3.2.1. Data Generation

The data were generated from a two-component bivariate normal mixture distribution with errors whose magnitudes are uniformly distributed. The data generation process is as follows.


$$z\_i \aleph\_2(\mathfrak{p}\_1, \mathfrak{L}\_1 + S\_i I\_2) + (1 - z\_i) \aleph\_2(\mathfrak{p}\_2, \mathfrak{L}\_2 + S\_i I\_2)\_{\prime\prime}$$

where *I*<sup>2</sup> denotes the 2-dimensional identity matrix.

The parameter values are set as follows; *<sup>μ</sup>*<sup>1</sup> = (−10, 0)*T*, *<sup>μ</sup>*<sup>2</sup> = (10, 0)*T*, <sup>Σ</sup><sup>1</sup> = <sup>Σ</sup><sup>2</sup> = <sup>100</sup>*I*2, *<sup>n</sup>* = 200, *τ*<sup>1</sup> = *τ*<sup>2</sup> = 0.5, and *S* = 100. We chose these parameter values so that there will be quite many points near the classification boundary: these points tend to have high classification uncertainties. We want to see, under MCLUST-ME and under MCLUST, how the error magnitudes, *Si*, will affect the estimated classification uncertainties (defined in (14)) of the points.
