I have found some Stan code to model survival data with covariates with a Weibull regression distribution and Low Information priors (https://github.com/jburos/biostan/blob/master/inst/stan/weibull_survival_model.stan) (for an implementation: https://rstudio-pubs-static.s3.amazonaws.com/435225_07b4ab5afa824342a4680c9fb2de6098.html). The model can be formulated as such (see http://ceur-ws.org/Vol-1218/bmaw2014_paper_8.pdf):

\begin{equation} p\left(t_{i} | \boldsymbol{x}_{i}, v_{i}, \boldsymbol{\beta}, \alpha\right)=\alpha^{v_{i}} t_{i}^{v_{i}(\alpha-1)} \exp \left(v_{i} \boldsymbol{\beta}^{\mathrm{T}} \boldsymbol{x}_{i}-t_{i}^{\alpha} \exp \left(\boldsymbol{\beta}^{\mathrm{T}} \boldsymbol{x}_{\boldsymbol{i}}\right)\right) \end{equation}

intercept and shape:

\begin{equation} \begin{aligned} \beta_{0} & \sim \mathrm{N}\left(0,10^{2}\right) \\ \log \alpha & \sim \mathrm{N}\left(0,10^{2}\right) \end{aligned} \end{equation}

covariates:

\begin{equation} \begin{aligned} \beta_{j} & \sim \mathrm{N}\left(0, \sigma_{s}^{2} \sigma_{j}^{2}\right), \text { for } j=1, \ldots, m_{b g} \\ \sigma_{j}^{2} & \sim \operatorname{Inv}-\chi^{2}(1), \text { for } j=1, \ldots, m_{b g} \\ \sigma_{s} & \sim \operatorname{Half}-\mathrm{N}\left(0,10^{2}\right) \end{aligned} \end{equation}

The issue is that the fit is not close enough to the data. Instead I am attempting to fit a mixture of Weibull distributions with Dirichlet priors. I have found an R-Package “DPWeibull” (https://cran.r-project.org/web/packages/DPWeibull/DPWeibull.pdf) that does that and was wondering how much effort it would take to port the method to Stan and if someone would be interested to help. The model is described on page 7.

My background is that I have just started using Stan in September and have never fitted a mixture model in Stan.