Markov Chain Approximations For Term Structure Models (original) (raw)

Summary. The major implementational problem for reversible jump MCMC is that there is commonly no natural way to choose jump proposals since there is no Euclidean structure in the parameter space to guide our choice. In this paper we consider mechanisms for guiding the proposal choice. The first group of methods is based upon an analysis of acceptance probabilities for jumps. Essentially, these methods involve a Taylor series expansion of the acceptance probability around certain canonical jumps, and turns out to have close ...

We compare alternative numerical methods for approximating solutions to continuous-state dynamic programming (DP) problems. We distinguish two approaches: discrete approximation and parametric approximation. In the former, the continuous state space is discretized into a finite number of points N , and the resulting finite-state DP problem is solved numerically. In the latter, a function associated with the DP problem such as the value function, the policy function, or some other related function is approximated by a smooth function of K unknown parameters. Values of the parameters are chosen so that the parametric function approximates the true function as closely as possible. We focus on approximations that are linear in parameters, i.e. where the parametric approximation is a linear combination of K basis functions. We also focus on methods that approximate the value function V as the solution to the Bellman equation associated with the DP problem. In finite state DP problems...

this paper we combine a purely stochastic approach method to represent rainfall variability in space with purely deterministic RCM predictions, linking the two sources of information within a Bayesian framework. Fuentes and Raftery (2001) consider a similar problem for SO 2 concentrations. Gelfand, Zhu and Carlin (2000) consider the problem of spatial data with dierent support. Figure 1 illustrates the type of data that we consider. The plots correspond to monthly rainfall over a region in Nebraska during May 1989. The left panel shows the output of the RCM, the right panel is obtained by using the interp function in Splus. Notice that the RCM produces a substantial overestimation of the rainfall in the eastern part of the region and some underestimation in the western part. A purely stochastic representation of the rainfall process is achieved by tting the truncated normal model to the observed point values by using a Bayesian approach in a similar fashion to Sanso and Guenni (1998...