Lowland multimodality detection and jittering

In A better jittering approach for discretization acknowledgment in density estimation, I discussed the jittering approach that improves Quantile-Respectful Density Estimation for discrete distributions and continuous-discrete mixtures. In this post, I will show a brief example of how such an approach improves the accuracy of the Lowland multimodality detection.

Let us consider a sample of $2000$ elements from the standard normal distribution rounded to the first decimal place. In the figure below, we can see that this discretization spoils the multimodality detection and leads to five detected modes.

In the following figure, the same sample is used, but jittering is applied, which leads to a single detected mode.

As we can see, the jittering patch works as expected and fixes the multimodality detection issue.