Identifying the underlying TCP variant from passive measurements is important for several reasons, e.g., exploring security ramifications, traffic engineering in the Internet, etc. In this paper, we are interested in investigating the delay characteristics of widely used TCP algorithms that exploit queueing delay as a congestion signal. Hence, we present an effective TCP variant identification methodology from traffic measured passively by analyzing β, the multiplicative back-off factor to decrease the cwnd on a loss event, and the queueing delay values. We address how the β as a function of queueing delay varies and how the TCP variants of delay-based congestion control algorithms can be predicted both from passively measured traffic and real measurements over the Internet. We further employ a novel non-stationary time series approach from a stochastic nonparametric perspective using a two-sided Kolmogorov-Smirnov test to classify delay-based TCP algorithms based on the α, the rate at which a TCP sender's side cwnd grows per window of acknowledged packets, parameter. Through extensive experiments on emulated and realistic scenarios, we demonstrate that the data-driven classification techniques based on probabilistic models and Bayesian inference for optimal identification of the underlying delay-based TCP congestion algorithms give promising results. We show that our method can also be applied equally well to loss-based TCP variants.