By Shashikant Nishant Sharma

Here are some more advanced statistical methods used in various fields:

Bayesian Statistics

1. Bayesian Inference – A method of statistical inference in which Bayes’ theorem is used to update the probability for a hypothesis as more evidence or information becomes available.
2. Markov Chain Monte Carlo (MCMC) – A class of algorithms that sample from a probability distribution based on constructing a Markov chain.
3. Bayesian Network – A graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph.

Multivariate Analysis

1. Principal Component Analysis (PCA) – A technique used to emphasize variation and bring out strong patterns in a dataset by transforming it into a set of orthogonal (uncorrelated) variables called principal components.
2. Canonical Correlation Analysis (CCA) – A way of inferring information from cross-covariance matrices.
3. Multidimensional Scaling (MDS) – A means of visualizing the level of similarity of individual cases of a dataset.

Machine Learning Techniques

1. Support Vector Machines (SVM) – A supervised learning model used for classification and regression analysis.
2. Random Forest – An ensemble learning method that operates by constructing multiple decision trees during training and outputting the class that is the mode of the classes or mean prediction of the individual trees.
3. Neural Networks – A series of algorithms that attempt to recognize underlying relationships in a set of data through a process that mimics the way the human brain operates.

Survival Analysis

1. Cox Proportional Hazards Model – A regression model used to explore the relationship between the survival time of subjects and one or more predictor variables.
2. Kaplan-Meier Estimator – A non-parametric statistic used to estimate the survival function from lifetime data.

Structural Equation Modeling (SEM)

1. Path Analysis – A form of SEM that examines the directed dependencies among a set of variables.
2. Latent Variable Models – Models that include variables that are not directly observed but are inferred from other variables that are observed (measured).

Time Series Analysis

1. ARIMA (AutoRegressive Integrated Moving Average) – A popular statistical method for time series forecasting.
2. GARCH (Generalized Autoregressive Conditional Heteroskedasticity) – A statistical model for estimating the volatility of stock returns and other financial series.

Spatial Statistics

1. Kriging – A group of geostatistical techniques used to interpolate the value of a random field at an unobserved location from observations at nearby locations.
2. Spatial Autocorrelation – The correlation of a variable with itself through space.

Hierarchical Models

1. Hierarchical Linear Models (HLM) – Models that account for data that is nested (e.g., students within schools, patients within hospitals).
2. Bayesian Hierarchical Models – Models that use Bayesian methods to estimate the parameters of hierarchical models.

Advanced Hypothesis Testing

1. Permutation Tests – Non-parametric tests that involve the rearrangement of the data to determine the distribution of the test statistic under the null hypothesis.
2. Bootstrapping – A resampling method used to estimate the distribution of a statistic by sampling with replacement from the original data.

Functional Data Analysis

1. Functional Principal Component Analysis (FPCA) – Extends PCA to data that can be represented as functions rather than vectors.
2. Functional Linear Models – Models that relate functional responses to functional or scalar predictors.

These methods are used in various advanced fields and can handle complex datasets and sophisticated modeling scenarios.