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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 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...

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...

Decision Making: P-value Method

Decision Making: P-value Method

The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim is also stated. These statements can act as null and alternative hypotheses: a null hypothesis would be a neutral statement while the alternative hypothesis can...

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...

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

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Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations

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Optimal policy for uncertainty estimation concurrent with decision making.

Xiaodong Li¹, Ruixin Su¹, Yilin Chen²

¹CAS Center for Excellence in Brain Science and Intelligence Technology, Institute of Neuroscience, Chinese Academy of Sciences, Shanghai 200031, China; University of Chinese Academy of Sciences, Beijing 100049, China.

|March 16, 2023

Summary

This summary is machine-generated.

This study introduces a new way to measure uncertainty in decision-making, showing how it interacts with choices. The findings offer a value-based framework for understanding perceptual decisions and uncertainty.

Keywords:

CP: Neuroscience confidence decision making drift-diffusion model meta-cognition multiple choices reaction time uncertainty value

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Area of Science:

Cognitive Neuroscience
Decision Science

Background:

Decision-making frequently involves uncertain information, impacting choices.
Uncertainty is a quantity influenced by sensory evidence and cognitive factors.
Current models often do not fully capture the interplay between uncertainty and decision formation.

Purpose of the Study:

To develop a method for subjects to report uncertainty independently of a decision.
To investigate how explicitly reporting uncertainty affects perceptual decision-making.
To establish a value-based theoretical framework for studying uncertainty in cognitive processes.

Main Methods:

Adapted the random-dot motion direction discrimination task.
Enabled subjects to indicate uncertainty before making a decision.
Measured choices, reaction times, and uncertainty responses.
Developed a value-based model using a drift-diffusion process.

Main Results:

The model successfully accounts for key behavioral patterns in decision-making and uncertainty reporting.
Individual variations in decision-making and uncertainty were explained by the model.
The addition of an uncertainty option significantly impacted perceptual decision strategies.

Conclusions:

A novel value-based framework for studying uncertainty and perceptual decisions has been established.
This framework provides insights into the interaction between uncertainty computation and decision optimization.
The approach is applicable for future research into the neural mechanisms of decision-making and uncertainty.