Questions tagged [uncertainty]
A broad concept concerning lack of knowledge, especially the absence or imprecision of quantitative information about a process or population of interest.
545 questions
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Standard error on elements in covariance matrix?
I have multiple random (gaussian) variables.
Just as one can calculate the standard error on the mean, I expect to be able to calculate standard error on the variances and standard error on the ...
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The meaning of "a region of data space where the model is poorly constrained"
In reading "Understanding Measures of Uncertainty for Adversarial Example Detection" (Gal, Lewis) - https://arxiv.org/abs/1803.08533, I came across the following line:
"we want to ...
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Probabilistic machine learning models: parameter uncertainty
Consider models such as DeepAR, ngboost and other frameworks to the general problem of predicting the parameters of some parametric distribution with some black-box function, call it f(X). The ...
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Distributions as Features in Machine Learning
The Problem
Let's assume I have a problem that seems perfect for supervised learning. However, some of the measurements I would like to use as features are not point estimates but are instead ...
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Uncertainty/Standard Deviation of Monte Carlo methods
I am using a Monte Carlo method to estimate the expected value of the results of certain simulations.
Consider this simplified case: $X, Y$ are independent random variables and $g(X,Y)$ is a nonlinear ...
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How to represent the interval or uncertainty on regression predictions in an 'experimental vs predicted' plot?
Using an example similar to the one from R predict, simulate some independent variable ($x$) data, map them to an observed ...
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Take into account uncertainty in ground-truth in a classification
I need to evaluate the accuracy of a prediction model (binary classification), given that I have some kind of uncertainty on the ground truth measurement.
The model predicts the occurrence of an event ...
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When to use standard deviation versus standard error in linear error propagation
I have a question about linear error propagation. Let's say that I want to use an equation to calculate n, where n = (PV)/(RT) (eq.1)
I only take one measurement of P, and one measurement of T, but I ...
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How to model an uncertain (or erroneous) truncation effect on a random variable?
Let $ V_a $ be a random variable which is truncated at a value $v_c$. Therefore, the updated density function of truncated $V_a$ is given by,
$$ f(v_a| V_a\leq v_c) = \frac{g(v_a)}{F(v_c)}$$
where $g(...
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How to measure uncertainty in binary data?
I want to clusterize binary data, so each object is vector of 50 binary values. For real number I can measure standard deviation in each cluster, or something like that. What can I use for binary data?...
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What is the best way to fit data with multiple y-values per x-value and and get standard error at an extrapolated value?
I am running an experiment where I am collecting data for 3 x-values, say X = [x1, x2, x3] (each x > 0).
For each of the x ...
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Absence and presence of uncertainties in a data
In the photo attached, I am comparing the D, Ra, H, and AED values of Glutinous rice in Songkhla (see 4th to the last row) to the rest of the values. I understand why most of it has uncertainty ...
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MLE with Model Uncertainty
I am trying to estimate the amount of background in some physics data by using MLE to fit a weighted sum of a signal and background distribution to the data where the weights indicate what percentage ...
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How to find an intersection of confidence intervals [closed]
I need to calculate the uncertainty level of the intersection point of two lines given that we know the confidence intervals (CI) for both lines.
Is the intersection of lines CIs would be a ...
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Bootstrapping (aleatoric and epistemic) risk score uncertainty
I am working on various risk score estimation problems. I assume individual subjects are associated with a true risk
$$r_i = f(x_i; \epsilon_i), \quad 0 \leq r_i \leq 1,$$
where $x_i$ is some ...
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What is the uncertainty of Leave-one-out-cross-validation method?
I have used the LOOCV to validate my model. As we know, the LOOCV method is a special case of cross-validation where the number of folds equals the number of instances in the data set. Thus, the ...
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Risk score uncertainty quantification
I am working on various risk score estimation problems. I assume individual subjects are associated with a true risk
$$ r_i = f(x_i, \varepsilon)$$
where $x_i$ is some available information about the ...
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Algorthm for discerning which top X values in a list are statistically ranked higher than the bottom Y
Given a ranked list, which contains values with high uncertainty, I would like to remove as many of the middle values that have high overlap in uncertainties as possible, and be left with more or less ...
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How to determine uncertainty of data from a bayesian posterior distribution
I am a bit confused as to how we determine the uncertainty of a set of data from Bayesian Analysis.
In my specific case, I am asked the following:
Assume $f(x,x_0)$ as the correct model for the ...
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Learned Loss Attenuation for Classification
In the paper What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision? they propose loss functions that capture aleatoric uncertainty. My question heavily relies on understanding of ...
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Testing for difference in means between two groups for which each measurement has a unique associated uncertainty
I am wondering what type of statistical test would be appropriate to test for a difference in means between two groups for which each measurement has a different uncertainty. For example, I want to ...
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How do I make different distributions objectively comparable?
I have some model, $f(x)$, that takes in some input and produces some output. Now my input are random variables distributed according to some distribution. The output are also random variables with ...
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Random Forest - varying seed to quantify uncertainty
I would like to quantify the uncertainty of a Random Forest binary classifier.
The idea that popped in my mind was to fit the Random Forest 100 times with different seeds. Computing the variance of ...
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What is the relationship between the residuals of an objective function and the uncertainties of the minimizer values?
Consider I have some optimization problem and an objective function $f(x, y, z)$.
$f$ is defined using the sum of squared residuals, i.e. for some function $g$, we have $f(x, y, z) = \sum[g(x, y, z) - ...
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Whats the best representation of variables with large uncertainty
When express results with uncertainty it's common that sometimes these uncertainty pass the limit allowed of the variable.
For example, training a classificator model with an expected accuracy we ...
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111
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Extending F1 score to classification with uncertainty
I have a classifier that can return yes, no's and "maybe"s.
The maybe indicates that we don't have certainty in a prediction because the data point is is not sufficiently close to it's ...
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Weighted mean and error propagation, again
I was trying to implement the method proposed by @whuber in this question to average some of my data. For example:
$62.7\pm 6.8$
$65.3\pm 0.94$
$66.5 \pm 6.0$
$71.8 \pm 7.8$
So far, I have two ...
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What is the relationship between model uncertianty and model parameter count?
I'm looking for references, information and/or existing theory behind the relationship between the uncertainty in a given model vs its complexity/parameter count. The situation I have in mind is using ...
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How to compare two quantities with uncertainties?
I've got two instruments that measure one quantity. One of them is regarded to be more precise, therefore, I use this measurement as a reference. Then, I take two measurements of the same quantity ...
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Model uncertainty in a logistic regression model - binomial proportion confidence interval
In my line of work I have seen people quantify general model uncertainty, when using a logistic regression model, with an Agresti-Coull confidence interval. I am not convinced that this is correct, ...
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Departure from uniformity histogram
Let us consider the histogram of a random variable. It is uniform up to a certain value $\bar{x}$, while beyond it a growth is present,as shown in the figure. I would like to obtain an estimate of the ...
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Is it possible to use a Gibbs sampler for uncertainty propagation?
Situation:
10 basic numeric properties are predicted using quantile regression forest, then they are put into a desicion rule system to decide land management. The desicion rules result in one class (...
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Uncertainty estimation in the input space
my input is an array between 0 and 1000 and the output is the corresponding system velocity. The input value is randomly generated (for instance by using the function in Python ...
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Uncertainty over set of slopes from least-squares
I got several slopes, of the same measurement, taken in different samplings. All slopes come from least-squares fit, which allows to determine a stadard error associated to that slope, but how do I ...
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Bayes theorem with errors
I have a situation in which I want to calculate, for a given $y$ (which I measure experimentally), the probability distribution of $x$ i.e. $p(x|y)$ (actually what I need is the value of x for which ...
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Error bars through simulation
Supose I have made an experiment and got three sets of measurements :
$$X=\{x_1,...,x_n\}$$
$$Y=\{y_1,...,y_n\}$$
$$Z=\{z_1,...,z_n\}$$
I also have three sets of standard errors for each measurement:
$...
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variance of partial covariance
Consider three non independent random variables : $Z,Z_i,Z_j$, the partial covariance is given by:
$$pcov(Z_i,Z_j;Z)=cov(Z_i,Z_j)-\frac{cov(Z_i,Z)cov(Z_j,Z)}{var(Z)}$$
Suppose I know estimates of all ...
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Uncertainty on covariance
I think this is an easy question but I didn't find any convincing answer yet:
In an experiment I have made two sets of measurements for two random variables $X$ and $Y$:
$$X=(x_1,...,x_N)$$
$$Y=(y_1,.....
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Estimate uncertainty of window average
I have some random process $y(t)$ that represent an unknown signal combined with some random high frequency positive feedback noise, that is noise amplitude grows with the value of the signal.
I think ...
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What is the difference between a non-zero nugget and a noise term in Kriging/GPR?
With some Gaussian Process Regression/Kriging models, it's possible to specify both a non-zero nugget, and a noise term. For example, in Scikit-learn's GPR model, there is an ...
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What is the frequentist interpretation of uncertainty vs. variability?
I have been reading Begg, Welsh, and Bratvold (2014), which is an excellent and lucid discussion of the distinction between uncertainty and variability (from a petro/geostatistics perspective). The ...
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The law of large numbers and coin flip probability
I really appreciate some help with the mathematics behind an example I came across:
Suppose a fair coin flip where you are getting a 50% chance for heads. If you want to be 98% certain to make a ...
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confidence intervals versus probability bounds
I performed a Monte Carlo simulation of a multi-input parameter system and generated a 95% Confidence Interval (CI) of the response output mean. The input parameters were all normally distributed with ...
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Uncertainty when substracting average from the same data set
I have a data set with its own measurement uncertainties. Then I do averaging of the population and use standard error of the mean as the uncertainty for the average.
My question is, I need to ...
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Uncertainity band in Neural networks
I am working on a problem where I have to give the uncertainty band of my predictions like the image attached.
I have seen a StackExchange solution for this, but in the solution code, we are using ...
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Given a population of values which each have unique uncertainties, how do I determine the mean and standard deviation of the population?
I'm trying to determine if a material has a different spectroscopic response under different conditions. In short, I measure 100 points on the sample, and the data output at each point is a data ...
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Determining the precision of a range
Supposing that I have 2 measured values which cover a range Y and Z and the actual value "X" is somewhere in the middle. How can I calculate the precision of the range? I expected to ...
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What uncertainties to use when fitting a distribution model to binned sample data?
A common task is to fit to a sample of $N$ data $x_i$ (assumed 1D for the sake of argument) a model $p(x|a)$ (normalized to unit integral) for their distribution with some parameters $a$. One way is ...
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Error propagation for cubic relationship
I have the cubic relationship between two variables, x and y, and I need to find the error in x.
y = ax^3 + bx^2 + cx + d
I have the values for the coefficients and their respective uncertainties. I ...
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How can I find the uncertainty of derivatives? [duplicate]
Suppose I have a quadratic (weighted) least-square fit result obtained from a given set of data:
$$
f(x) = \underbrace{-0.243(\pm0.3324)}_{quad\_a}x^2\underbrace{-0.921(\pm0.061)}_{quad\_b}x\...
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