1. Descriptive statistical analysis: This is the most basic statistical method, which is mainly used to collect, sort out and describe data. Including data classification, sorting, calculating average, median, mode and so on.

2. Inference statistical analysis: This method is mainly used to infer the overall characteristics from the sample data. The commonly used inference statistical methods include hypothesis testing, confidence interval estimation and regression analysis.

3. Experimental design: Experimental design is a very important part of probability and statistics learning. It includes randomized experimental design, block design and Latin square design.

4. Time series analysis: This method is mainly used to study time-varying data. Commonly used time series analysis methods include autoregressive model, moving average model and autoregressive moving average model.

5. Bayesian statistics: this is a statistical method based on probability theory, which is mainly used to deal with uncertain information. Commonly used Bayesian statistical methods include Bayesian theorem, Bayesian network and so on.

6. Multivariate statistical analysis: This method is mainly used to process multivariate data. Commonly used multivariate statistical analysis methods include principal component analysis, factor analysis and cluster analysis.

7. nonparametric statistics: this method does not depend on the distribution type of data, and is suitable for all types of data. Commonly used nonparametric statistical methods include rank sum test, sign test, Kruskal-Wallis test and so on.

8. Advanced statistical methods: These methods are mainly used to deal with complex statistical problems, such as survival analysis, mixed effect model, generalized linear model, etc.

The above are the main research methods of probability and statistics papers, and different research problems need to choose different methods.