数理统计学

The core task of this step is to select a practical statistical problem and obtain an appropriate dataset for analysis. Choose research questions from core course content and practical application scenarios, which can be descriptive statistics, inferential statistics, regression analysis, machine learning, or Bayesian statistics. Data is the foundation of statistical analysis, and selecting an appropriate dataset is crucial.

• Select specific statistical problems from practical application scenarios, clarify research objectives and analysis needs, which can be business analytics, scientific research, or social survey problems
• Data acquisition: obtain real data from public databases (such as UCI, Kaggle, National Bureau of Statistics, WHO, PubMed), or generate data through simulation, ensuring data quality and applicability
• Develop analysis plan: clarify analysis objectives, select appropriate statistical methods, develop data analysis process, and determine evaluation metrics and expected outcomes

The core task of this step is to clean and preprocess raw data, and understand data characteristics through exploratory data analysis. Real-world data often has problems such as missing values, outliers, and noise, and data preprocessing directly affects the quality of analysis results. Exploratory analysis can help discover patterns, trends, and anomalies in data, providing guidance for subsequent modeling.

• Data cleaning: handle missing values (deletion, imputation), outliers (identification, treatment), duplicate data, perform data type conversion and standardization, ensuring data quality
• Descriptive statistics: calculate statistics such as mean, median, variance, quantiles, and understand distribution characteristics and concentration/dispersion trends of each variable
• Exploratory analysis: use histograms, box plots, scatter plots, heatmaps and other visualization methods to explore data distribution, relationships between variables, and abnormal patterns, using Python (Pandas, Matplotlib, Seaborn) or R for analysis

The core task of this step is to select appropriate statistical models for modeling and analysis based on the research problem and data characteristics. Apply statistical theories and methods learned in the course to build statistical models of data, and perform parameter estimation, hypothesis testing, prediction, or classification. Statistical modeling requires considering model assumptions, model selection, and model diagnostics.

• Model selection: choose appropriate statistical models according to research problems and data types (such as linear regression, logistic regression, time series, Bayesian models, machine learning algorithms, etc.)
• Model fitting: use R, Python (Scikit-learn, StatsModels, PyTorch) or other statistical software to fit models, estimate parameters, and perform hypothesis testing and interval estimation
• Model diagnostics: test model assumptions (such as normality, homoscedasticity, independence), perform residual analysis, detect multicollinearity and outliers, and evaluate model fitting effects

The core task of this step is to conduct comprehensive evaluation of the established statistical models and provide reasonable statistical interpretation of results. Model evaluation includes multiple dimensions such as prediction performance, generalization ability, and robustness. Result interpretation needs to be combined with actual background, translating statistical conclusions into practically meaningful insights, avoiding statistical misuse and over-interpretation.

• Model evaluation: use cross-validation, training/test set splitting and other methods to evaluate model prediction performance, calculate evaluation metrics such as accuracy, precision, recall, F1 score, AUC, MSE, R²
• Model comparison: compare performance of different models, select the optimal model, and analyze advantages, disadvantages, and applicable scenarios of each model
• Result interpretation: explain practical meaning of model parameters, conduct causal inference or correlation analysis, discuss the difference between statistical significance and practical significance, and provide reasonable conclusions and suggestions

The core task of this step is to organize the entire statistical analysis process and results into a standardized data analysis report, and present research results in a clear and intuitive way. Data analysis reports require clear structure, standardized charts, and clear conclusions, being both professionally rigorous and easy to understand. Result presentation needs to choose appropriate presentation methods according to audience characteristics.

• Write analysis report: organize content according to data analysis report standards, including background introduction, data description, method explanation, result analysis, conclusion suggestions, appendix, with standardized citations (APA or GB/T 7714)
• Data visualization: produce high-quality statistical charts and visualization works, use Tableau, Power BI or Python (Plotly, Seaborn) to create interactive or static charts
• Result presentation: create presentation slides (PPT) for reporting, design data dashboards, prepare technical documentation and reproducible code (using R Markdown or Jupyter Notebook)