One of the paradigms of quantum mechanics is the statistical nature of measurements: the result of measurements is indeed described by a probability distribution function (PDF), and measuring the same observable in identical systems will give different outcomes in accordance with this distribution. The PDF carries very detailed information about the system, going much beyond the simple average. Here I exploit the Matrix Product Operator (MPO) representation of the Generating Functions to efficiently perform local measurements in one-dimensional spin systems using Tensor Network Methods, both in and out-of-equilibrium. Finally, inspired by such formulation, I show some preliminary results connecting MPS with Neural Network Quantum States.