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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

10.9K
An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

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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....
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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

9.0K
A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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Confidence Coefficient01:24

Confidence Coefficient

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Monte Carlo profile confidence intervals for dynamic systems.

E L Ionides1, C Breto2, J Park2

  • 1Department of Statistics, The University of Michigan, Ann Arbor, MI, USA ionides@umich.edu.

Journal of the Royal Society, Interface
|July 7, 2017
PubMed
Summary
This summary is machine-generated.

Profile likelihood methods address Monte Carlo uncertainty in complex models, enabling reliable frequentist inference even when computation cannot eliminate error. This facilitates scientific investigation in challenging areas like disease transmission.

Keywords:
likelihood-based inferencepanel dataphylodynamic inferencesequential Monte Carlospatio-temporal datatime series

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Area of Science:

  • Statistics
  • Computational Statistics
  • Epidemiology

Background:

  • Monte Carlo methods are crucial for likelihood-based inference in intractable models.
  • Standard inference methods assume negligible Monte Carlo error, which is often unachievable with large datasets and complex models.

Purpose of the Study:

  • To develop profile likelihood methodology for frequentist inference that accounts for Monte Carlo uncertainty.
  • To investigate the application of this methodology to computationally challenging dynamic latent variable models.

Main Methods:

  • Development of profile likelihood methodology to incorporate Monte Carlo uncertainty.
  • Application to nonlinear dynamic models using genetic sequence and panel time-series data.

Main Results:

  • The proposed methodology provides reliable frequentist inferences in the presence of non-negligible Monte Carlo error.
  • Demonstrated successful inference for infectious disease transmission models.

Conclusions:

  • Profile likelihood offers a robust approach to statistical inference for complex models where Monte Carlo error is significant.
  • The methodology is applicable to various data types including time-series and spatio-temporal data.