Probability statistics is a discipline that studies the regularity of random phenomena, and it has a wide range of research directions. The following are some common probability statistics dissertation research directions:
1.Stochastic Processes and Markov Chains: the study of the evolution of the laws of random variables, such as Brownian motion, Poisson process, and so on.
2. Limit Theorem and Law of Large Numbers: the study of convergence of sequences of random variables, such as the Central Limit Theorem, the Law of Large Numbers, and so on.
3. Parameter estimation and hypothesis testing: study how to estimate and test the overall parameters based on sample data, such as great likelihood estimation, confidence intervals.
4. ANOVA and regression analysis: study the effect of multiple independent variables on the dependent variable, such as linear regression, ANOVA, etc.
5. Time series analysis: study the forecasting and modeling of time series data, such as ARIMA model, GARCH model and so on.
6. Bayesian statistics: study of inference methods based on a priori information, such as Bayesian formula, Bayesian networks, etc.
7. Non-parametric statistics: the study of inference methods that do not depend on the assumption of the overall distribution, such as kernel density estimation, rank sum test and so on.
8. High-dimensional data analysis: the study of methods to deal with high-dimensional data, such as principal component analysis, cluster analysis, etc..
9. Survival analysis: study of time-to-event data, such as survival function, Cox proportional risk model.
10. spatial statistics: study of spatial data analysis methods, such as geographically weighted regression, spatial autocorrelation analysis.