The study of random events and results, including concepts like probability distributions, hypothesis testing, and regression analysis.
Basic Concepts of Probability Theory: Understanding probability, events, and probability axioms helps one to develop a foundation in probability theory.
Counting Techniques: One needs to learn various methods of counting, such as permutations and combinations, to solve a wide range of probability problems.
Probability Distributions: Probability distributions help to define and understand the probability of different outcomes. Common probability distributions include binomial, normal, Poisson, and exponential.
Bayes' Theorem: It is a fundamental concept in probability theory that can be used to update one's prior beliefs given new information.
Random Variables: Understanding random variables enables one to associate probabilities with key economic and financial variables and also calculate measures of central tendency.
Descriptive Statistics: Tools such as mean, median, mode, and standard deviation are used to describe data and gain a better understanding of it.
Sampling Theory: Sampling theory allows one to draw inferences about a larger population based on a sample size selected randomly.
Estimation Theory: In statistics, estimation theory involves the process of estimating population parameters from a sample based on probability distributions.
Hypothesis Testing: It involves testing a hypothesis with the correct level of statistical significance in order to provide conclusions.
Time Series Analysis: In econometrics, this involves analyzing a time series of data points to identify trends, seasonality, or other patterns.
Regression Analysis: Regression analysis is a powerful tool used to model the relationship between two or more variables.
Panel Data Analysis: Panel data analysis is a sophisticated method of data analysis that accounts for the correlation between observations over time.
Maximum Likelihood Estimation: This method allows one to find the set of parameters that maximize the likelihood of observing a set of data points.
Correlation and Causality: In economics, it is essential to make causal inferences between different variables. Correlation does not imply causation.
Multivariate Analysis: This refers to techniques that analyze the relationship between multiple variables, such as multiple regression or factor analysis.
Non-parametric Methods: When data lacks a parametric distribution, non-parametric methods, such as bootstrap and permutation tests used to analyze data.
Machine Learning: Machine learning can be used for a variety of tasks, such as predicting outcomes, identifying patterns, or classifying data points.
Big Data Analytics: Given readily available big data, it involves the application of statistical methods to derive insights and make predictions.
Experimental Design: When running an experiment, it is important to understand the different types of designs and how to analyze data.
Monte Carlo Methods: Monte Carlo methods involve using random sampling to obtain numerical solutions to complex problems.
Descriptive statistics: The branch of statistics that deals with the collection, analysis, and interpretation of data. It includes measures of central tendency, variability, and correlation.
Inferential statistics: The branch of statistics that focuses on making predictions or generalizations about a population based on data collected from a sample. It includes hypothesis testing, confidence intervals, and regression analysis.
Probability theory: The branch of mathematics that deals with the study of random events and their likelihood of occurrence. It involves the use of probability distributions, probability density functions, and probability mass functions.
Bayesian statistics: A type of probability theory that involves updating probabilities based on new data or evidence. It is useful in decision making and predicting uncertain events.
Time series analysis: The statistical analysis of data collected over a period of time. It involves the identification of trends, seasonal variations, and cyclical patterns.
Spatial statistics: The statistical analysis of data collected over a geographical area or space. It includes the study of spatial patterns, spatial autocorrelation, and spatial regression.
Multivariate analysis: The statistical analysis of data involving multiple variables. It includes factor analysis, cluster analysis, and principal component analysis.
Nonparametric statistics: The branch of statistics that does not assume a specific distribution or form of the data. It includes rank-based tests and distribution-free tests.
Econometric analysis: The application of statistical methods to economic data. It includes regression analysis, time series analysis, and panel data analysis.
Simulation and Monte Carlo methods: The use of computer-based simulations to model and analyze complex systems. It involves generating random numbers and using them to simulate the behavior of a system.