6 1 MARCO TEÓRICO
6.1.8 Infiltración en los suelos.
As discussed in each component of this thesis, extensions and development of the proposed and adapted methods can be followed. Indeed, the development of Bayesian modelling approaches for prediction of patient survival presents many possibilities for future work. As discussed in Chapter 4, it may be worthwhile to pursue the Reversible Jump Markov Chain Monte Carlo (RJMCMC), proposed by Green (1995) and described in a general context by Lunn et al. (2009) as an alter- native approach to post-analysis model comparison and BMA. It may be possible to apply this model comparison by transforming the Weibull model to the extreme value model.
The other research area that is not featured in this thesis but presents opportuni- ties for future work is the use of random censoring (Liu, 2012, Miller, 1998) in the simulation study to generate the data in Chapter 5. This censoring mechanism is also commonly encountered in practice and could have been explored to investigate the impact of different censoring mechanisms on mixture model estimation.
The research in Chapter 6 indicated that BMA approach enables us to provide more precise predictions of patient survival. However, this study only involved three candidate models. More models can be obviously included in the analysis. This
7.2. FUTURE WORK 139
study has also focused on the marginal likelihood p(D | Qs) estimation methods
based on the Laplace approximation. However, other approaches are also possible. Indeed marginal likelihood estimation is possible using nested sampling (Skilling, 2006), where the marginal likelihood is viewed as the expectation, with respect to the prior, of the likelihood. The other approach is Chib’s method (Chib and Greenberg, 1995), that presented a generic method which can be applied to output from the Gibbs sampler. Applying BMA to other datasets, other applications where robust prediction is desired.
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