Probabilistic Uncertainty Quantification in Scientific Measurements

Develop a sophisticated uncertainty quantification framework for scientific measurement data that goes beyond traditional error propagation methods. Create a Bayesian probabilistic model capable of handling complex, multi-dimensional measurement uncertainties across different experimental domains. Implement advanced Monte Carlo sampling techniques, design visualization methods for uncertainty landscapes, and generate comprehensive uncertainty budgets that include systematic and random error components. The solution should provide interactive reporting mechanisms allowing researchers to explore uncertainty distributions interactively.