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On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
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The human brain processes information for decision-making using one of two routes: an intuitive system and a rational system (Epstein, 1994; popularized by Kahneman, 2011 as System 1 and System 2, respectively). The intuitive system is quick, impulsive, and operates with minimal effort, relying on emotions or habits to provide cues for what to do next, while the rational system is logical, analytical, deliberate, and methodical. Research in neuropsychology suggests that the...
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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. However, sometimes, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the...
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Related Experiment Video

Updated: Nov 27, 2025

A Tactile Automated Passive-Finger Stimulator TAPS
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Guessing with a Bit of Help.

Nir Weinberger1, Ofer Shayevitz2

  • 1Institute for Data, Systems, and Society and Laboratory for Information & Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

This study quantifies the value of limited information bits for guessing random data. Limited bits significantly improve guessing accuracy, with potential for optimal performance using specific functions.

Keywords:
boolean functionsfourier analysisguessing momentsguessing with a helperhypercontractivitymaximum entropystrong data-processing inequalities

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Area of Science:

  • Information Theory
  • Computer Science
  • Probability Theory

Background:

  • Investigates the utility of a small number of information bits for improving data guessing.
  • Focuses on scenarios where Alice guesses an independent and identically distributed (i.i.d.) random vector using bits from Bob, who observed it via a memoryless channel.

Purpose of the Study:

  • To determine the value of a fixed number of information bits (k) for a guesser.
  • To analyze the guessing ratio, defined as the ratio of guessing moments with and without Bob's bits.

Main Methods:

  • Analysis of dictator and majority functions for upper bounds on the guessing ratio.
  • Application of maximum entropy and Fourier-analytic/hypercontractivity arguments for lower bounds.
  • Extension of maximum entropy argument to general channels using the strong data-processing inequality constant.

Main Results:

  • Provided two upper bounds for the guessing ratio for uniform binary vectors over a binary symmetric channel.
  • Established lower bounds using maximum entropy and Fourier analysis.
  • Derived a general lower bound for binary uniform input channels.

Conclusions:

  • The study provides bounds on the guessing ratio, quantifying the value of limited information.
  • Conjectures that greedy dictator functions may achieve optimal guessing ratios for certain channels.
  • Extends information-theoretic bounds to general memoryless channels.