temporal processes. Stat Model 2:299–314
Wolpert RL, Ickstadt K (1998) Poisson/gamma random field models for spatial statistics. Biometrika 85:251–267
Xiao S, Kottas A, Sansó B (2015) Modeling for seasonal marked point processes: an analysis of evolving hurricane occurrences. Ann Appl Stat 9:353–382
Xu K, Wikle CK, Fox NI (2005) A kernel-based spatio-temporal dynamical model for nowcasting weather radar reflectivities. J Am Stat Assoc 100:1133–1144
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The author wishes to thank Igor Prünster and the editors Tommaso Proietti and Ruggero Bellio for the invitation to write this discussion. This work was supported in part by the National Science Foundation under award SES-1631963.
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Kottas, A. Discussion of paper “nonparametric Bayesian inference in applications” by Peter Müller, Fernando A. Quintana and Garritt L. Page. Stat Methods Appl 27, 219–225 (2018). https://doi.org/10.1007/s10260-017-0398-7
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DOI: https://doi.org/10.1007/s10260-017-0398-7