bayesHistogram: Smoothing of a uni- or bivariate histogram using Bayesian G-splines

Description

A function to estimate a density of a uni- or bivariate (possibly censored) sample. The density is specified as a mixture of Bayesian G-splines (normal densities with equidistant means and equal variances). This function performs an MCMC sampling from the posterior distribution of unknown quantities in the density specification. Other method functions are available to visualize resulting density estimate.

This function served as a basis for further developed bayesBisurvreg, bayessurvreg2 and bayessurvreg3 functions. However, in contrast to these functions, bayesHistogram does not allow for doubly censoring. Bivariate case:

Let $Y_{i,l},\; i=1,\dots,N,\; l=1,2$ be observations for the $i$th cluster and the first and the second unit (dimension). The bivariate observations $Y_i=(Y_{i,1},\,Y_{i,2})',\;i=1,\dots,N$ are assumed to be i.i.d. with a~bivariate density $g_{y}(y_1,\,y_2)$. This density is expressed as a~mixture of Bayesian G-splines (normal densities with equidistant means and constant variance matrices). We distinguish two, theoretically equivalent, specifications.

[object Object],[object Object] Univariate case:

It is a~direct simplification of the bivariate case.

Usage

bayesHistogram(y1, y2,
   nsimul = list(niter = 10, nthin = 1, nburn = 0, nwrite = 10),
   prior, init = list(iter = 0),
   mcmc.par = list(type.update.a = "slice", k.overrelax.a = 1,
                   k.overrelax.sigma = 1, k.overrelax.scale = 1),
   store = list(a = FALSE, y = FALSE, r = FALSE),
   dir = getwd())

Arguments

response for the first dimension in the form of a survival object created using Surv.

response for the second dimension in the form of a survival object created using Surv. If the response is one-dimensional this item is missing.

nsimul

a list giving the number of iterations of the MCMC and other parameters of the simulation. [object Object],[object Object],[object Object],[object Object]

prior

a list that identifies prior hyperparameters and prior choices. See the paper Komárek and Lesaffre (2008) and the PhD. thesis Komárek (2006) for more details. Some prior parameters can be guessed by the function itself. If you want to

init

a list of the initial values to start the McMC. Set to NULL such parameters that you want the program should itself sample for you or parameters that are not needed in your model. [object Object],[object Object],[object Object],[o

mcmc.par

a list specifying further details of the McMC simulation. There are default values implemented for all components of this list. [object Object],[object Object],[object Object],[object Object]

store

a~list of logical values specifying which chains that are not stored by default are to be stored. The list can have the following components. [object Object],[object Object],[object Object]

dir

a string that specifies a directory where all sampled values are to be stored.

Value

A list of class bayesHistogram containing an information concerning the initial values and prior choices.

References

Gilks, W. R. and Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling. Applied Statistics, 41, 337 - 348.

Komárek, A. (2006). Accelerated Failure Time Models for Multivariate Interval-Censored Data with Flexible Distributional Assumptions. PhD. Thesis, Katholieke Universiteit Leuven, Faculteit Wetenschappen.

Komárek, A. and Lesaffre, E. (2008). Bayesian accelerated failure time model with multivariate doubly-interval-censored data and flexible distributional assumptions. Journal of the American Statistical Association, 103, 523--533.

Komárek, A. and Lesaffre, E. (2006b). Bayesian semi-parametric accelerated failurew time model for paired doubly interval-censored data. Statistical Modelling, 6, 3--22. Neal, R. M. (2003). Slice sampling (with Discussion). The Annals of Statistics, 31, 705 - 767.