Fisher is the single most important figure in 20th century statistics. This talk examines his influence on modern statistical thinking, trying to predict how Fisherian we can expect the 21st century to be. Fisher's philosophy is characterized as a series of shrewd compromises between the Bayesian and frequentist viewpoints, augmented by some unique characteristics that are particularly useful in applied problems. Several current research topics are examined with an eye toward Fisherian influence, or the lack of it, and what this portends for future statistical developments. Based on the 1996 Fisher lecture, the article closely follows the text of that talk.

It has been suggested that Gauss used the method of least squares on a data set published in 1799. The data set and its adjustment are reexamined, and it is concluded that the result of Gauss cannot be obtained by the least-squares method nor by any other approach mentioned by Gauss.

It is argued that the determination of bioequivalence involves a decision, and is not purely a problem of inference. A coherent method of decision-making is examined in detail for a simple trial of bioequivalence. The result is shown to differ seriously from the inferential method, using significance tests, ordinarily used. The reason for the difference is explored. It is shown how the decision-analytic method can be used in more complicated and realistic trials and the case for its general use presented.

This article examines methods, issues and controversies that have arisen over the last decade in the effort to organize sequences of DNA base information into homogeneous segments. An array of different models and techniques have been considered and applied. We demonstrate that most approaches can be embedded into a suitable version of the multiple change-point problem, and we review the various methods in this light. We also propose and discuss a promising local segmentation method, namely, the application of split local polynomial fitting. The genome of bacteriophage $\lambda$ serves as an example sequence throughout the paper.

Computing (ratios of) normalizing constants of probability models is a fundamental computational problem for many statistical and scientific studies. Monte Carlo simulation is an effective technique, especially with complex and high-dimensional models. This paper aims to bring to the attention of general statistical audiences of some effective methods originating from theoretical physics and at the same time to explore these methods from a more statistical perspective, through establishing theoretical connections and illustrating their uses with statistical problems. We show that the acceptance ratio method and thermodynamic integration are natural generalizations of importance sampling, which is most familiar to statistical audiences. The former generalizes importance sampling through the use of a single "bridge" density and is thus a case of bridge sampling in the sense of Meng and Wong. Thermodynamic integration, which is also known in the numerical analysis literature as Ogata's method for high-dimensional integration, corresponds to the use of infinitely many and continuously connected bridges (and thus a "path"). Our path sampling formulation offers more flexibility and thus potential efficiency to thermodynamic integration, and the search of optimal paths turns out to have close connections with the Jeffreys prior density and the Rao and Hellinger distances between two densities. We provide an informative theoretical example as well as two empirical examples (involving 17- to 70-dimensional integrations) to illustrate the potential and implementation of path sampling. We also discuss some open problems.

We discuss selected applications of statistical theory and practice as motivated by and applied to environmental sciences. Included in the presentation are illustrations on how the interaction between environmental scientists and quantitative researchers has been used to enhance and further learning in both areas, and how this interaction provides a source of further challenges and growth for the statistical community.