This volume is a compressed survey containing recent results on statistics of stochastic processes and on identification with incomplete observations. It comprises a collection of papers presented at the Shoresh Conference 2000 on the Foundation of Statistical Inference. The papers cover the following areas with high research activity:- Identification with Incomplete Observations, Data Mining,- Bayesian Methods and Modelling,- Testing, Goodness of Fit and Randomness,- Statistics of Stationary Processes.