In many practical situations, we need to combine the results of measuring a local value of a certain quantity with results of measuring average values of this same quantity. For example, in geosciences, we need to combine the seismic models (which describe density at different locations and depths) with gravity models which describe density averaged over certain regions. Similarly, in estimating the risk of an epidemic to an individual, we need to combine probabilities describe the risk to people of the corresponding age group, to people of the corresponding geographical region, etc. In this paper, we provide general techniques for solving such model fusion problems.
To properly perform data and model fusion, we need to know the accuracy of different data points. Sometimes, this accuracy is not given. For such situations, we describe how this accuracy can be estimated based on the available data.