Feature	Variational Inference (VI)	Markov Chain Monte Carlo (MCMC)
Goal	Find best approximation in a tractable family	Generate exact samples from true posterior (asymptotically)
Accuracy	Biased (approximate); underestimates uncertainty	Unbiased (converges to true posterior)
Speed	Fast; scales to large datasets	Slow; often impractical for big data
Optimization	Gradient-based; deterministic	Sampling-based; stochastic
Parallelization	Easily parallelizable (e.g., mini-batches)	Hard to parallelize (chains are sequential)
Tuning	Choose variational family ( \mathcal{Q} )	Choose proposal distribution, step size, etc.
Uncertainty quantification	Can be too confident (KL(q∥p) is mode-seeking)	More reliable posterior coverage
Use cases	Real-time inference, VAEs, large-scale Bayesian models	Small-data settings, diagnostics, gold-standard inference