In the database community, work on information extraction (IE) has centered on two themes: how to effectively manage IE tasks, and how to manage the uncertainties that arise in the IE process in a scalable manner. Recent work has proposed a probabilistic database (PDB) based declarative IE system that supports a leading statistical IE model, and an associated inference algorithm to answer top-k-style queries over the probabilistic IE outcome. Still, the broader problem of effectively supporting general probabilistic inference inside a PDB-based declarative IE system remains open. In this paper, we explore the in-database implementations of a wide variety of inference algorithms suited to IE, including two Markov chain Monte Carlo algorithms, Viterbi and sum-product algorithms. We describe the rules for choosing appropriate inference algorithms based on the model, the query and the text, considering the trade-off between accuracy and runtime. Based on these rules, we describe a hybrid approach to optimize the execution of a single probabilistic IE query to employ different inference algorithms appropriate for different records. We show that our techniques can achieve up to 10-fold speedups compared to the non-hybrid solutions proposed in the literature.