using the score function and observed information matrix. @wagner2011bayesian develops a Gibbs sampler based on the data augmentation method of @fruhwirth1994data and proposes a variable selection scheme. The major drawback of these methods is that they are computationally expensive as they require many iterations to achieve convergence. Their convergence is hindered by the auto-correlation of the effect parameters induced by the random walk prior process.

The aim of this paper is to propose a fast and efficient alternative inference methodology for PEH models. The PS methodology is based on Sequential Monte Carlo (SMC) methods, commonly known as particle smoothing algorithms [@briers2010smoothing; @fearnhead2010sequential]. These algorithms are specifically designed to sample effectively from state-space models, of which PEH models is one instance. The main advantages of PS algorithms are that: i) they require no functional approximation of the likelihood, ii) they break a multidimensional problem into sequences of smaller dimensional problems. This makes them computationally fast and highly efficient especially when the number of intervals partitioning the study period is relatively large.

To be more specific, I apply the PS algorithm of @fearnhead2010sequential, which relies on three particle filtering approximations: a forward particle filter which propagates information forwards in time, a backward 