Bayesian Model Choice of Grouped t-copula

One of the most popular copulas for modeling dependence structures is t-copula. Recently the grouped t-copula was generalized to allow each group to have one member only, so that a priori grouping is not required and the dependence modeling is more flexible. This paper describes a Markov chain Monte Carlo (MCMC) method under the Bayesian inference framework for estimating and choosing t-copula models. Using historical data of foreign exchange (FX) rates as a case study, we found that Bayesian model choice criteria overwhelmingly favor the generalized t-copula. In addition, all the criteria also agree on the second most likely model and these inferences are all consistent with classical likelihood ratio tests. Finally, we demonstrate the impact of model choice on the conditional Value-at-Risk for portfolios of six major FX rates

Bayesian Analysis of Nested Logit Model by Markov Chain Monte Carlo

We develop a Markov Chain Monte Carlo (MCMC) algorithm for estimating nested logit models in a Bayesian framework. Appropriate "heating target" and reparameterization techniques are adopted for fast mixing. For illustrative purposes, we have implemented the algorithm on two real-life examples involving 3-level structures. The first example involves Social Security's disability determination process, Lahiri et al. (1995). The second one is taken from Amemiya and Shimono's (1989) model of labor supply behavior of the aged. We applied a combination of various convergence criteria to ensure that the chain has converged to its target distribution.Discrete Choice, Random Utility Maximization, MCMC, Mixing Speed.

Calculating the Expected Value of Sample Information using Efficient Nested Monte Carlo: A Tutorial

Objective: The Expected Value of Sample Information (EVSI) quantifies the economic benefit of reducing uncertainty in a health economic model by collecting additional information. This has the potential to improve the allocation of research budgets. Despite this, practical EVSI evaluations are limited, partly due to the computational cost of estimating this value using the "gold-standard" nested simulation methods. Recently, however, Heath et al developed an estimation procedure that reduces the number of simulations required for this "gold-standard" calculation. Up to this point, this new method has been presented in purely technical terms. Study Design: This study presents the practical application of this new method to aid its implementation. We use a worked example to illustrate the key steps of the EVSI estimation procedure before discussing its optimal implementation using a practical health economic model. Methods: The worked example is based on a three parameter linear health economic model. The more realistic model evaluates the cost-effectiveness of a new chemotherapy treatment which aims to reduce the number of side effects experienced by patients. We use a Markov Model structure to evaluate the health economic profile of experiencing side effects. Results: This EVSI estimation method offers accurate estimation within a feasible computation time, seconds compared to days, even for more complex model structures. The EVSI estimation is more accurate if a greater number of nested samples are used, even for a fixed computational cost. Conclusions: This new method reduces the computational cost of estimating the EVSI by nested simulation