Inference for stochastic processes. This research involved the extension of classical asymptotic theory for independent observations to dependent data arising from stochastic processes. The approach to demonstrating asymptotic normality of maximum likelihood estimators that appeared in Ann. Statist. (1980) is of wide applicability. Subsequent work involved asymptotic conditional inference and asymptotic ancillarity in nonergodic models. The case of a branching process was analysed in Ann. Statist. (1986) and a general approach appeared in Ann. Statist. (1992). Asymptotic theory of Bayesian inference for stochastic processes. New results appear in J. R. Statist. Soc. B (1987) and Bayesian Statistics 4 (1992). In particular, this work tackled problems arise when information on different parameters grow at different rates. Other related work. (i) Asymptotic behaviour of spacings, with application to multiple outlier detection (Ann. Statist., 1986); (ii) asymptotic problems associated with the prequential approach (Scand. J. Statist., 1992); (iii) asymptotic theory based on a suitable function of time and the unknown parameters (Biometrika, 1992). Higher-order asymptotic theory. Research has focused on connections between Bayesian and (conditional) frequentist inferences. See my discussions of A. P. Dawid (J. R. Statist. Soc. B, 1991) and D. A. Pierce and D. Peters (J. R. Statist. Soc. B, 1992) and the papers Biometrika (1995 x2), J. R. Statist. Soc. B (1999) and Ann. Statist. (2000) (for predictive inference) and Biometrika (2005).