Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Probability in Statistics01:14

Probability in Statistics

13.4K
Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
13.4K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

72
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
72
Probability Distributions01:32

Probability Distributions

7.2K
 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...
7.2K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

722
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
722
Binomial Probability Distribution01:15

Binomial Probability Distribution

11.1K
A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
11.1K
Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

3.3K
A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
3.3K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026
Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026
Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026
Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026
Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026
Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: Jul 15, 2025

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

12.1K

Asymptotically Optimal Adversarial Strategies for the Probability Estimation Framework.

Soumyadip Patra1, Peter Bierhorst1

  • 1Department of Mathematics, University of New Orleans, New Orleans, LA 70148, USA.

Entropy (Basel, Switzerland)
|September 28, 2023
PubMed
Summary
This summary is machine-generated.

The probability estimation framework (PEF) certifies randomness in quantum nonlocality experiments. This study proves PEF

Keywords:
Bell inequalitiesasymptotic equipartition propertydevice-independent quantum random number generationmin-entropyquantum nonlocality

More Related Videos

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity
07:28

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity

Published on: January 21, 2017

7.0K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.6K

Related Experiment Videos

Last Updated: Jul 15, 2025

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

12.1K
Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity
07:28

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity

Published on: January 21, 2017

7.0K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.6K

Area of Science:

  • Quantum Information Theory
  • Foundations of Physics
  • Experimental Quantum Physics

Background:

  • Quantum nonlocality experiments require robust randomness certification.
  • The probability estimation framework (PEF) is a key tool for this purpose.
  • Understanding adversarial attacks is crucial for experimental validity.

Purpose of the Study:

  • To provide a self-contained proof of the asymptotic optimality of the PEF method.
  • To refine characterization of optimal adversarial attacks on the PEF protocol.
  • To analyze the robustness of PEF against experimental deviations and adversarial strategies.

Main Methods:

  • Direct estimation of outcome probabilities conditioned on measurement settings and side information.
  • Asymptotic analysis of the probability estimation framework.
  • Application to the (2,2,2) Bell scenario to derive analytic characterizations of adversarial attacks.
  • Extension to quantum-limited and no-signalling adversaries in various Bell scenarios.

Main Results:

  • A self-contained proof of the asymptotic optimality of the PEF method.
  • Analytic characterization of optimal no-signalling adversarial attacks in the (2,2,2) Bell scenario.
  • Demonstration of the PEF method's asymptotic robustness to experimental deviations.
  • Analysis of adversarial attacks in extended Bell scenarios.

Conclusions:

  • The PEF method is asymptotically optimal and robust for randomness certification in quantum nonlocality experiments.
  • The refined analysis provides better characterization of adversarial strategies.
  • Results extend to more complex adversarial models and higher-dimensional Bell scenarios.