Computational methods for probabilistic decision trees

Decision tree models may be more realistic if branching probabilities (and possibly utilities) are represented as distributions rather than point estimates. However, numerical analysis of such "probabilistic" trees is more difficult. This study employed the Mathematica computer algebra system to implement and verify previously described probabilistic methods. Both algebraic approximations and Monte Carlo simulation methods were used; in particular, simulations with beta, logistic-normal, and triangular distributions for branching probabilities were compared. Algebraic and simulation methods of sensitivity analysis were also implemented and compared. Computation required minimal programming and was reasonably fast using Mathematica on a standard personal computer. This study verified previously published results, including methods of sensitivity analysis. Changing the input distributional form had little effect. Computation is no longer a significant barrier to the use of probabilistic methods for analysis of decision trees.