Rudolph's initial appointment in Cambridge was in 1972 as Assistant Director of Research in the Department of Medicine (Fenners) which is now known as the Deptartment of Public Health & Primary Care. His research interest soon became firmly focussed on the development and applications of advanced statistical methods for clinical diagnoses. His research group expanded and later became a Medical Informatics Unit (1985) within the Dept. of Public Health & Primary Care. His research produced several novel statistical methods for classifying clinical images. For his work he received in 2012 the Bolzano Medal for Advancement of Mathematical Sciences from the Czech Academy of Sciences.
In 1977-1978 he was a University Proctor. This stimulated his interest in the administrative aspects of the University and in 1979 he was elected as member of the Council of the University and subsequently a member of the Financial Board (1982-2002). He was chairman of several of Board’s committees such as the Joint Telecommunications Committee that was responsible for conversion of over 60 telephone departmental and college switchboards into one large digital system serving all Departments and Colleges.
In 1982 he was elected Fellow of Wolfson College, where he served as Tutor (1984-1989), Senior Tutor (1989-1992) and Vice-President (1996-2000).
After political changes in the Eastern Europe in 1989 he was able to visit his birthplace (Prague) again and in 1992 became a Knight Commander of the Order of St. Wenceslas. After retiring from his Cambridge post in 2004 he worked at the Czech Economics University in Prague (2004-2012), where he set up and taught a new course on statistical pattern recognition. In 2012 he became the Chief Scientific Adviser of the Czech Government. With a change of government in 2014 he resigned and moved back to Cambridge.
He has held the following positions:
- Assistant Director of Research, Deptartment of Medicine
- University Proctor
- University Lecturer, Department of Community Medicine
- Director, Medical Informatics Unit, Dept. of Public Health & Primary Care
- Professor, Faculty of Management, University of Economics (Prague)
- Chief Scientific Adviser, Government of the Czech Republic