Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

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...

Uncertainty: Overview

Uncertainty: Overview

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.

Propagation of Uncertainty from Systematic Error

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...

Propagation of Uncertainty from Random Error

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...

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

Confidence Intervals

Confidence Intervals

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...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

A physics-informed alternative to Richardson-Lucy deconvolution across SNR regimes without iteration cutoffs.

Nature communications·2026

Same author

Optimization of first-line treatment selection in advanced pancreatic adenocarcinoma using artificial intelligence.

NPJ precision oncology·2026

Same author

Ribosomal allostery as a potential regulator of bacterial dormancy.

Nature communications·2026

Same author

Mitochondria directly interact with the nuclear pore complex.

Nature·2026

Same author

Stochastic colonization and host-to-host transmission shape gut bacterial variability.

bioRxiv : the preprint server for biology·2026

Same author

Simulation-based inference captures non-Markovian effects as exemplified in protein production kinetics through cell division.

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Correlated clustering and projection for dimensionality reduction.

Machine learning: science and technology·2026

Same journal

An Attention-based Spatio-Temporal Neural Operator for Evolving Physics.

Machine learning: science and technology·2026

Same journal

MDCrow: automating molecular dynamics workflows with large language models.

Machine learning: science and technology·2026

Same journal

CAP: Commutative algebra prediction of protein-nucleic acid binding affinities.

Machine learning: science and technology·2026

Same journal

FDDM: Unsupervised Medical Image Translation with a Frequency-Decoupled Diffusion Model.

Machine learning: science and technology·2026

Same journal

Depthwise-Dilated Convolutional Adapters for Medical Object Tracking and Segmentation Using the Segment Anything Model 2.

Machine learning: science and technology·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Sep 8, 2025

A Data-Driven Approach to Quantifying Immune States in Sepsis

A Data-Driven Approach to Quantifying Immune States in Sepsis

Published on: February 7, 2025

Mamba time series forecasting with uncertainty quantification.

Pedro Pessoa^1,2, Paul Campitelli^1,2, Douglas P Shepherd^1,2

¹Center for Biological Physics, Tempe, AZ, United States of America.

Machine Learning: Science and Technology

|July 24, 2025

Summary

This summary is machine-generated.

State space models like Mamba show promise for time series forecasting but lack accurate uncertainty quantification. Our Mamba-ProbTSF method enhances Mamba by modeling predictive uncertainty, improving forecast reliability for electricity and traffic data.

Keywords:

Time Series Forecasting non-linear dynamics state space models uncertainty quantification

More Related Videos

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

Published on: July 1, 2014

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Related Experiment Videos

Last Updated: Sep 8, 2025

A Data-Driven Approach to Quantifying Immune States in Sepsis

A Data-Driven Approach to Quantifying Immune States in Sepsis

Published on: February 7, 2025

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

Published on: July 1, 2014

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Area of Science:

Machine Learning
Time Series Analysis
Probabilistic Forecasting

Background:

State space models, including Mamba, are increasingly used for time series forecasting due to their sequence pattern recognition capabilities.
Existing Mamba implementations show significant mean errors in electricity consumption (approx. 8%) and traffic occupancy (approx. 18%) benchmarks.
There is a need to quantify the uncertainty in Mamba forecasts to distinguish between inaccuracy and inherent data variability.

Purpose of the Study:

To develop a method for quantifying the predictive uncertainty of Mamba-based time series forecasts.
To introduce a dual-network framework, Mamba-ProbTSF, for probabilistic forecasting using the Mamba architecture.
To evaluate the performance and reliability of Mamba-ProbTSF against existing methods.

Main Methods:

Proposed a dual-network framework integrating Mamba for probabilistic time series forecasting.
One network generates point forecasts; a second network models predictive uncertainty by estimating variance.
Implemented the Mamba with probabilistic TSF (Mamba-ProbTSF) tool, with code available on GitHub.

Main Results:

Achieved reduced Kullback-Leibler divergence (10^-3 for synthetic, 10^-1 for real-world data), indicating improved probability distribution modeling.
Validated that true trajectories fall within the predicted two-sigma uncertainty interval approximately 95% of the time for benchmark datasets.
Demonstrated consistently lower forecast errors and more reliable uncertainty quantification compared to DeepAR and ARIMA.

Conclusions:

Mamba-ProbTSF effectively quantifies predictive uncertainty in Mamba forecasts, enhancing reliability for time series forecasting tasks.
The method shows superior performance over leading probabilistic forecasting models like DeepAR and ARIMA.
The framework holds potential for application in stochastic processes, including Brownian motion and molecular dynamics.