  Combining data has become an indispensable tool for managing the current
diversity and abundance of data. But, as data complexity and data volume swell,
the computational demands of previously proposed models for combining data
escalate proportionally, posing a significant challenge to practical
implementation. This study presents a sequential consensus Bayesian inference
procedure that allows for a flexible definition of models, aiming to emulate
the versatility of integrated models while significantly reducing their
computational cost. The method is based on updating the distribution of the
fixed effects and hyperparameters from their marginal posterior distribution
throughout a sequential inference procedure, and performing a consensus on the
random effects after the sequential inference is completed. The applicability,
together with its strengths and limitations, is outlined in the methodological
description of the procedure. The sequential consensus method is presented in
two distinct algorithms. The first algorithm performs a sequential updating and
consensus from the stored values of the marginal or joint posterior
distribution of the random effects. The second algorithm performs an extra
step, addressing the deficiencies that may arise when the model partition does
not share the whole latent field. The performance of the procedure is shown by
three different examples -- one simulated and two with real data -- intending
to expose its strengths and limitations.
