1. Universal lossless data compression
1.1. A link between coding and estimation 
 
 
1.1.1. Coding and Shannon entropy 
 
 
1.1.2. Instantaneous codes 
 
 
 
 
 
 
1.2. Universal coding and mixture codes 
 
 
1.2.1. The Bayesian approach 
 
 
1.2.2. The minimax approach 
 
 
1.2.3. Oracle inequalities 
 
 
 
 
 
 
1.3. Lower bounds for the minimax compression rate 
 
 
1.4. Mixtures of i.i.d. coding distributions 
 
 
1.5. Double mixtures and adaptive compression 
 
 
1.5.1. General principle 
 
 
1.5.2. The context tree weighting coding distribution 
 
 
1.5.3. Context tree weighting without initial context 
 
 
1.5.4. Weighting of trees of arbitrary depth