  Multidimensional scaling is widely used to reconstruct a map with the points'
coordinates in a low-dimensional space from the original high-dimensional space
while preserving the pairwise distances. In a Bayesian framework, the current
approach using Markov chain Monte Carlo algorithms has limitations in terms of
model generalization and performance comparison. To address these limitations,
a general framework that incorporates non-Gaussian errors and robustness to fit
different types of dissimilarities is developed. Then, an adaptive inference
method using annealed Sequential Monte Carlo algorithm for Bayesian
multidimensional scaling is proposed. This algorithm performs inference
sequentially in time and provides an approximate posterior distribution over
the points' coordinates in a low-dimensional space and an unbiased estimator
for the marginal likelihood. In this study, we compare the performance of
different models based on marginal likelihoods, which are produced as a
byproduct of the adaptive annealed Sequential Monte Carlo algorithm. Using
synthetic and real data, we demonstrate the effectiveness of the proposed
algorithm. Our results show that the proposed algorithm outperforms other
benchmark algorithms under the same computational budget based on common
metrics used in the literature. The implementation of our proposed method and
applications are available at https://github.com/nunujiarui/GBMDS.
