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
2
votes
0
answers
43
views
Epistemic uncertainty in classical probability
I've been a statistician for a long time and have recently moved towards more information theoretic research. Because of this, the question of epistemic uncertainty in classical probability has been ...
1
vote
0
answers
27
views
Unreliability attenuation correction affects Cohen's d and its standard error. How do I use uncertainty propagation to estimate the correct SE?
Assume I am using Cohen's d to quantify some kind of effect. Since Cohen's d is defined (simplified) as $$d = \frac{MD}{\sigma_x}$$ $MD$ reflects a differences in means, which is standardized by the ...
- 163
4
votes
0
answers
71
views
Major discordance between uncertainties estimated by `predictInterval()` and `bootMer()` for binomial GLMM with cloglog link
We have been using predictInterval() from the merTools package to bootstrap uncertainty for binomial GLMM models (complementary ...
1
vote
1
answer
48
views
The interpretation of the term "uncertainty" in statistics vs. information theory vs. machine learning
I have an ensemble model consisting from multiple classifiers and I wish to quantify the uncertainty of the predictions the ensemble model makes. From an information theory / machine learning ...
- 5,907
3
votes
1
answer
33
views
Error propagation in variance calculation
Let's assume that I have $n$ measurements $\mathbf{x} = (x_1, ..., x_n)$ of a given quantity $X$, e.g. regression coefficients. Each $x_i$ has a corresponding standard error $SE_i$. I'd like to ...
- 75
0
votes
0
answers
59
views
Terminology for types of errors and uncertainty: intrinsic? fitting?
Say I have a sequence of given variables $x_i$, $i=1,\ldots,n-1$ and the response $y_i$ and we explore the model $y_i\sim \text{Normal}(\alpha x_i,\sigma^2)$ with $y_i$ independent of $y_j$ for $i\neq ...
- 111
0
votes
0
answers
14
views
When do I use standard deviation of a variable vs. error propagation of that variable when determining uncertainty?
Let's say I have 2 quantities to measure, $x$ and $y$. They do not have uncertainty but I can make repeated measurements to determine their uncertainty via standard deviation. Then say I want to find $...
Jonah George
1
vote
1
answer
22
views
Error estimation in weighted cubic fitting
Given the dataset $(t_i, y_i)$ with absolute errors $\varepsilon_{y_i}$, I want to fit a weighted cubic function and get the errors on interpolated values $\hat{y}(t)$:
$$
\hat{y}(t) = \sum^{3}_{j=0}...
- 113
0
votes
0
answers
35
views
Heteroscedastic variance prediction constant where it should not be
I am trying to make predictions about the heterscedastic noise in my dataset. I have an FPN already set up, treating the variance as an additional class. My dataset is the aerial semantic segmentation ...
0
votes
0
answers
14
views
Comparing two (derived) quantities for which uncertainty is known
I need to determine if two quantities, A and 𝐵, with their associated uncertainties, $u_A$ and $u_B$, are statistically different.
Both quantities have been derived from measurements.
The ...
1
vote
1
answer
34
views
Models with Uncertainty in Y
Let's say I have data with predictors x1, x2, x3...xn for a variable y. I have essentially imputed y using a Bayesian analysis, which means I have a posterior distribution for each value of y. To ...
- 107
1
vote
1
answer
54
views
How do I estimate the standard deviation of the measured variables in linear regression?
Assuming a linear model:
$$
y = \alpha x + \beta
$$
I make n observations of $(x_i,y_i)$.
Each observation is subject to a measure uncertainty that I assume to be normally distributed with mean = 0 ...
- 601
0
votes
0
answers
13
views
Is TTA (test-time augmentation) somehow related to Bayesian DL?
I'm trying to make up a taxonomy of UQ methods for deep learning models, if possible (this paper provides a nice overview imo, albeit in a specific field).
Currently there's cluster of UQ approaches I'...
1
vote
0
answers
29
views
Is the variance formula for error propagation useful when f is not normally distributed?
I make n measurements of different properties. E.g. the weight and the volume of an object (n=2).
Since there are uncertainties in the measurements I model this as
n independent random variables $X_i$ ...
- 601
4
votes
1
answer
119
views
Uncertainty of ANN outputs as distribution parameters
It is not an uncommon practice to train neural network models via negative log likelihood $-\mathcal{L}(x, y_{true}, \mu, \sigma)$ to estimate both a location ($\mu$) and a scale ($\sigma$), such that ...
- 167
1
vote
2
answers
148
views
Relative vs. absolute error bars in log-scaled plots
There's conflicting info from seemingly knowledgeable sources about the correct way to show error bars on a log-scaled plot.
$log_{10}(x \pm \Delta x)$ shows the absolute error. On the one hand, it's ...
- 165
2
votes
0
answers
69
views
What is the distribution of a ratio of two normal distributions? [duplicate]
Assume that I have a resistor with an unknown resistance R. I measure the current trough it, I, and the voltage across it, U.
I can then estimate R:
$$
\hat{R} = \frac{U}{I}
$$
Let us assume I get the ...
- 601
1
vote
0
answers
19
views
Neural networks with uncertainties in training data
I have used Flax to train a neural network to fit a model to some data. All of the data points have a known uncertainty, as in each row has both a value and an uncertainty. (To be more explicit: the ...
- 3,132
0
votes
0
answers
22
views
Propagation of uncertainties for high signal-to-noise ratio measurements
I am writing mass spectrometry data reduction software which calculates 4He volumes, and I have some questions about the propagation of uncertainties.
The system in question measures helium volumes by ...
- 113
1
vote
0
answers
21
views
Getting accurate Uncertainty from MFVI?
I wanted to know if there has been any research on methods to improve the accuracy of Mean-Field Variantional Inference (which doesn't discard the mean-field approximation). Apparently it is known to ...
- 451
1
vote
1
answer
87
views
Errors on cubic fits are relative to the order of magnitude of the y-data, not fit quality
I am writing some mass spec data reduction software (specifically, residual gas analysis mass spectrometry). I recently implemented a cubic fitting algorithm as an optional feature, however, some of ...
- 113
0
votes
0
answers
15
views
How to determin the theoretical prediction limit for a complex process?
how can we find out what is the theoretical prediction limit for a complex process?
For example, for a coin toss (on average) the prediction limit is 50%, that is we cannot predict better than this ...
- 73
0
votes
0
answers
19
views
How can uncertainties in a generative model be propagated to an overall log-likelihood?
I am trying to use a Bayesian approach to carry out model selection and estimate the posterior distributions for parameters in a peak fitting scenario (quasi elastic neutron scattering). The ...
- 101
0
votes
0
answers
31
views
How to aggregate the uncertainty around many predictions?
I have predicted trends for hundreds of time series. Each trend prediction comes with its own upper and lower bound at each time step. I would like to aggregate these trends and report them. Taking ...
- 417
0
votes
0
answers
25
views
Estimating variance from several samples
If several samples are taken from a distribution, say Gaussian, each sample having size n1,n2,n3,... and the SD of the underlying distribution is estimated from each of the samples, how can those ...
- 152
2
votes
0
answers
20
views
Distribution of tuples in chaotic sequences
I study infinite aperiodic sequences like Thue-Morse.
Simple substitution rules allow you to get even more complex.
I'm interested in the distribution of tuples in such sequences.
For example, in Thue-...
- 253
0
votes
0
answers
18
views
Combining Variation and Uncertainty from Replicate measurements
I have 3 measurements from 3 independent experiments {m_1, m_2, m_3}.
I have another 3 measurements that are used to scale the m measurements {n_1, n_2, n_3} from the same experiment (different from m)...
- 11
0
votes
1
answer
54
views
Quantifying prediction uncertainty using deep ensembles: How to combine Laplace distributions?
For a regression problem, I want to train an ensemble of deep neural networks to predict the labeled output as well as the uncertainty, similar to the approach presented in the paper Simple and ...
- 1
1
vote
1
answer
62
views
Parameter uncertainty in curve fitting
My real problem has a much more complexity and a different function than following. However, for the sake of simplicity assume I have a data that can be described as a one dimensional Gaussian ...
- 173
1
vote
1
answer
32
views
Mean difference Confidence interval Repeated measures anova
I´m doing 4 repeated measures (T1, T2, T3 and T4) with each subject in the same conditions to calculate repeatability. I have 10 subjects.
Could be correct to report posthoc mean differences 95% ...
- 91
1
vote
0
answers
36
views
Error propagation: How to sum errors over 2D grid?
I have a dataset with worldwide mass change data and their uncertainty from glaciers. Both have dimensions 720,360,45 with the first two dimensions 'i,j' (lat,lon) coordinates and the third dimension '...
- 11
0
votes
0
answers
42
views
Calculating the uncertainty of a very complicated variable
You have taken $N \gg 1$ measurements of a group of variables $V$. You want to estimate the value of a quantity $\mu$ that can be estimated from these variables. Fortunately you have a formula $\mu(V)$...
- 111
4
votes
1
answer
53
views
Determination of the uncertainty of the cosine of the half angle of a measured angle
I am trying to determine the uncertainty of the cosine of the angle, $\beta$, when the angle that is measured is $2\beta$. If the uncertainty in the measurement of $2\beta$ is 1 degree, then is the ...
- 43
0
votes
0
answers
34
views
Binomial Test for data with normally distributed messurement error
I have a series of measurements and I want to perform a binomial test to see if the chance of exceeding some value $a$ is less or equal to some $p_0$. The measurement has some error which is normally ...
- 63
1
vote
1
answer
52
views
Standard error calculation for difference in means
In the case of two independent samples, the formula for standard error of the difference in means is given by :
$$\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$$
Even though we are talking about a ...
- 681
0
votes
0
answers
75
views
Confidence and prediciton intervals for power law fit
I would like to determine confidence intervals and prediction intervals for a noisy dataset that follows a power law distribution.
I have a dataset that (to my eye) follows power law behavior in the ...
2
votes
0
answers
42
views
Doesn't aggregating time series sometimes throw away quantifiable uncertainty?
Introduction
From time-to-time I hear a claim that it is better to forecast on aggregated data because it is more "stable" or has less uncertainty.
Here is an example, although I know I have ...
- 9,660
0
votes
0
answers
32
views
Unifying predictions from the same model but with differing assumptions
I'm working with the same dataset and I'm exploring several approaches to modelize it. Each model applies the same model but operates under different assumptions, such as:
Stationarity vs. Non-...
- 1
2
votes
1
answer
62
views
Detecting a single change point within an interval with a certain probability
I have a dataset $D$ of binary values, with length $|D|$. There is some unknown $d \in \left[1,2,\ldots,|D|\right]$ (usually, $d$ will be somewhere in the middle) such that, for any $i<d$, $D_i$ ...
- 227
0
votes
0
answers
22
views
How can I combine fully measured with partially measured outcomes in an IPD (Network) Meta-Analysis?
I was asked to help in an Individual-Patient Data (IPD) Network Meta-Analysis (NMA). Outcomes are supposed to measure combined scores of condition 1 and condition 2 (thus: $Score=Score_1 + Score_2$), ...
- 1,262
1
vote
0
answers
50
views
Binomial Test with uncertin data
I got observational data whether some elements of a population have certain characteristic or not. I want to see if the probability for carrying that characteristic is less than some threshold. This ...
- 63
1
vote
1
answer
132
views
Calculate mean and standard deviation of the ratio of two dependent variables
I have an instrument of which I would like to understand the uncertainty on the measurements taken, so that every time that I perform a single measurement, I can apply the error obtained and therefore ...
- 111
2
votes
0
answers
17
views
Looking to extract patterns from sequences of codes
I have the following problem: I have a registration of people who enter a building, I have the name, entry date and end date. I also have the times at which events occur inside the building.
I want to ...
- 205
1
vote
0
answers
71
views
Uncertainty in values predicted using a linear regression
I am quite new to statistical analysis, so this question might seem a bit obvious. My problem is the following. I have performed a simple linear regression between two sets of values without ...
- 11
1
vote
0
answers
43
views
Derivations of loss functions for learning loss attenuation in Bayesian DL
I'm fairly new to Bayesian deep learning, so sorry if this is a silly question.
I'm trying to implement the work in this paper: What Uncertainties Do We Need in Bayesian Deep Learning for Computer ...
- 11
1
vote
0
answers
39
views
Fitting uncertainty vs. bootstrap uncertainty
I'm currently working with some power law data of the form:
$Y_i = \beta \times X_i ^{-\gamma} $
Where $Y_i$ are my measurements at point $X_i$. The uncertainty on $X_i$ is vanishingly small and can ...
3
votes
2
answers
77
views
How can I assess case-level uncertainty of classification using logistic regression?
I'm hoping to fit a binary logistic regression to be used to predict the binary outcome for new cases/observations. I'm wondering if there is any way to gauge uncertainty of a prediction for ...
- 31
0
votes
0
answers
57
views
How can Bootstrapping explain the uncertainty of a statistic?
I have been reading about bootstrapping, and sampling distributions, and find it odd that people use these techniques to describe uncertainty.
As I understand it, the sampling distribution shows ...
- 667
5
votes
1
answer
47
views
How can I quantify uncertainty for a least squares estimator in a multivariate linear regression with covariance structure?
Suppose that we have
$$\mathbf{y}\sim\text{N}(\mathbf{X}\boldsymbol{\beta},\sigma^2\mathbf{M}\mathbf{M}'),$$ and let $\boldsymbol{\hat{\beta}}$ be the least squares estimator for $\boldsymbol{\beta}$. ...
- 2,073
1
vote
0
answers
43
views
Coefficient covariance matrix of inverse probability weighted regression
I am interested in computing an estimate $\hat\Sigma_\hat\beta$ of the asymptotic covariance matrix of the parameter estimates $\hat\beta$ in a regression of $Y$ on $\{X, Z\}$, weighted by weighs $\...
- 36.8k