1 Introduction

2 Combining probability samples  
2.1 Multiple probability samples and missingness patterns  
2.2 Two approaches for probability data integration  

3 Combining probability and non-probability samples  
3.1 Combining a probability sample with a non-probability sample  
3.2 Setup and assumptions  
3.3 Propensity score weighting  
3.4 Calibration weighting  
3.5 Mass imputation approach  
3.6 Doubly robust estimation  

4 Combining probability and big data  
4.1 Big data sample  
4.2 Scenario 1: leverage auxiliary information in big data to improve efficiency  
4.3 Scenario 2: leverage probability sampling designs to correct for selection bias  

5 Concluding remarks