*3.1. Simulation 1: Clustering Performance*

We simulated data from bivariate normal mixture distribution with different parameter settings, and applied both MCLUST-ME and MCLUST to partition the data into two clusters. The purpose of this simulation is twofold: first, to investigate the degree of improvement in clustering performance by incorporating known error distributions, and second, to study how error structure affects clustering result.

#### 3.1.1. Data Generation

The data were generated from a two-component bivariate normal mixture distribution, where each point is either error-free or associated with some known, constant error covariance. The data generation process is as follows.


$$z\_i \text{N}\_2(\mathfrak{mu}\_1, \mathfrak{L}\_1 + h\_i \mathbf{A}) + (1 - z\_i) \text{N}\_2(\mathfrak{mu}\_2, \mathbf{E}\_2 + h\_i \mathbf{A}) .$$

Values of the above parameters are as follows; *μ*<sup>1</sup> = (0, 0)*T*, *μ*<sup>2</sup> = (8, 0)*T*, Σ<sup>1</sup> = 64*I*2, Σ<sup>2</sup> = 16*I*2, *n* = 300, *τ*<sup>1</sup> = *τ*<sup>2</sup> = 0.5, and Λ = 36*I*2. As the values of *zi* provide us with the true memberships of each observation, we are able to use them to evaluate externally the performance of clustering methods in consideration.

3.1.2. Simulation Procedure

The simulation proceeds as follows.


The membership for each observation as well as MLEs upon convergence will be recorded.
