Identifying elephant flows is very important in developing effective and efficient traffic engineering schemes. In addition, obtaining the statistics of these flows is also very useful for network operation and management. On the other hand, with the rapid growth of link speed in recent years, packet sampling has become a very attractive and scalable means to measure flow statistics; however, it also makes identifying elephant flows become much more difficult. Based on Bayes' theorem, this paper develops techniques and schemes to identify elephant flows in periodically sampled packets. We show that our basic framework is very flexible in making appropriate trade-offs between false positives (misidentified flows) and false negatives (missed elephant flows) with regard to a given sampling frequency. We further validate and evaluate our approach by using some publicly available traces. Our schemes are generic and require no per-packet processing; hence, they allow a very cost-effective implementation for being deployed in large-scale high-speed networks.