Specification of the prior distribution for a Bayesian model is a central part of the Bayesian workflow for data analysis, but it is often difficult even for statistical experts. Prior elicitation transforms domain knowledge of various kinds into well-defined prior distributions, and offers a solution to the prior specification problem, in principle. In practice, however, we are still fairly far from having usable prior elicitation tools that could significantly influence the way we build probabilistic models in academia and industry. We lack elicitation methods that integrate well into the Bayesian workflow and perform elicitation efficiently in terms of costs of time and effort. We even lack a comprehensive theoretical framework for understanding different facets of the prior elicitation problem.Why are we not widely using prior elicitation? We analyze the state of the art by identifying a range of key aspects of prior knowledge elicitation, from properties of the modelling task and the nature of the priors to the form of interaction with the expert. The existing prior elicitation literature is reviewed and categorized in these terms. This allows recognizing under-studied directions in prior elicitation research, finally leading to a proposal of several new avenues to improve prior elicitation methodology.

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The Finnish national hospital discharge registers from 1985 and 1988 have been analysed by the National Board of Health. Results are provided for all the 21 Finnish hospital districts and central communal organizations. The small area variation phenomenon in hospital utilization cannot be explained by demographic or epidemiological factors. Rather, the variations seem to be largely due to organizational factors. The project aims to develop a data processing system capable of handling information on one million patients rapidly and economically, and show the results in an intelligible form as a table with standard headers or as a map illustration. Maps are superior to traditional statistical tables in demonstrating regional variations in health care utilization and in mortality. Maps based on small administrative units are useful for many purposes. These maps are, however, relatively 'noisy' due to substantial random variation. Coordinate-based mapping is a method to overcome some of these difficulties. It is based on linking hospital discharge and mortality data with exact address data. The method allows mapping independent of administrative boundaries. Several examples of coordinate-based maps are given. The method is used in Finland for annual analysis of hospital use.

Active learning is usually applied to acquire labels of informative data points in supervised learning, to maximize accuracy in a sample-efficient way. However, maximizing the accuracy is not the end goal when the results are used for decision-making, for example in personalized medicine or economics. We argue that when acquiring samples sequentially, separating learning and decision-making is sub-optimal, and we introduce a novel active learning strategy which takes the down-the-line decision problem into account. Specifically, we introduce a novel active learning criterion which maximizes the expected information gain on the posterior distribution of the optimal decision. We compare our decision-making-aware active learning strategy to existing alternatives on both simulated and real data, and show improved performance in decision-making accuracy.