If you are interested in working with me as a PhD student, please note that the PhD programme in Edinburgh is relatively short compared to those in (say) the US, normally 3 to 3.5 years with no required coursework, and most students enter with a master's degree or equivalent. I expect prospective students to already have strong programming and mathematical and/or statistical skills, as well as some relevant research experience (e.g., undergraduate or master's thesis in statstical NLP, machine learning, or computational psycholinguistics). If you feel you may need more experience in some of these areas, one option to consider is the Centre for Doctoral Training in Data Science, which is a 4-year programme with coursework in the first year.
Please take a look at some of my publications to get an idea of the kinds of things I'm interested in and the methods I use. If you think your interests are a good match to mine, feel free to contact me for further information. I will be much more likely to respond if you include some information about yourself such as a transcript or CV as well as what research area you hope to pursue.
Finally note that if you apply to the standard PhD programme, you'll be applying to ILCC, my institute within Informatics, so you should look at the general information for prospective students on the ILCC website.