Abstract
Numerical approximations are often used to implement the Bayesian paradigm in analytically intractable parametric models. We focus on embedded integration rules which are an attractive numerical integration tool and present theoretical results which justify their use in a Bayesian integration strategy.
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Cools, R. (1992) A survey of methods for constructing cubature formulae. In T. O. Espelid and A. Genz (eds) Numerical Integration—Recent Developments, Software and Applications, NATO ASI Series C, 357, 1–24, Kluwer, Dordrecht.
Cools, R. and Haegemans, A. (1989) On the construction of multi-dimensional embedded cubature formulae. Numerische Mathematik, 55, 735–45.
Cools, R. and Rabinowitz, P. (1993) Monomial Cubature Rules Since ‘Stroud’: A Compilation. Journal of Computational and Applied Mathematics, 48, 309–26.
Dellaportas, P. (1990) Imbedded integration rules and their applications in Bayesian analysis. Unpublished PhD thesis, University of Plymouth, UK.
Dellaportas, P. and Wright, D. E. (1991) Positive embedded integration in Bayesian analysis. Statistics and Computing, 1, 1–12.
Dellaportas, P. and Wright, D. E. (1992) A numerical integration strategy in Bayesian analysis. In J. M. Bernado, A. Berger, P. Dawid and A. F. M. Smith (eds) Bayesian Statistics 4, pp. 601–606, Oxford University Press.
Engels, H. (1980) Numerical quadrature and cubature. Academic Press, New York.
Gelfand, A. E. and Smith, A. F. M. (1990) Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.
Naylor, J. A. and Smith, A. F. M. (1982) Applications of a method for the efficient computation of posterior distributions. Applied Statistics, 31, 3, 214–25.
Rabinowitz, P., Kautsky, J., Elhay, S. and Butcher, J. C. (1987) On sequences of imbedded integration rules. In P. Keast and G. Fairweather (eds) Numerical Integration—Recent Developments, Software and Applications, NATO ASI Series C, 230, 113–39, Reidel, Dordrecht.
Shaw, J. E. H. (1987) Aspects of numerical integration and summarisation. In J. M. Bernado, M. H. DeGroot, D. V. Lindley and A. F. M. Smith (eds) Bayesian Statistics 3, pp. 411–28, Oxford University Press.
Stroud, A. (1971) Approximate Calculation of Multiple Integrals. Prentice-Hall, Englewood Cliffs, N.J.
Tierney, L. and Kadane, J. (1986) Accurate approximations for posterior moments and marginals, Journal of the American Statistical Association, 81, 82–6.
Turnbull, B. W., Brown, B. W. Jr and Hu, M. (1974) Survivorship analysis of heart transplant data. Journal of the American Statistical Association, 69, 74–80.
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Cools, R., Dellaportas, P. The role of embedded integration rules in Bayesian statistics. Stat Comput 6, 245–250 (1996). https://doi.org/10.1007/BF00140868
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DOI: https://doi.org/10.1007/BF00140868