This dissertation explores data fusion methodology to deduce an overall inference from the data gathered from multiple heterogeneous sources. Typically, if there existed a data source in which the data were reliable and unbiased, then data fusion would not be necessary. Data fusion methodology combines data form multiple diverse sources so that the desired information - such as the population mean - is improved despite redundancies, inaccuracies, biases, and inflated variability in the data. Examples of data fusion include estimating average demand from similar sources, and integrating fatality counts from different media sources after a catastrophe. The approach in this study combines "inputs" from distinct sources so that the information is "fused." Another way of describing this process is "data integration." Important assumptions are 1. Several sources provide "inputs" for information used to estimate parameters of a probability distribution. 2. Since distributions for the data from the sources are heterogeneous, some sources are less reliable. 3. Distortions, bias, censorship, and systematic errors may be more prominent in data from certain sources. 4. The sample size of sources data, number of "inputs," may be very small. Examples of information from multiple sources are abundant: traffic information from sensors at intersections, multiple …