Let φ = {φ 1 ...φ T } denote a T-dimensional random vector, where each φ t might for example correspond to a sense probability at time t. We define a prior which encourages smooth change of parameters at neighboring times, in terms of a first order random walk on the line (graphically shown in Figure 2, and the chains of φ and ψ in Figure 1(left)).
we define this prior as an intrinsic Gaussian Markov Random Field (iGMRF; Rue and Held 2005), which allows us to model the change of adjacent parameters as drawn from a normal distribution, e.g.