|An Introduction to Gaussian Processes in Psychology|
Joseph W. Houpt1 and Gregory E. Cox2
1Wright State University, Dayton, Ohio
2Indiana University, Bloomington, Indiana
While point estimates, such as mean response times, have been the focus of many studies in scientific psychology, there is increasing appreciation of the value of functional data. In some cases it is possible to reduce the functional data to points and use the familiar statistics with those estimates, however, to take full advantage of the power of functional data, we need statistical tools specifically for functional data. In this workshop we will introduce the use of Gaussian processes for functional data. Much as the Gaussian distribution is the foundation of many statistical analyses of point data, the Gaussian process has the potential to be used for many types of analyses of functional data.
We will begin the workshop with a general introduction to the Gaussian process. This will include some basic properties, with a bias toward those properties that are most important to psychological researchers. We will then highlight some of the more familiar statistical tools that can be reframed in terms of Gaussian processes. This will lead into a more in depth discussion of Gaussian process regression.
Once we have introduced Gaussian process regression, we will work with participants to analyze functional data using R statistical software with packages available on CRAN. We will have two data sets available for learning the techniques. One data set is a set of paths of mouse movements in a simple decision making task. With the second dataset, we will use Gaussian processes to estimate psychometric curves in a visual detection task. Tutorial participants are also encouraged to bring their own data, which may benefit from analysis with Gaussian processes.