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Related Concept Videos

Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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...
Probability Histograms01:17

Probability Histograms

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.
Probability in Statistics01:14

Probability in Statistics

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Classification of Signals

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Related Experiment Video

Updated: May 29, 2026

A Tactile Automated Passive-Finger Stimulator (TAPS)
19:44

A Tactile Automated Passive-Finger Stimulator (TAPS)

Published on: June 3, 2009

On bayes risk consistent pattern recognition procedures in a quasi-stationary environment.

L Rutkowski1

  • 1Department of Electrical Engineering, Technical University of Cz¿stochawa, Cz¿stochowa, Poland.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary

Pattern recognition procedures based on orthogonal series estimates are Bayes risk consistent. These methods retain their asymptotic properties even in nonstationary random environments, enhancing their robustness.

Related Experiment Videos

Last Updated: May 29, 2026

A Tactile Automated Passive-Finger Stimulator (TAPS)
19:44

A Tactile Automated Passive-Finger Stimulator (TAPS)

Published on: June 3, 2009

Area of Science:

  • Machine Learning
  • Statistical Inference
  • Pattern Recognition

Background:

  • Orthogonal series estimates are used for probability density function estimation.
  • Previous work by Van Ryzin and Greblicki established Bayes risk consistency for these procedures.
  • The robustness of these procedures in dynamic environments was not fully explored.

Purpose of the Study:

  • To investigate the asymptotic properties of pattern recognition procedures in nonstationary environments.
  • To determine if the Bayes risk consistency holds under changing environmental conditions.
  • To extend the applicability of these pattern recognition methods.

Main Methods:

  • Analysis of pattern recognition procedures derived from orthogonal series estimates.
  • Mathematical proofs to demonstrate the preservation of asymptotic properties.
  • Consideration of specific conditions under which robustness is maintained.

Main Results:

  • The study proves that the pattern recognition procedures retain their asymptotic properties.
  • These properties are maintained even when the random environment is nonstationary.
  • The findings confirm the resilience of the methods under dynamic conditions.

Conclusions:

  • Pattern recognition procedures based on orthogonal series estimates are robust.
  • These methods maintain desirable statistical properties in nonstationary settings.
  • The research expands the utility of these procedures in complex, evolving environments.