Applied Statistics Is A Way Of Thinking, Not Just A Toolbox

Grouping (Genus)

Tools (Species)

Exploratory Data Analysis (EDA)

Packaging of tools for quick insights; emphasis on graphics, usually for observational data: e.g., Box-Plots, Bubble Graphs, CART, Clustering, Density Plots, Histograms, k-NN, Outlier Detection, Scatterplots, Smoothing, Time-series plots, et al. 

Statistical DM (Data Mining)

Rebranding of EDA; more discussion of some topics and less of others.  Data Mining is used to straddle data analysis and data management.  

Statistical ML (Machine Learning)

The data-analysis part of the ML packaging of statistics and data management tools with a machine learning engine, e.g., Topic Modeling, Support Vector Machines, Random Forests, Tree-Based and Rule-Based Regression and Classification, Genetic Algorithms, Gradient Boosting, Neural Networks, et al. 

Statistical Learning

Evolving definition, at least partly a repackaging/rebranding of Statistical ML, e.g. Linear and Polynomial Regression, Logistic Regression and Discriminant Analysis; Cross-Validation/Bootstrapping, model selection and regularization methods (Ridge and Lasso); Nonlinear Models, Splines and Generalized Additive Models; Tree-Based Methods, Random Forests and Boosting; Support-Vector Machines.  Some Unsupervised Learning Methods are discussed: Principal Components and Clustering (K-Means and Hierarchical).

Statistical DS (Data Science)

Evolving definition, rebranding of applied statistics; more discussion of some topics and less of others.  Data Science was coined as a rebranding of applied statistics and now it is used to straddle data analysis and data management.    

Bayesian

Techniques that assume a prior distribution for the parameters–its a long story, e.g., Naive Bayes, Hierarchical Bayes, et al.

Predictive Analytics

Rebranding of Predictive Modeling

Multivariate Statistics

Clustering, Factor Analysis, Principal Component Analysis, Structure Equation Modeling, et al.

Spatial Statistics

Packaging of tools for modeling spatial variability, e.g.,  Thin-plate Splines, Inverse Distance Weighting, Geographically Weighted Regression.

Parametric Statistics

All tools making parametric assumptions; e.g., Regression

Nonparametric Statistics

All tools not making parametric assumptions; they still make assumptions: e.g., Association Analysis, Neural Networks, Order Statistics, Rank Statistics, Quantile Regression, et al.

Semi-parametric

Family of models containing both parametric and non-parametric components (e.g. Cox-proportional hazard model)

Categorical Data Analysis

Statistics for a categorical response, e.g., Contingency Tables, Cochran-Mantel-Haenszel Methods, General Linear Models, Loglinear Models, Logit Models, Logistic Regression, et al.

Time Series/Forecasting

Tools modeling a time (or location) dependent response; e.g., ARIMA, Box-Jenkins, Correlograms, Spectral Decomposition [Census Bureau]

Survival Analysis

Statistics to perform time-to-event analysis (also called duration analysis), e.g., Cox Proportional Hazard, Kaplan-Meier, Life Tables, et al. 

Game Theory

Statistics tools for modeling contests. 

Text Analytics

Tools for extracting information from text. 

Cross Validation/Data Splitting

Model validation techniques with no replacement for assessing statistical results, e.g., K-fold Cross-Validation, Sequential Validation

Resampling Techniques With Replacement

Model validation techniques with replacement for assessing statistical results, e.g., Permutation Tests, Jackknife, Bootstrapping, et al.

Six Sigma

Repacking of statistics common to manufacturing with clever organizational ideas. 

Quality/Process Control

Statistics for processes, usually observational data, e.g., X-Bar Charts, R Charts, [Manufacturing]

DoS (Design of Samples)

Statistics for collecting sampling units, e.g., Simple Random, Systematic, Stratification, Clustering, Probabilities Proportional to Size, Multi-stage Designs, Small Area Estimation, Discrete Choice, Conjoint Analytics [Census Bureau; Marketing]

DoE (Design of Experiments)

Tools for assigning treatments to experimental units, e.g., Completely Randomized, Randomized Blocks, Factorial Designs, Repeated Measures, Split-Plot, Response Surface Models, Crossover Designs, Nested Designs, Clinical Modifications [Agriculture; Pharmaceuticals]

DSim (Design of Simulation)

Artificial generation of random processes to model uncertainty; Monte Carlo, MarkovChains,

Stochastic Processes

Models for processes (with uncertainty), e.g., Birth-Death Processes, Markov Chains, Markov Processes, Poison Processes, Renewal Processes, et al. 

Areas awaiting a formal name

E.g., high dimensional problems (p>>n); et al.