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Due to the recent advancements in wearables and sensing technology, healthscientists are increasingly developing mobile health (mHealth) interventions.In mHealth interventions, mobile devices are used to deliver treatment toindividuals as they go about their daily lives. These treatments are generallydesigned to impact a near time, proximal outcome such as stress or physicalactivity. The mHealth intervention policies, often called just-in-time adaptiveinterventions, are decision rules that map an individual's current state (e.g.,individual's past behaviors as well as current observations of time, location,social activity, stress and urges to smoke) to a particular treatment at eachof many time points. The vast majority of current mHealth interventions deployexpert-derived policies. In this paper, we provide an approach for conductinginference about the performance of one or more such policies using historicaldata collected under a possibly different policy. Our measure of performance isthe average of proximal outcomes over a long time period should the particularmHealth policy be followed. We provide an estimator as well as confidenceintervals. This work is motivated by HeartSteps, an mHealth physical activityintervention.

Off-Policy Estimation of Long-Term Average Outcomes with Applications to Mobile Health