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.

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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 $\mu(V)$...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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-...
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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 $i<d$, $D_i$ ...
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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: $Score=Score_1 + Score_2$), ...
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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 ...
Adrian 's user avatar
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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How does the training set size affect the uncertainty (variance) of performance estimation?

I am reading this paper which discusses the factors that affect the uncertainty (variance) in the performance estimation of a learner. The authors say (p. 2, "The monotonicity of the learning ...
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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 $\boldsymbol{\beta}$. ...
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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 $\...
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MCMC uncertainties vanish

I'm trying to fit a signal modelled by a Lorentzian ($f(x) = \frac{\text{Amplitude}}{1 + 4((x-\text{center})/\text{width}^2)}$), thus I have 3 parameters : Amplitude, Central frequency and width. I ...
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Parameter uncertainly estimation in nonlinear optimization

I appreciate if somebody introduces me some books on parameter uncertainty estimation or parameter confidence interval estimation in nonlinear optimization. For the linear regression I understand that ...
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How to calculate the uncertainty of fitting parameter in a nonlinear model

I have a cost function which is: (F(X,B)-Y)*(F(X,B)-Y) F is my model, B are my fitting ...
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How put uncertainty shading on a linear fit [duplicate]

I have a scatter plot and only my y values have uncertainty. I obtained a linear fit to my data (using curve_fit from ...
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Dataset to apply Sobol Indices

I am working on a project based on Sobol indices. I am looking for a dataset to apply Sobol indices. I need to show a basic demonstration of this method. Specifically, I want to identify which inputs ...
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How do i apply conformal prediction to achieve voxel-wise uncertainty quantification in a 3D binary segmentation problem?

Context: Typically in an image segmentation problem we go from the model's output logits to sigmoids to discrete labels (0 or 1 in this case). Akin to a binary classification problem, we can set up a ...
Amir Vahdani's user avatar
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Optimization landscape and relationship to parameter uncertainties

In linear/nonlinear regression we try to find the minimum for the sums of squares as a function of the model parameters. For a one dimensional system this is just a simple 2D curve. Parameter on the x ...
rhody's user avatar
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Propagating uncertainty in a Markov chain with absorbing states

Consider a Markov model with two absorbing states $a$ and $e$ and three transient states, with an associated transition probability matrix like so: $$\begin{pmatrix} 1 & 0 & 0 & 0 & 0 \...
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Contour plots limitations for stats models

My team prefers to present the models by using contour plots. Although I understand that they are looking nice I don't like them because they don't present the model's uncertainty but only the mean. ...
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Distance between two distributions with uncertainty / measurement error

I have two empirical distributions $X$ and $Y$, both with the same number of samples (a few thousand). $X$ are true values, they are accurate (i.e. no uncertainty). Values of $Y$, on the other hand, ...
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Estimating variance based on parameters

I have a list of measurements $y_1,\ y_2,\ ...,\ y_n$ of quantity $Y$ and a list of parameters associated with each measurement $(A,\ B,\ ...)_j,\ j=1...n$. The distribution of $Y$ is symmetric, but ...
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How to test statistical improvement under model prediction uncertainty?

I have a regression model, predicting a popularity of a text. I have its performance metrics on test set, e.g. RMSE and MAE. This gives me an uncertainty estimate about its predictions. Now I want to ...
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Definition of Uncertainity

I have some confusion regarding Measurement Uncertainty. In some books/articles it is defined wrt true value as "Uncertainty in the average of measurements is the range in which true value is ...
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MC Dropout without weight decay -- how is the model precision calculated?

In the original [MC Dropout paper][1], the variance is calculated as the sum of two contributions, an sample variance (over the multiple forward passes), var$(y)$, plus a term quantifying the inverse ...
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Assessing uncertainty calibration in regression using the CDF

I have a labelled data set with $n$ data points $(x_i, y_i)$ with $x_i \in \mathbb{R}^k$ and $y_i \in \mathbb{R}$ and I trained a model $f: \mathbb{R}^k \to \mathbb{R} \times \mathbb{R}^+$ on some of ...
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Uncertainty of a distribution of classification results

Let us assume that a classification DNN is trained and dropout or model ensembling has produced n samples of a classification distribution. The two methods which I have seen to quantify uncertainty in ...
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Conformal prediction nonconformity measure

I want to implement offline inductive conformal prediction for a bianry classificstion task but I have an issue with finding an appropriate nonconformity measure. Shafer proposes the Nearest neighbor ...
Dom's user avatar
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How evaluate predictions when for each prediction there are multiple true values?

My case, as it seems to me, should be quite common, yet I cannot find any information. The situation is as follows: there is a regression model, and for each predicted value, there are multiple true ...
Peter's user avatar
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What can you do with quantified uncertainty in latent variable time-series models?

Uncertainty quantification in latent variable models is a topic I am interested in, but I am struggling to grasp the difference between what you can do with quantified parameter uncertainty and ...
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In what conditions do MC-Dropout-based uncertainties fail to be expressive?

I trained a neural network with dropout regularization and computed uncertainty scores for predictions on a test set. However, I found that these uncertainties exhibit a very weak correlation (Pearson:...
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4 votes
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Uncertainty of the area of a Gaussian curve atop a linear background

I have some data from a counting-based spectroscopy experiment. Each data point is an (Energy, Rate) pair. One such data set looks like this: I choose to fit this data to a Gaussian curve plus a ...
BohemianTapestry's user avatar
1 vote
1 answer
187 views

Neural network regression - predicting mean and standard deviation

I have a dataset where for the same input, you get slightly varying results. In the final dataset I am using there are 4 input/output pairs for every input where the input is exactly the same but the ...
Tim Driessen's user avatar
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Missing data/ uncertainty in GAMM Random Effect variable

I am facing an issue with a GAMM that I am attempting to fit. I am modeling fish catch in response to several variables (see model below). I am using the mgcv's gamm() function to do so. ...
megsruppUNBC's user avatar
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Generating "surrogate data" to calculate error on estimators

We have a dataset in the form of a time series $Y_n$. We assume it follows an underlying parametric distribution $f(n,\beta)$, $\beta$ being the parameters. From the observed dataset, we get an ...
Barbaud Julien's user avatar
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Calculate the average of absolute values of a measurement with a measurement error

I have a few parameters; each is measured imprecisely with a known but unique random measurement error. We can assume that the error is normally distributed, with mean 0 and known variance (different ...
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Very Basic Question - Propagation of Error and Fold Changes in Medicine

Say you have measured three conditions (x, y, and z) together and at three separate times (three replicates). These raw values are normally distributed and in a linear space. You use those three ...
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How can you estimate uncertainty of a binary measurement?

I am working on an experiment which detects signals as a a function of time. There can be a trigger, but no signal (0) or a trigger with a signal (1). We are interested in how the ratio (likelihood of ...
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Combining GUM Type A and Type B uncertainties

Assume $N$ measurements of the same parameter, i.e. a surface temperature $\vartheta_\mathrm{surf}$, were obtained using one single measuring chain (temperature sensor, cables, ADC ...). Furthermore, ...
albert's user avatar
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Confidence interval for a rate where there is uncertainty around the exposure (number of days)

We'd like to test if two rates (number of occurrences / number of days) are statistically different for a paper. However, for one of the rates (let's say Rate A), we have uncertainty around the ...
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How to estimate Mean with Uncertainty of a selected sample from variable A, that occured when variable B met some condition?

I am trying to find the mean of a sample from time-series of variable 'A', consisting of all 'A' values that occured when the concurrent Variable 'B' met some condition. I know that the A measurments ...
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