Hamiltonian Monte Carlo

Efficient Sampling in High Dimensions

Standard MCMC methods can struggle in high-dimensional spaces. Hamiltonian Monte Carlo (HMC) improves efficiency by incorporating gradient information to guide sampling.

Core Insight

HMC treats sampling as a physical system:

• parameters are treated as positions

• gradients act as forces

This allows the sampler to move more efficiently through the probability space.

Advantages

• faster convergence

• reduced random walk behaviour

• improved performance in high dimensions

Application at MorMag

HMC is relevant in:

• complex Bayesian models

• high-dimensional parameter estimation

• advanced probabilistic frameworks

As such, it supports scalable modelling within the Quant Lab.

Conclusion

HMC provides a more efficient alternative to traditional MCMC, particularly in complex modelling environments.