Gaussian process prior

A Gaussian process prior is a way to express uncertainty about a function before observing any data. Think of it as a flexible, mathematical way to say, “I believe the function could look like this, with some variation,” where "this" is described by a pattern of possible shapes and their likelihoods. It provides a probabilistic framework so that, when actual data is observed, the prior can be updated to produce better predictions. Essentially, it's a tool that models functions as smooth, continuous entities, allowing us to make informed guesses even in the absence of complete information.