Increasing the information gained from biological data is a crucial aspect of statistical inference. In the first part of this work, we aimed to understand the impact of model accuracy to reduce sample numbers. We focused on the comparison between frequentist and Bayesian statistics for a classical behavioral test of mice. Our results demonstrate that the versatility of Bayesian models facilitates efficient analysis of sparse and complex data.

In the second part of this work, we applied this knowledge to analyze the complex mechanism of epigenetic regulation in the initiation and guidance of cell differentiation. With a broad variety of different activating and repressive modifications, histones play an integral role during this process. Previous studies revealed that different combinations of histone modifications determine the level of gene expression and prime genes for future regulation. However, it is less understood which changes in the epigenetic profile initiate an altered gene expression. The goal of this thesis was to explore the dynamics in the histone landscape that drive the differentiation of a cell.

An ideal system to investigate this process is the differentiation of proliferating into hypertrophic chondrocytes during endochondral bone formation. Both cell types are defined by distinct expression profiles and the differentiation step is tightly controlled by numerous well-investigated regulatory genes. To identify if specific transitions between combinations of histone marks are linked to chondrocyte hypertrophy, I developed a Bayesian model analyzing the transitions of states of known lineage-specific genes between the two cell types. This way we could identify which epigenetic dynamics are most influential in guiding cell differentiation.

We demonstrated that throughout differentiation, gene repression is initiated by the addition of H3K27me3 to promoters still marked by several activating histone modifications, forming so-called repressed-active promoter states. To further investigate if this mechanism is specific for the differentiation between chondrocytes, we extended the Bayesian model to allow the analysis of multiple cell types and implemented it into a modular processing pipeline, called \emph{BATH}. By incorporating embryonic and mesenchymal stem cells into our analysis, we broadened our study to include earlier differentiation stages.

The analysis showed that similar to the differentiation of proliferating to hypertrophic chondrocytes, mesenchymal stem cells form repressed-active states to initiate the repression of lineage-initiating genes that are no longer expressed in mature chondrocytes.

In contrast, the pluripotency of embryonic stem cells has been associated with the decoration of lineage-specific genes with the so-called bivalent state, a combination of the activating promoter mark H3K4me3 and the repressive mark H3K27me3. When the cell commits to a particular cell fate, H3K27me3 will be lost on those genes associated with the respective cell type. However, in our analysis of embryonic stem cells, we did not detect an enrichment of the classical bivalent state.

Instead, we found an enrichment of the repressed-active promoter state on lineage-specific genes, carrying additional activating marks.

Just as bivalent promoters, the repressed-active promoter state loses H3K27me3 upon differentiation, indicating that the combination of repressive and activating marks is an important regulatory tool not limited to pluripotent stem cells but widely used to control gene activation and repression in a wide range of cell types.

The results and methodology presented in this work will help to gain a deeper understanding of epigenetic dynamics, not only for the chondrocyte lineage but cell differentiation in general.