This seems to be the week for us to plug our new books (and I’m eagerly awaiting John and Lynn’s The Gamble), so I thought I’d say a few words about *my* own new book (at the time of this writing, still available at 40% off if you pre-order from Amazon):

The above images represent a Gaussian process decomposition of the time series of number of births in the U.S. as recorded each day from 1969 through 1988. As you can see, births are less likely on the weekends and this trend has been increasing over the years. In addition, kids are most likely to be born in the last summer months, and there are also large effects on particular days, with many fewer babies born on major holidays.

That’s cool but it’s not really political science. What I want to (briefly) discuss here is, what does

Bayesian data analysis have to do with political science? Nowadays “Bayes” is commonly used to denote rational behavior, but that’s not we’re really talking about. We do have one chapter on decision making but most of the book is about learning from data.

In statistics there’s a lot of talk about “Bayesian inference,” but by Bayesian *data analysis* we mean something more. Here are the three steps of Bayesian data analysis:

1. Model building

2. Inference given a model

3. Model checking.

Step 2 is the glamour boy, but steps 1 and 3 are important too. In particular, step 3 is typically achieved using graphics, what is sometimes called “exploratory data analysis.”

Where does “Bayesian” come in? In Bayesian inference, all unknowns are represented by probability distributions. This fits well with a view of the world in which patterns are variable (for example, in which the incumbency advantage is larger for some congressmembers than others) and uncertain (so that we are suitably modest about our forecasts and our claims of general discoveries). At a technical level, Bayesian inference works well when fitting models with large numbers of parameters (such as the varying-intercept, varying-slope regressions that come into play when doing multilevel regression and poststratification). If you want to fit the best ideal-point models and do Mister P, you’ll want to understand Bayes.

What about political science? Bayes should be just as important in sociology or psychology or economics or medical research; these are all areas with large amounts of uncertainty and variation. I just happen to know more about political science than about these other fields. In addition, I have found political scientists to be admirably open in their choice of methods, hence there’s no particular resistance when introducing a new set of tools.

I don’t expect or recommend that political scientists *only* use Bayesian data analysis in their quantitative analyses. Rather, I recommend that they—you—become aware (to the best of your technical ability) of how these methods work, so you can use them in cases where they are most appropriate (these situations would include forecasting, multilevel modeling, inference for complex models with many parameters, and settings with weak data).

A link to the full table of contents for our book is here.