A higher-order approximation to the marginal posterior distribution for a scalar parameter of
interest in the presence of nuisance parameters is proposed. The approximation is obtained
using a matching prior. The procedure improves the normal first-order approximation and
has several advantages. It does not require the elicitation on the nuisance parameters,
neither numerical integration nor Monte Carlo simulation, and it enables us to perform
accurate Bayesian inference even for small sample sizes. Numerical illustrations are given …

We discuss higher-order approximations to the marginal posterior distribution for a scalar
parameter of interest in the presence of nuisance parameters. These higher-order
approximations are obtained using a suitable matching prior. The proposed procedure has
several advantages since it does not require the elicitation on the nuisance parameter,
neither numerical integration or MCMC simulation, and it enables us to perform accurate
Bayesian inference even for very small sample sizes. Numerical illustrations are given for …