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Binomial Probability Distribution01:15

Binomial Probability Distribution

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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,...
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Probability Distributions01:32

Probability Distributions

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 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...
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Poisson Probability Distribution01:09

Poisson Probability Distribution

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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
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Probability Histograms01:17

Probability Histograms

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A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
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Probability in Statistics01:14

Probability in Statistics

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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...
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Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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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...
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Related Experiment Video

Updated: Nov 10, 2025

A Tactile Automated Passive-Finger Stimulator TAPS
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Approximate Bayesian Computation for Discrete Spaces.

Ilze A Auzina1, Jakub M Tomczak1

  • 1Department of Computer Science, Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1111, 1081 HV Amsterdam, The Netherlands.

Entropy (Basel, Switzerland)
|April 3, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a new Approximate Bayesian Computation (ABC) method for discrete data, enhancing likelihood-free inference. The novel approach improves efficiency in complex black-box problems, offering a superior alternative for discrete random variables.

Keywords:
Approximate Bayesian ComputationMCMCMarkov kernelsdifferential evolutiondiscrete state space

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Area of Science:

  • Computational Statistics
  • Machine Learning
  • Statistical Inference

Background:

  • Many real-world processes are black-box problems, lacking accessible internal workings or defined likelihood functions.
  • Approximate Bayesian Computation (ABC) effectively addresses likelihood-free inference for continuous random variables.
  • A significant research gap exists for optimal likelihood-free inference methods for discrete random variables.

Purpose of the Study:

  • To develop and validate an optimal Approximate Bayesian Computation (ABC) method for discrete random variables.
  • To address the limitations of existing methods in handling black-box problems with discrete data.
  • To introduce a novel Markov kernel inspired by differential evolution for enhanced inference.

Main Methods:

  • An adjusted population-based Markov chain Monte Carlo (MCMC) ABC method was proposed.
  • Standard ABC parameters were redefined for discrete variables.
  • A novel Markov kernel, inspired by differential evolution, was introduced and integrated into the MCMC ABC framework.

Main Results:

  • The proposed Markov kernel demonstrated effectiveness on a likelihood-based disease network inference problem.
  • The complete likelihood-free inference method was successfully applied to a discrete QMR-DT network, binary neural networks, and neural architecture search.
  • The novel method and Markov kernel showed high potential and superiority over existing approaches for discrete data.

Conclusions:

  • The developed ABC method offers a powerful new tool for likelihood-free inference with discrete random variables.
  • The novel differential evolution-inspired Markov kernel significantly enhances the performance of ABC methods in discrete domains.
  • This research fills a critical gap, paving the way for more robust statistical inference in complex, black-box scenarios involving discrete data.