The standard way of choosing stochastic models (transition probabilities) in many cases turns out to be in disagreement with experiment, correctly described by quantum mechanics. For example it would allow electrons to freely travel through defected lattice of semiconductor, while we know that it is not a conductor - these electrons are statistically imprisoned (Anderson localization). Maximal Entropy Random Walk (MERW) allows to understand and repair this disagreement by choosing the transition probabilities accordingly to the basic for statistical physics: maximum entropy principle (Jaynes). MERW leads to stationary probability distribution exactly like predicted by quantum mechanics, for example with electrons prisoned in entropic well of semiconductor. I will also tell about other applications of MERW: to maximize capacity of informational channel or to analyze images and networks/graphs.