  Developing an efficient computational scheme for high-dimensional Bayesian
variable selection in generalised linear models and survival models has always
been a challenging problem due to the absence of closed-form solutions for the
marginal likelihood. The RJMCMC approach can be employed to samples model and
coefficients jointly, but effective design of the transdimensional jumps of
RJMCMC can be challenge, making it hard to implement. Alternatively, the
marginal likelihood can be derived using data-augmentation scheme e.g.
Polya-gamma data argumentation for logistic regression) or through other
estimation methods. However, suitable data-augmentation schemes are not
available for every generalised linear and survival models, and using
estimations such as Laplace approximation or correlated pseudo-marginal to
derive marginal likelihood within a locally informed proposal can be
computationally expensive in the "large n, large p" settings. In this paper,
three main contributions are presented. Firstly, we present an extended
Point-wise implementation of Adaptive Random Neighbourhood Informed proposal
(PARNI) to efficiently sample models directly from the marginal posterior
distribution in both generalised linear models and survival models. Secondly,
in the light of the approximate Laplace approximation, we also describe an
efficient and accurate estimation method for the marginal likelihood which
involves adaptive parameters. Additionally, we describe a new method to adapt
the algorithmic tuning parameters of the PARNI proposal by replacing the
Rao-Blackwellised estimates with the combination of a warm-start estimate and
an ergodic average. We present numerous numerical results from simulated data
and 8 high-dimensional gene fine mapping data-sets to showcase the efficiency
of the novel PARNI proposal compared to the baseline add-delete-swap proposal.
