Deterministic simulation models are used in many areas of science, engineering and policy-making. Typically, they are complex models that attempt to capture underlying mechanisms in considerable detail, and they have many user-specified inputs. The inputs are often specified by some form of trial-and-error approach in which plausible values are postulated, the corresponding outputs inspected, and the inputs modified until plausible outputs are obtained. Here we address the issue of more formal inference for such models. Raftery et al. (1995a) proposed the Bayesian synthesis approach in which the available information about both inputs and outputs was encoded in a probability distribution and inference was made by restricting this distribution to the submanifold specifid by the model. Wolpert (1995) showed that this is subject to the Borel paradox, according to which the results can depend on the parameterization of the model. We show that this dependence is due to the presence of a prior on the outputs. We propose a modified approach, called Bayesian melding, which takes full account of information and uncertainty about both inputs and outputs to the model, while avoiding the Borel paradox. This is done by recognizing the existence of two priors, one implicit and one explicit, on each input and output � these are combined via logarithmic pooling. Bayesian melding is then

In this paper, we examine the relative forecast accuracy of information markets versus expert aggregation. We leverage a unique data source of almost 2000 people’s subjective probability judgments on 2003 US National Football League games and compare with the “market probabilities ” given by two different information markets on exactly the same events. We combine assessments of multiple experts via linear and logarithmic aggregation functions to form pooled predictions. Prices in information markets are used to derive market predictions. Our results show that, at the same time point ahead of the game, information markets provide as accurate predictions as pooled expert assessments. In screening pooled expert predictions, we find that arithmetic average is a robust and efficient pooling function; weighting expert assessments according to their past performance does not improve accuracy of pooled predictions; and logarithmic aggregation functions offer bolder predictions than linear aggregation functions. The results provide insights into the predictive performance of information markets, and the relative merits of selecting among various opinion pooling methods.

Sigatures are on file in the Graduate School. iii In almost all walks of life, predicting uncertain future events plays an essential role in decision-making processes. However, information related to future events frequently exists only as dispersed opinions, insights, and intuitions of individuals. Each individual only knows a little, but aggregating the dispersed information together may make considerable contribution to decision making. This is typical in many domains including business, politics, and entertainment. Therefore, how to aggregate such dispersed information for useful decision support is a crucial task. Markets have shown great potential as one of the most effective mechanisms for gathering distributed information and generating accurate forecasts, often surpassing many existing methods in practice. This research studies information markets, markets that are specially designed for information aggregation and forecasting, from four different perspectives: theoretical examination, experimental evaluation, empirical analysis, and design.

We propose a technique for fusing the output of multiple Magnetic Resonance (MR) sequences to robustly and accurately segment brain lesions. It is based on an augmented multi-sequence hidden Markov model that includes additional weight variables to account for the relative importance and control the impact of each sequence. The augmented framework has the advantage of allowing 1) the incorporation of expert knowledge on the a priori relevant information content of each sequence and 2) a weighting scheme which is modified adaptively according to the data and the segmentation task under consideration. The model, applied to the detection of multiple sclerosis and stroke lesions shows promising results. 1