While mobile operator data (and specifically Call Detail Records, CDR) constitute an important source of evidence on population mobility, particularly in data-poor settings such as low- and middle-income countries (LMICs), they remain partial in terms of population coverage, and prone to representation biases which are difficult to measure, control, and correct for in the absence of independent auxiliary data. Although methodological development and research on the application of CDR data has progressed in recent years, few solutions have been offered so far for the adjustment of such representation biases in CDR-based indicators. The inherent biases of these data require correction through joint modelling with traditional data sources such as surveys. These problems of selection bias and representativity in general are common to all big data analyses, where often the erroneous assumption is made that the quantity of data renders representation bias negligeable. We propose here a method that corrects for such biases in CDR-derived indicators. We present the bias-correcting methodology we developed and applied to produce estimates of internal migration and sub-regional population change in three LMIC countries (Haiti, Ghana and the DRC). What is more, the method could be generalised to other types of estimates and big data datasets.