Are bayesian methods inherently sequential? Ie, to do sequential analysis (you don't know ahead of time exactly how much data you will collect) with frequentist methods requires special care; you can't just collect data until the p-value gets sufficiently small or a confidence interval becomes sufficiently short.
But when doing Bayesian analysis, is this a concern? Can we freely do things like collect data until a credible interval becomes sufficiently small?
 A: Rouder (2014) has a nice paper on this (written for psychologists), explaining why sequential testing (so-called data peeking) is fine from a Bayesian perspective. (Paper is freely available online if you do a search for it.) 
Schoenbrodt et al. (in press) present nice analyses showing how to use sequential analysis with Bayes factors to determine when to stop data collection. 
From a Bayesian parameter estimation procedure, John Kruschke has a very nice blog post that compares different Bayesian methods during sequential testing. 
Hope you find them of help.
References
Rouder, Jeffrey N. (2014). Optional stopping: No problem for Bayesians. Psychonomic Bulletin & Review, 21, 301-308.
Schoenbrodt, F. D., Wagenmakers, E.-J., Zehetleitner, M., & Perugini, M. (in press). Sequential hypothesis testing with Bayes factors: Efficiently testing mean differences. Psychological Methods.
A: SPRT is good example of a frequentist method that is sequential.
On the other hand, while Bayesian models have priors to overcome sparsity of data, the more data you have the "narrower" your posterior distribution becomes making it less suitable for online temporal learning.
