Choosing bin resolution remains a fundamental challenge in data visualization. Histogram bin optimization directly impacts analysis quality, especially when visualizations inform further statistical work. The article presents a rigorous Bayesian approach that determines how bins should scale with dataset size, transforming arbitrary visual choices into mathematically principled decisions.

The framework treats each histogram bin as a parameter with weights representing probability distributions. By applying a Dirichlet distribution as a prior, researchers can model expected density distributions before seeing data. Two strategies emerge: the sparse choice (α=1/K) for concentrated data and the uniform choice (α=1) for neutral starting assumptions.

This method converts density visualization from pixelated approximation to formal statistical modeling. The uniform prior adds one "virtual" observation to each bin, creating a balanced approach that prevents overfitting while capturing underlying data patterns. The resulting framework provides concrete guidance for determining optimal bin resolution based on actual dataset characteristics.