With the evolution of software-defined networking (SDN) paradigm, traffic management in data center networks has become flexible and scalable. The existing solution using OpenFlow, the rate-guaranteeing mechanism, is inefficient as it limits the rate of the flows by dropping batches of packets to achieve the desired throughput. In this paper, we propose BASIS, a solution based on Bayesian inference for providing proportional Quality of Service (QoS) guarantees to tenants in a datacenter network. With BASIS, the bandwidth of an outgoing congested link will be shared among the competing flows in proportion to the weights chosen by them. We use Bayesian inference to capture the history of flow arrival rates and their offered load using a single queue, and estimate the differential drop probabilities of flows in a way that respects the weights assigned to them on arrival. Unlike the rate-limiting approach, BASIS proactively drops a packet of a flow probabilistically to achieve the desired throughput and avoids dropping batches of packets. We evaluate the proposed solution in an emulated SDN platform and show that BASIS achieves the desired throughput with lesser number of packet drops than the existing approaches.