In this paper, we introduce an efficient independence-based algorithm for the induction of the Markov network (MN) structure of a domain from the outcomes of independence test conducted on data. Our algorithm utilizes a particle filter (sequential Monte Carlo) method to maintain a population of MN structures that represent the posterior probability distribution over structures, given the outcomes of the tests performed. This enables us to select, at each step, the maximally informative test to conduct next from a pool of candidates according to information gain, which minimizes the cost of the statistical tests conducted on data. This makes our approach useful in domains where independence tests are expensive, such as cases of very large data sets and/or distributed data. In addition, our method maintains multiple candidate structures weighed by posterior probability, which allows flexibility in the presence of potential errors in the test outcomes.