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Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

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...

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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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

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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...

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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.
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Cuantificación de la inferencia de la red con la suficiencia de los datos

Bharat Singhal¹, Jorge Luis Ocampo-Espindola², K L Nikhil³

¹Department of Electrical and Systems Engineering, Washington University in St Louis, St. Louis, Missouri 63130, USA.

IEEE transactions on network science and engineering

|August 28, 2025

Resumen

La determinación de la suficiencia de los datos es crucial para una inferencia de red precisa. Este estudio introduce un método estadístico que utiliza intervalos de confianza para cuantificar la variabilidad de los datos, garantizando una reconstrucción fiable de la topología de la red.

Palabras clave:

Intervalos de confianza Inferencia de la red Topología de la red Osciladores no lineales

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Área de la Ciencia:

Ciencia de los sistemas complejos
Ciencia de las redes
Inferencia estadística

Sus antecedentes:

La inferencia de red reconstruye la conectividad del sistema a partir de datos, vital para comprender los sistemas físicos, biológicos y químicos.
Los métodos actuales basados en datos a menudo pasan por alto la cuestión crítica de la suficiencia de datos para una topología de red precisa.
La reconstrucción precisa de la red requiere suficiente variabilidad de los datos para inferir de manera confiable las estructuras subyacentes.

Objetivo del estudio:

Desarrollar un método estadístico para evaluar la suficiencia de los datos en la inferencia de red.
Cuantificar la incertidumbre en la conectividad de red inferida basada en la variabilidad de los datos.
Asegurar que las topologías de red inferidas reflejen con precisión la verdadera estructura de red subyacente.

Principales métodos:

Utilización de intervalos de confianza paramétricos para definir los límites de las intensidades de conexión reales.
Desarrollo de una técnica para evaluar la variabilidad de los datos para la precisión de la inferencia de red.
Aprovechando la cuantificación de la incertidumbre para la conectividad inferida.

Principales resultados:

El método estadístico propuesto determina efectivamente la suficiencia de los datos para la inferencia de red.
La validación en las redes de osciladores Kuramoto y Stuart-Landau demuestra la precisión del método.
La aplicación exitosa a los datos de la red de osciladores electroquímicos experimentales confirma el poder predictivo.

Conclusiones:

La técnica de suficiencia de datos desarrollada es esencial para una inferencia de red confiable.
Este método mejora la confiabilidad de las reconstrucciones de la topología de red.
Proporciona una medida cuantitativa para garantizar datos suficientes para un análisis preciso del sistema.