We present an introduction to a novel model of an individual and group opinion dynamics, taking into account different ways in which different sources of information are filtered due to cognitive biases. The agent based model, using Bayesian updating of the individual belief distribution, is based on the recent psychology work by Dan Kahan. Open nature of the model allows to study the effects of both static and time-dependent biases and information processing filters. In particular, the paper compares the effects of two important psychological mechanisms: the confirmation bias and the politically motivated reasoning. Depending on the effectiveness of the information filtering (agent bias), the agents confronted with an objective information source may either reach a consensus based on the truth, or remain divided despite the evidence. In general, the model might provide an understanding into the increasingly polarized modern societies, especially as it allows mixing of different types of filters: psychological, social, and algorithmic.