Bayesian Non-Parametrics (BNP)

Bayesian Non-Parametrics (BNP) is a Statistical approach within Bayesian inference that utilizes infinitely dimensional objects like functions or probability distributions as priors. This allows for remarkable flexibility and avoids the need for pre-specifying a rigid model structure.

BNP is a powerful framework for situations where the underlying data distribution is unknown or complex. However, the computational demands and theoretical underpinnings can be challenging for beginners.

Notes:

• BNP models employ priors that are not limited to a fixed number of parameters, but rather can adapt to the complexity of the data (Infinite-Dimensional Priors).
• Unlike traditional parametric models with a set number of parameters, BNP models offer greater flexibility and are less reliant on strong prior assumptions.
• BNP models often center around priors that represent probability distributions themselves, I.e. focusing on random probability measures, allowing the data to "speak for itself" in determining the underlying distribution.
• Dirichlet Process (DP) is a widely used BNP model for mixture modeling, while Gaussian Process Priors (GPP) are another example for continuous data.
• Inference in BNP models can be computationally intensive compared to simpler models due to the inherent complexity of infinite-dimensional objects.