business decision making Review of probability theory.pptx
- 1. Review of probability theory Probability theory is one of the most important concepts to learn. Probability Theory is the backbone of many Data Science concepts, such as Inferential Statistics, Machine Learning, Deep Learning, etc. This article explores the basic concepts of Probability Theory required to excel in the Data Science field.
- 2. •Probability is an estimation of how likely a certain event or outcome will occur. •It is typically expressed as a number between 0 and 1, reflecting the likelihood that an event or outcome will take place, where 0 indicates that the event will not happen, and 1 indicates that the event will definitely happen. •For example, if there is an 80% chance of rain tomorrow, then the probability of it raining tomorrow is 0.8.
- 3. • Probability can be calculated by dividing the number of favorable outcomes by the total number of outcomes of an event. • Probability Formula
- 4. Why Probability? • Let’s review a few reasons that make probability one of the most important concepts in Data Science. • Classification Problem - In Machine Learning, classification-based models provide the probability that the input belongs to a particular class or label. For example, if our task is to predict whether a given email is spam or not, then the ML model would give probabilities associated with both possible outcomes/classes. • Models Based on Probability Theory/Framework - In Data Science, many Machine Learning models are based on probability frameworks. For example, the Naive Bayes Classifier, Monte Carlo Markov Chain, Gaussian Processes, etc. • Model Trained on Probability Theory/Framework - Many ML models are trained using algorithms based on Probability Theory/Framework. For example, Maximum Likelihood Estimation, etc.
- 5. • Model Tuned By Probability Theory/Framework - Techniques based on Probability Theory/Framework, such as Bayesian Optimization, etc., are used to tune the hyperparameters used in ML model development. • Model Evaluation - In Classification Problems, many model evaluation metrics, such as ROC, AUC, etc., require predicted probabilities.
- 6. Terminologies Used in Probability Theory Let’s explore some of the most commonly used terminologies in Probability Theory. Experiment • In Probability Theory, an Experiment or Trial is defined as a procedure with a fixed and well-defined set of possible outcomes. It is a process or study that is carried out to understand the likelihood of the occurrence of certain events. • Outcomes in an experiment are defined as the actual results of the trial. The outcomes of an experiment can be either discrete (e.g., the result of a coin toss) or continuous (e.g., the height of a person).
- 7. • An experiment is generally carried out repeatedly to gather sufficient data to make reliable predictions about the likelihood of different outcomes occurring. • For example, if you want to calculate the probability of flipping a coin and getting tails, you can conduct an experiment by flipping a coin many times and counting the number of times the outcome is tails. • The result of the experiment would be the probability of getting tails as an outcome, which would be equal to the number of tails observed divided by the total number of coin flips.
- 8. Sample Space • Sample Space is defined as the set of all possible outcomes of an experiment. • For example, rolling a cube has six possible outcomes. Its sample space can be represented as S = {1,2,3,4,5,6}. Similarly, sample space for flipping a coin can be written as S = {head, tails}. • Events • In Probability Theory, an Event is one or more possible outcomes of an experiment. It is typically defined as a subset of the sample space of an experiment. • For example, in the case of flipping a coin, it has two possible outcomes - head and tails. • So we can say that any trial has the possibility of two events - getting tails or getting heads.
- 9. Random Variable • A Random Variable is a numerical and mathematical framework used to represent the outcome of the experiment. For example, in a flipping coin experiment, a random variable can be defined as X, where X = 0 represents heads and X = 1 represents tails. • Any random variable for an experiment can only take well-defined outcomes, and the probability distribution function of the random variable can describe the probabilities associated with each possible outcome.
- 10. Independent Events • In Probability Theory, Independent Events are events that do not affect each other. Any two events are considered Independent Events if the outcome of one event does not impact the likelihood of the occurrence of another event. For example, if the experiment is flipping a coin two times, these two coin flips are independent events because the outcome of the first coin flip does not impact the outcome of the second coin flip. • The probability of Independent Events can be calculated by multiplying the probabilities of the individual events.
- 11. • In contrast, dependent events affect each other. For example, if the experiment is drawing two cards from a deck of playing cards, then both events are dependent, as the first event will modify the likelihood of the occurrence of the second event. Joint Events • In Probability Theory, events that occur simultaneously or at the same time are defined as Joint Events. For example, in the case of rolling two dice simultaneously, outcomes on both dice will be considered joint events.