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Related Concept Videos

Expected Value01:15

Expected Value

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:In the equation, x is an event, and P(x) is the probability of the event occurring.The expected value has practical applications in decision theory.This text is adapted from Openstax, Introductory Statistics, Section 4.2 Mean or Expected Value and...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
Probability Distributions01:32

Probability Distributions

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 probability...
Probability in Statistics01:14

Probability in Statistics

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...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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Published on: March 1, 2022

A trick for computing expected values in high-dimensional probabilistic models.

Christian Leibold1

  • 1Department Biology II, Ludwig-Maximilians-University Munich and Bernstein Center for Computational Neuroscience Munich, Grosshaderner Strasse 2, Planegg, Germany. leibold@bio.lmu.de

Network (Bristol, England)
|December 14, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a numerical trick to simplify calculations for high-dimensional neural representations. It offers an alternative to complex Monte-Carlo methods for computing expected values in sensory coding.

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Area of Science:

  • Computational neuroscience
  • Neural coding theory

Background:

  • Sensory stimuli are encoded by thousands of neurons in parallel, creating high-dimensional data.
  • Analyzing these high-dimensional representations presents significant computational challenges, particularly in calculating expected values from probability distributions.

Purpose of the Study:

  • To present a novel numerical trick for overcoming precision issues in high-dimensional computations.
  • To offer a simpler alternative to existing indirect methods like Monte-Carlo sampling for expected value calculations.

Main Methods:

  • A new numerical trick is described to address the problem of required high numerical precision.
  • This method bypasses the need for direct, computationally intensive calculations.

Main Results:

  • The described numerical trick effectively overcomes the challenge of high numerical precision.
  • It provides a straightforward alternative to stochastic sampling techniques.

Conclusions:

  • The proposed numerical trick simplifies computations in high-dimensional neural representations.
  • This offers a more accessible approach for analyzing sensory coding compared to traditional methods.