I'm performing Bayesian model averaging (BMA) on 4 models describing the log-death rate. The four model are the Lee-Carter $$\log m_x(t) = \alpha_x + \beta_x\kappa_t+\epsilon_{x,t},$$

the Renshaw-Haberman $$\log m_x(t) = \alpha_x + \beta_x\kappa_t+\gamma_x\iota_{t-x}+\epsilon_{x,t},$$

Currie's APC $$\log m_x(t) = \alpha_x + \kappa_t+\iota_{t-x}+\epsilon_{x,t},$$ and the Plat $$\log m_x(t)= \alpha_x + \kappa^{[1]}_t+\kappa^{[2]}_t (\bar{x}-x)+\iota_{t-x}+\epsilon_{x,t}$$

where $\kappa_t$ is an univariate time series, $(\kappa^{[1]}_t,\kappa^{[2]}_t)$ is a bivariate time series, $\alpha_x, \beta_x$ and $\gamma_x$ are age factors and $\gamma_{t-x}$ is the cohort factor. To average these four models I'm using the product space method, which consists of using a categorical variable on index. It's well known that this kind of approach could create some problems, for example the chains of the categorical variable don't mix very well (or they just don't move from one model selected). So what I was trying to do was to use Carlin & Chib's approach of the pseudo-prior distributions of parameters when the model is not selected by the categorical variable but I suspect that I cannot use the same parameters for different models, since they give different estimates of them. Do you suggest to use different parameters for each model?


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