Information and Probabilistic Modelling of Uncertainty
Learn about the basic principles of information and probabilistic modelling of uncertainty with this free online course.
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The mathematical ways of measuring information to reduce uncertainty form the core components of this course in probabilistic modelling. The course begins by describing information and uncertainty as a process that selects one or more objects from a set of objects. You will study how probabilistic models incorporate uncertainty, which continues through to the outputs of the model. Next, you will discover how propagating uncertainty allows you to determine a range of forecasting values and study how the implied probability distribution for a chosen output metric is determined. Following this, you will be taught how a probabilistic model provides an estimate for the unknown variables. This will include the significance of probability mass functions and interval scales in distributing the probabilities over the random variable’s values. The course also explains how the limit theorems describe the asymptotic behaviour of sequences of random variables, based on normalized partial sums of another series of random variables.
Have you ever wondered how much information is revealed when answering simple questions? This course will explore quantifying the amount of information in events, random variables and distributions. You will be taught how a stochastic model is used for processing situations that have randomness or uncertainty. This will ascertain the aspects of the problem being studied, how probabilities are assigned to events within the model and how they can be used to make predictions or supply other relevant information about the process. In addition, you will learn about ascertaining the ‘information value’ of a communicated message by measuring the degree of randomness using entropy. This will include the process of measuring the average ambiguity of the signal received in the message and a measure of the probability with which a specific result is expected to happen. You will also study how hashing transforms a set of characters in a message into a shorter length representing the information.
Finally, you will learn about the process of determining the closeness of two distributions based on total distance variations. You will discover the significance of relative entropy in analyzing product measures and how the intrinsic measurements of distance are key to understanding minimum and maximum convergence rates. Generating samples from a distribution using uniform randomness will be broken down for you. By taking this course, you will develop expertise in quantifying information. The most useful probabilistic models for capturing and exploring risk assessments will be revealed. ‘Information and Probabilistic Modelling of Uncertainty’ is an informative course aimed at incorporating random variables and probability distributions into the model of an event or phenomenon. This course lays the foundation for learners to develop their interests in more specific areas, such as automatic speech recognition, probabilistic expert systems and statistical theories of vision. So, why wait? Enrol in this course and enhance your skills in the area of modelling uncertainty using probabilistic methods.Start Course Now
Information and Probabilistic Modelling
Information and Probabilistic Modelling - Learning Outcomes
Information and Modelling Uncertainty
Basic Concepts of Probability
Estimates of Random Variables and Limit Theorems
Information and Probabilistic Modelling - Lesson Summary
Uncertainty, Compression and Entropy
Uncertainty, Compression and Entropy - Learning Outcomes
Shannon Entropy and Random Hashing
Mathematical Measure of Uncertainty
Uncertainty, Compression and Entropy - Lesson Summary
Randomness and Entropy
Randomness and Entropy - Learning Outcomes
Randomness and Total Variation Distance
Measuring Randomness in a Random Variable
Typical Sets and Entropy
Randomness and Entropy - Lesson Summary
By the end of this course you will be able to:
- Define information in the context of a mathematical notion
- Explain the basic concepts of probability
- Discuss the procedure for modelling uncertainty in information
- Outline the methods of estimating unknown variables
- Describe the various methods of quantifying information
- Discuss the relationship between uncertainty and data compression
- Outline the concept of Shannon entropy and random hashing
- Identify the relationship between entropy and random variable
- Explain the method of determining the total variation distance
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