We now assume further that the parameters θ are themselves drawn from a probability distribution. We can then frame our inverse problem as trying to find this probability distribution for θ given the observed values of the data y, and denote this probability distribution as P (θ|y) (the vertical line indicates that the values of y are given). In Bayesian inference, P (θ|y) is termed the posterior probability density or posterior distribution; this is the distribution that we want to approximate.