Metropolis-Adjusted Langevin Algorithm

Gradient-Informed Sampling

The Metropolis-adjusted Langevin algorithm (MALA) combines stochastic sampling with gradient information.

MALA proposes new states using:

• current position

• gradient of the log-probability

This improves sampling efficiency compared to purely random proposals.

Balance

MALA sits between:

• simple random-walk methods

• more complex HMC approaches

Application at MorMag

Used for:

• refining posterior estimates

• improving sampling efficiency

• enhancing model stability

Conclusion

MALA provides a practical middle ground between simplicity and efficiency in probabilistic sampling.