Stochastic Reserving

Chapter 14's discussion of stochastic reserving methods doesn't seem quite right.

Consider chapter 9.1, page 24. The application of Bayesian/MCMC methods to, say, the ODP model or the Negative Binomial model is actually in respect of the parameters of the distribution in the model, rather than the claims directly.

For instance, in the ODP model, Bayesian/MCMC methods can give us a posterior distribution of the row/column/corner parameters, given a prior distribution and the likelihood of the data observations (calculated in a GLM framework). This distribution may then be plugged in to the ODP model in order to estimate the increments in each cell.

The important point here is that these methods give us a distribution of the parameters for the model - not a distribution for the claims themselves. The distribution of the claims comes from the combination of the distribution of the parameters with the model structure.

In other words, Bayesian/MCMC methods give us a way of determining the parameter uncertainty associated with a model. The process uncertainty comes in later when we actually "run" the model with the simulated parameter values.

Now, the notes say that "Under the Bayesian theory framework, the prior distribution of the predicted variable, e.g. claim numbers [or] amounts [...] is first chosen based on judgement or experience. Then the posterior distribution of the predicted variable is calculated using Bayes' formula." This is quite wrong: we are actually choosing a prior / determining a posterior for the parameters of our model (e.g. the row and column parameters) rather than for the claims. The notes make it seem that Bayesian methods are being used to determine process uncertainty directly, which isn't the case.

Essentially, Bayesian/MCMC methods are exactly analogour to bootstrap methods: both provide a way of getting the parameter uncertainty.