Reference Analysis of the Dynamic Linear Model

Abstract

Ahstract. We consider the analysis of normal dynamic linear models subject to reference (vague or Uninformative) initial priors on the state parameters and observational variance. New sequential updating equations and the related smoothing or filtering recurrences are derived for such reference analyses. The case of no evolution noise is highlighted, as this is of key practical importance and interest. Practical questions concerning prediction and collinearity are discussed, as are particular features of special models.

An introduction to Bayesian reference analysis: inference on the ratio of multinomial parameters

“…Papers which contain explicit analysis of specific reference distributions include Bernardo (1977Bernardo ( , 1978Bernardo ( , 1979Bernardo ( , 1980Bernardo ( , 1982Bernardo ( , 1985, Bayarri (1981Bayarri ( , 1985, Ferrándiz (1982Ferrándiz ( , 1985, Sendra (1982), Eaves (1983aEaves ( , 1983bEaves ( , 1985, Bernardo and Bayarri (1985), Chang and Villegas (1986), Hills (1987), Mendoza (1987Mendoza ( , 1988, Bernardo and Girón (1988), Lindley (1988), , 1992a, 1992b, 1992c, Pole and West (1989), Chang and Eaves (1990), Polson and Wasserman (1990), Ye and Berger (1991), Stephens and Smith (1992), Liseo (1993), Ye…”

“…Papers which contain explicit analyses of reference distributions include Bernardo (1977Bernardo ( , 1978Bernardo ( , 1979Bernardo ( , 1980Bernardo ( , 1982Bernardo ( , 1985, Bayarri (1981, Ferra Ândiz (1982,1985), Sendra (1982), Eaves (1983aEaves ( , b, 1985, Bernardo and Bayarri (1985), Chang and Villegas (1986), Hills (1987), Mendoza (1987Mendoza ( , 1988, Bernardo and Giro Ân (1988), Lindley (1988), Bernardo (1989, 1992a, b, c), Pole and West (1989), Chang and Eaves (1990), Clarke and Barron (1990), Polson and Wasserman (1990), Severini (1991), Ye and Berger (1991), Ghosh and Mukerjee (1992), Stephens and Smith (1992), Liseo (1993), Ye (1993Ye ( , 1994Ye ( , 1995, Berger and Yang (1994), Kubokawa and Robert (1994), Yang andBerger (1994, 1996), du Plessis et al (1995), Datta and Ghosh (1995d), Ghosh et al (1995), Sun and Ye (1995), Yang and Chen (1995), Ghosal (1996), Ghosh and Yang (1996), Reid (1996), Sun and Ye (1996),…”