Null hypotheses, significance testing and all that jazz

Some amazing articles I've recently read in my ample spare time:

1. The Insignificance of Null Hypothesis Significance Testing
Jeff Gill
Political Research Quarterly, Vol. 52, No. 3 (Sep., 1999), pp. 647-674
doi:10.2307/449153

2. Andrew Gelman's article

3. And this one: http://www.npwrc.usgs.gov/resource/methods/statsig/index.htm

4. Bowers and Gelman on Exploratory Data Analysis with Hierarchical Linear Models (AKA Multilevel models)

Suitably stunned into silence, the reader may then have the following practical question: how to present one's HPD intervals in a journal, and what else to present?

Here's an answer from Doug Bates.