Related Experiment Video
Updated: Oct 25, 2025
09:23
Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
Published on: August 16, 2017
8.3K
Entropy, Information, and the Updating of Probabilities
1Physics Department, University at Albany-SUNY, Albany, NY 12222, USA.
Entropy (Basel, Switzerland)
|August 6, 2021
Summary
This review introduces the Maximum Entropy (ME) method, a unified inference framework. It integrates Bayesian and entropic approaches, handling diverse data and prior information effectively.
Area of Science:
- * Statistical inference
- * Information theory
- * Bayesian probability
Background:
- * Reviews a pragmatic approach to the method of maximum entropy.
- * Defines an epistemic notion of information relative to Bayesian beliefs.
- * Highlights the role of ideally rational agents in inference.
Purpose of the Study:
- * To present the Maximum Entropy (ME) method as a general inference framework.
- * To unify entropic and Bayesian methods into a single scheme.
- * To explore the pragmatic derivation and application of the ME method.
Main Methods:
- * Utilizes an eliminative induction process for updating probability distributions.
- * Employs logarithmic relative entropy as a universal updating tool.
- * Incorporates arbitrary priors and constraints within the ME framework.
Main Results:
- * The ME method unifies Maximum Entropy (MaxEnt) and Bayes' rules as special cases.
- * Logarithmic relative entropy is identified for its universal applicability and role in recognizing prior information and independence.
- * The framework handles arbitrary priors and constraints, unifying inference.
Conclusions:
- * The ME method offers a unified and general scheme for statistical inference.
- * It extends beyond selecting a single posterior to analyzing probability distribution differences.
- * Provides a bridge to theories of fluctuations and large deviations in probability.
Related Concept Videos
01:20Entropy and the Second Law of Thermodynamics
3.4K
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
3.4K
02:39Entropy
32.3K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
32.3K
01:18Entropy
3.0K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.0K
01:10Entropy Change in Reversible Processes
2.8K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.8K
01:14The Second Law of Thermodynamics
6.1K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
6.1K
01:32Probability Distributions
10.1K
The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
10.1K