Implementation of Bayesian inference on cognitive science research question
A good starting point is probably Alex Etz's Understanding Bayes blog post series. He also co-authored a related paper that should be a great starting point: How to become a Bayesian in eight easy steps: An annotated reading list (link is to pre-print).

Richard Morey's BayesFactor blog is great resource for understanding the Bayesian model comparison approach. He has authored many papers that are relevant, but the blog is the best starting point for learning about the approach.

For a really accessible textbook, John Kruschke's Doing Bayesian Data Analysis is an excellent and thorough treatment of the use of Bayesian parameter estimation in data analysis.  This approach is a bit different from the model comparison approach, but the conceptual ideas are the same. A related paper that motivates the approach in the book is available here.