This thesis considers extensions of the standard independent hidden Markov model approach previously used by TNO for modelling printer nozzles. These extensions introduce parametrised transition probabilities and incorporate interactions between neighbouring nozzles to better capture the real-world printing process. The aim of this thesis is to investigate Bayesian methods to infer their model parameters. Although not the goal of this thesis, accurate parameter estimation paves the way for diagnosing nozzle malfunctions, ultimately improving printer performance.

The first method is a sampling algorithm with adaptive proposal distributions. We then present two variational inference (VI) algorithms, which aim to minimise the divergence between an approximate and true posterior of the unknown parameters. The first VI method makes use of model-specific approximations, while the latter is more flexible. The adaptive sampler, however, remains the most general of the three algorithms in addition to being asymptotically unbiased.

On synthetic data, all methods were capable of producing good estimates of the model parameters. When a good initialisation is available, the sampling method may be faster than the VI approaches; however, if no good start is known, the other methods may be preferred. The runtimes of the algorithms appeared to grow linearly with the number of nozzles. In addition, a linear scaling with the number of time steps appeared plausible.

While the methods performed well on the toy models studied here, their efficacy must be confirmed on more complex systems and demonstrated in real-world applications. If runtimes prove prohibitive, sub-sampling approaches or stochastic variational inference methods could be investigated.