Supplementary Material for "Sonification of Markov-chain Monte Carlo Simulations"

##### **Example E0:** Using audification of particle trajectories (section 3.3 in the paper).

Listen to a single particle converging to a mode in a three-modal density function p. This example corresponds to figure 2 in the paper. Files:[WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930311/E0a.wav).

Listen to a similar particle with an increased friction coefficient of 0.9996. On each step, the kinetic energy is reduced to E(t+1) = 0.9996 E(t), resulting in an exponential decay of energy. Sounds: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930312/E0b.wav)

##### **Example E1:** Audification of particle trajectories started at McMC steps (section 5.1 in the paper).

The Audification of 100 McMC steps in a distribution p with 3 modes

- Soundfile: [WAVE-File](https://pub.uni-bielefeld.de/download/2930310/2930313/E1.wav)

##### **Example E2:** Using McMC process stream, AIB stream and McMC details stream as introduced in the paper
This examples are discussed in the paper in section 5.2.
<br>

**(a)** dataset: 3 clusters in 6 dimensional space. T = 0.01

- McMC stream: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930322/E2a_stream1.wav)
- McMC details stream: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930323/E2a_stream2.wav)
- AIB stream: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930324/E2a_stream3.wav)
- All streams together: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930321/E2a_mix.wav)

**(b)** dataset: 3 clusters in 6 dimensional space. T = 0.002

- McMC stream: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930326/E2b_stream1.wav)
- McMC details stream: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930327/E2b_stream2.wav)
- AIB stream: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930328/E2b_stream3.wav)
- All streams together: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930325/E2b_mix.wav)

**(c)** dataset: 6 clusters in 6 dimensional space, T = 0.008

- McMC stream: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930330/E2c_stream1.wav)
- McMC details stream: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930331/E2c_stream2.wav)
- AIB stream: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930332/E2c_stream3.wav)
- All streams together: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930329/E2c_mix.wav)

**(d)** dataset: 3 clusters in 6 dim. space, T = 0.002, p computed by kernel density estimation but now with a kernel of bandwidth sigma such that p is unimodal.

- All streams together: [WAVE-file](https://pub.uni-bielefeld.de/download/2930310/2930333/E2d_mix.wav)

##### **Example E3:** Sonification of McMC simulations for handwritten digits (section 5.3 in the paper)

##### **Example E4:** Sonification of McMC simulations for Bayesian Models (section 5.4 in the paper)

##### **Example E5:** Sonification of McMC simulation on iris dataset
This examples are discussed in the paper in section 5.5. The following examples are sonification with
<table BORDER WIDTH="70%" align="center" >
<tbody><tr>
<td>bandwidth scaling exponent</td>
<td>soundfile</td>
</tr>
<tr>
<td>0.5</td>
<td><a href="https://pub.uni-bielefeld.de/download/2930310/2930336/mcmc_iris1_bw0.5.wav">WAVE-file</a></td>
</tr>
<tr>
<td>0.25</td>
<td><a href="https://pub.uni-bielefeld.de/download/2930310/2930337/mcmc_iris1_bw0.25.wav">WAVE-file</a> </td>
</tr>
<tr>
<td>0</td>
<td><a href="https://pub.uni-bielefeld.de/download/2930310/2930338/mcmc_iris1_bw0.wav">WAVE-file</a></td>
</tr>
<tr>
<td>-0.25</td>
<td><a href="https://pub.uni-bielefeld.de/download/2930310/2930340/mcmc_iris1_bw-0.25.wav">WAVE-file</a></td>
</tr>
<tr>
<td>-0.5</td>
<td><a href="https://pub.uni-bielefeld.de/download/2930310/2930339/mcmc_iris1_bw-0.5.wav">WAVE-file</a></td>
</tr>
<tr>
<td>-0.75</td>
<td><a href="https://pub.uni-bielefeld.de/download/2930310/2930341/mcmc_iris1_bw-0.75.wav">WAVE-file</a></td>
</tr>
<tr>
<td>-1</td>
<td><a href="https://pub.uni-bielefeld.de/download/2930310/2930343/mcmc_iris1_bw-1.wav">WAVE-file</a></td>
</tr>
</tbody></table>

### **例 E0：** 利用粒子轨迹的声学转换（论文第3.3节）。
聆听单个粒子在三维密度函数p中收敛至某一模态的过程。本例对应论文中的图2。文件：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930311/E0a.wav)。

聆听具有增加摩擦系数0.9996的类似粒子。每一步中，动能减少至E(t+1) = 0.9996 E(t)，导致能量呈指数衰减。声音：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930312/E0b.wav)。

### **例 E1：** 从McMC步骤开始进行粒子轨迹的声学转换（论文第5.1节）。

在具有3个模态的分布p中，对100个McMC步骤进行声学转换。

- 声音文件：[WAVE-文件](https://pub.uni-bielefeld.de/download/2930310/2930313/E1.wav)

### **例 E2：** 使用论文中介绍的McMC过程流、AIB流和McMC细节流

这些示例在论文的第5.2节中进行讨论。
<br>

**(a)** 数据集：6维空间中的3个簇。T = 0.01

- McMC流：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930322/E2a_stream1.wav)
- McMC细节流：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930323/E2a_stream2.wav)
- AIB流：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930324/E2a_stream3.wav)
- 所有流合并：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930321/E2a_mix.wav)

**(b)** 数据集：6维空间中的3个簇。T = 0.002

- McMC流：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930326/E2b_stream1.wav)
- McMC细节流：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930327/E2b_stream2.wav)
- AIB流：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930328/E2b_stream3.wav)
- 所有流合并：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930325/E2b_mix.wav)

**(c)** 数据集：6维空间中的6个簇，T = 0.008

- McMC流：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930330/E2c_stream1.wav)
- McMC细节流：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930331/E2c_stream2.wav)
- AIB流：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930332/E2c_stream3.wav)
- 所有流合并：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930329/E2c_mix.wav)

**(d)** 数据集：6维空间中的3个簇，T = 0.002，p通过核密度估计计算，但现在的核带宽为sigma，使得p成为单模态。

- 所有流合并：[WAVE文件](https://pub.uni-bielefeld.de/download/2930310/2930333/E2d_mix.wav)

### **例 E3：** 对手写数字的McMC模拟进行声学转换（论文第5.3节）。

### **例 E4：** 对贝叶斯模型的McMC模拟进行声学转换（论文第5.4节）。

### **例 E5：** 对iris数据集上的McMC模拟进行声学转换
这些示例在论文的第5.5节中进行讨论。以下示例是使用
<table BORDER WIDTH="70%" align="center" >
<tbody><tr>
<td>带宽缩放指数</td>
<td>声音文件</td>
</tr>
<tr>
<td>0.5</td>
<td><a href="https://pub.uni-bielefeld.de/download/2930310/2930336/mcmc_iris1_bw0.5.wav">WAVE文件</a></td>
</tr>
<tr>