Page 394 - Special Topic Session (STS) - Volume 3

STS551 Stephen Wu et al.
Let us consider a set of data that contains n data subsets, = { | = 1, … , }.

When we want to infer using , the two types of hierarhical Bayesian
models, named M1 and M2 model, are basically assuming if can take only a
single value for all data subsets or not, respectively (Fig. 1). Table 1
demonstrate the theory of Bayesian inference for those two cases.

Figure 1: Bayesian network for (a) model of single-data structure (M1), and
(b) model of hierarchical data structure (M2).

In most cases, completely analytical solutions are not available for the posterior PDF
of the hyperparameters. An estimation method based on importance sampling (IS)
can be used. Luckily, in our simple linear problem,

Table 1: Comparison between single and hierarchical data structure

analytical solutions can be achieved Wu et al. [2018].

Let us consider three different data sets for this case study, with random input
ranging from 0 to 10, = 1, = = 0.2 and 20 data set with 50 data

point in each set (a total of 1000 data points), i.e., = 20 and = 50 for all

.

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