[en] Grouped data occur frequently in practice, either because of limited resolution of
instruments, or because data have been summarized in relatively wide bins. A
combination of the composite link model with roughness penalties is proposed to
estimate smooth densities from such data in a Bayesian framework. A simulation
study is used to evaluate the performances of the strategy in the estimation of a
density, of its quantiles and rst moments. Two illustrations are presented: the rst
one involves grouped data of lead concentrations in the blood and the second one
the number of deaths due to tuberculosis in The Netherlands in wide age classes.
Disciplines :
Mathematics
Author, co-author :
Lambert, Philippe ; Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales
Eilers, Paul H.C.; Universiteit Utrecht > Faculty of Social and Behavioural Sciences
Language :
English
Title :
Bayesian density estimation from grouped continuous data
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Bibliography
Atchadé Y.F., and Rosenthal J.S. On adaptive Markov chain Monte Carlo algorithms. Bernoulli 11 (2005) 815-828
Berry S.M., Carroll R.J., and Ruppert D. Bayesian smoothing and regression splines for measurement error problems. Journal of the American Statistical Association 97 (2002) 160-169
Boneva L.I., Kendall D.G., and Stefano I. Spline transformations. three new diagnostic aids for the statistical data-analyst. Journal of the Royal Statistical Society, Series B 33 (1971) 1-71
Braun J., Duchesne T., and Stafford J.E. Local likelihood density estimation for interval censored data. The Canadian Journal of Statistics 33 (2005) 39-60
Brezger A., and Lang S. Generalized structured additive regression based on Bayesian P-splines. Computational Statistics and Data Analysis 50 (2006) 967-991
Eilers P.H.C. Ill-posed problems with counts, the composite link model, and penalized likelihood. Statistical Modelling 7 (2007) 239-254
Eilers P.H.C., and Marx B.D. Flexible smoothing with B-splines and penalties (with discussion). Statistical Science 11 (1996) 89-121
Gamerman D. Efficient sampling from the posterior distribution in generalized linear models. Statistics and Computing 7 (1997) 57-68
Haario H., Saksman E., and Tamminen J. An adaptive Metropolis algorithm. Bernoulli 7 (2001) 223-242
Hasselblad V., Stead A.G., and Galke W. Analysis of coarsely grouped data from the lognormal distribution. Journal of the American Statistical Association 75 (1980) 771-778
Jullion A., and Lambert P. Robust specification of the roughness penalty prior distribution in spatially adaptive bayesian P-splines models. Computational Statistics and Data Analysis 51 (2007) 2542-2558
Lambert P. Archimedean copula estimation using Bayesian splines smoothing techniques. Computational Statistics and Data Analysis 51 (2007) 6307-6320
Lambert P., and Eilers P.H. Bayesian proportional hazards model with time varying regression coefficients: A penalized Poisson regression approach. Statistics in Medicine 24 (2005) 3977-3989
Lang S., and Brezger A. Bayesian P-splines. Journal of Computational and Graphical Statistics 13 (2004) 183-212
Roberts G.O., and Rosenthal J.S. Optimal scaling of discrete approximations to Langevin diffusions. Journal of the Royal Statistical Society, Series B 60 (1998) 225-268
Roberts G.O., and Tweedie R.L. Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli 24 (1996) 341-363
Sheather S.J., and Jones M.C. A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society, Series B 53 (1991) 683-690
Thompson R., and Baker R.J. Composite link functions in generalized linear models. The American Statistician 30 (1981) 125-131
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