👉 PVC, or Probabilistic Vector Calculus, is a mathematical framework that extends classical vector calculus to handle uncertainty and probabilistic reasoning. It generalizes concepts like gradients, divergence, and curl to stochastic settings, allowing for the analysis of systems with random variables and noise. In PVC, vectors are treated as probability distributions rather than deterministic entities, enabling the calculation of expectations and variances of vector fields. This is particularly useful in machine learning, signal processing, and other fields where data inherently contains uncertainty. The core idea is to represent functions of random variables using operators that preserve probabilistic properties, such as the expectation operator, thus providing a robust mathematical foundation for dealing with noisy or incomplete data.
