Statistical inference for Markov chains with applications to credit risk

The R Package stagedtrees for Structural Learning of Stratified Staged Trees

“…By default, it computes the confidence intervals for the probability parameters for all stages in the staged tree given in input; confidence intervals can be computed only for a single variable by specifying it in parm. Five methods are available: wald, waldcc, wilson, goodman and quesenberry-hurst (see e.g., Möstel, Pfeuffer, and Fischer 2020).…”

“…2.5 % 97.5 % Age=Child|1 0.0258101180 0.075897181 Age=Adult|1 0.9241028192 0.974189882 Age=Child|2 0.0001411609 0.006645046 Age=Adult|2 0.9933549540 0.999858839 Age=Child|3 0.0907102352 0.140646387 Age=Adult|3 0.8593536135 0.909289765 There are two difficulties in estimating confidence intervals on staged trees: first, the presence of very small sample sizes for some vertices of the tree; second, the presence of highly unbalanced, almost degenerate, distributions, which may be caused by small sample sizes especially for vertices close to the leaves of the tree. Confidence intervals that have been estimated in one of these two scenarios may be therefore biased (for details, see Glaz and Sison 1999;Möstel et al 2020).…”