Technologies and services for the home environment can provide levels of independence for elderly people to support 'ageing in place'. Learning inhabitants' patterns of carrying out daily activities is a crucial component of these technological solutions with sensor technologies being at the core of such smart environments. Nevertheless, identifying high-level activities from low-level sensor events can be a challenge, as information may be unreliable resulting in incomplete data. Our work addresses the issues of learning in the presence of incomplete data along with the identification and the prediction of inhabitants and their activities under such uncertainty. We show via the evaluation results that our approach also offers the ability to assess the impact of various sensors in the activity recognition process. The benefit of this work is that future predictions can be utilised in a proposed intervention mechanism in a real smart home environment.