This essay encompasses a survey of over 65 different research papers and articles discussing the study of data mining time series data for activities of daily life. It looks at the evolution of different data mining and statistical analysis methods used on data in order to infer the actual activities originally being performed while occupants were under observation by sensors in a natural living environment. This paper discusses benefits to this area of research and describes some of the key challenges, both physical and technological, that makes activity inference challenging. Throughout the research that was performed it was found that algorithms based on Conditional Random Field or the Hidden Markov Model was the most successful statistical modelling methods used in data mining and inference of human activity.