By René de Borst, Nenad Bićanić, Herbert Mang, Günther Meschke
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Assessing the effect of an influenza vaccine in an encouragement design. Biostatistics 1, 69–88. , Lehmann, E. (1970). Basic Concepts of Probability and Statistics, second ed. Holden-Day, San Francisco. W. (1986). Statistics and causal inference. J. Amer. Statist. Assoc. 81, 945–970. W. (1989). It’s very clear. Comment on “Choosing among alternative nonexperimental methods for estimating the impact of social programs: The case of manpower training” by J. Heckman, V. Hotz. J. Amer. Statist. Assoc.
Multiple Imputation for Nonresponse in Surveys. Wiley, New York. B. (2000). The utility of counterfactuals for causal inference. P. Dawid, ‘Causal inference without counterfactuals’. J. Amer. Statist. Assoc. 95, 435–438. B. (1990). Comment: Neyman (1923) and causal inference in experiments and observational studies. Statist. Sci. 5, 472–480. B. (2004a). Multiple Imputation for Nonresponse in Surveys. Wiley, New York. B. (2004b). Direct and indirect causal effects via potential outcomes. Scand. J.
Indeed, for any sample size n and number of replicates k, I {pθ |Mnk } = nI {pθ |Mk }. Note, however, that Theorem 4 requires x to be a random sample from the assumed model. If the model entails dependence between the observations (as in time series, or in spatial models) the reference prior may well depend on the sample size; see, for example, Berger and Yang (1994), and Berger et al. (2001). The possible dependence of the reference prior on the sample size and, more generally, on the design of the experiment highlights the fact that a reference prior is not a description of (personal) prior beliefs, but a possible consensus prior for a particular problem of scientific inference.