A regression-scale model is of the form y = X\beta + \sigma\epsilon, where X is a fixed nxp design matrix, \beta\in\Real^p an unknown regression coefficient, \sigma>0 a scale parameter, and \epsilon represents an n-dimensional vector of errors whose density is known. Inference is usually made conditionally on the sample configuration a = (y - X\hat\beta)/\hat\sigma, where (\hat\beta, \hat\sigma) are the maximum likelihood estimates. Higher-order asymptotics provide very accurate approximations to exact conditional procedures thus avoiding multidimensional numerical integration. This paper presents how by means of the Metropolis-Hastings algorithm, a powerful Markov chain Monte Carlo technique which allows to simulate from distributions that are only known up to the normalizing constant, conditional properties of these methods can be assessed.
Conditional simulation for regression-scale models / Brazzale, Alessandra Rosalba. - In: JOURNAL OF THE ITALIAN STATISTICAL SOCIETY. - ISSN 1121-9130. - STAMPA. - 8:(1999), pp. 101-113.