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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Gaussian Process Regression with independent variable uncertainty on datapoints
Imagine that I have a set of $N$ (training) datapoints $\left\{(x_n,y_n)\right\}_{n=1}^N$, with error bars/uncertainties on each datapoint along both the $x$- and $y$-directions, written as $\left\{(\...
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Sampling uncertainty of posterior probability distribution
I'm working on a problem with 3 possible outcomes and a bunch of features. I have a regression model that outputs probabilities for each category and I'd like to extend these probabilities to ...
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Propagating uncertainty through nested random forest models
Does anyone know if there are methods for propagating the prediction intervals (i.e. uncertainty) of nested surrogate models, specifically random forests? When I say nested, I mean that a second model ...
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Learning the uncertainty of a regression model
I have a regression GAM (General Additive Model) and I want to learn its epistemic uncertainty( the variance of my residuals or predictions as a function of my input).
I have already used a bayesian ...
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MC dropout deep learning
I would like to compute the uncertainty of my deep learning model using MC dropout. My original model contains already one dropout and I am satisfied with its performance. To compute the uncertainty, ...
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Propagating uncertainties of constants in division
I have two constants, $A$ and $B$, with associated uncertainties $\sigma_A$ and $\sigma_B$, from observational errors, for example. I need to perform calculations with these constants, by for example ...
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How to estimate uncertainty in Markov chain simulations
Consider how I fit a Markov chain to my data with R:
...
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Error on the mean for discrete histogram
Suppose I have a discrete histogram, in this case the number of votes for each rating (1-5 stars) for a product.
I can calculate the sample mean easily enough, and get an average score for this ...
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Slope uncertainty of linear regression with negative $R^2$ value
When I have a linear regression and I want to determine uncertainty in the slope from the quality of the fit (ignoring any uncertainty from error bars for now), I generally use
$$
\sigma_m = m \sqrt{\...
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Fitting a curve knowing points uncertainty
I have a set of points X and Y that represent a curve. It is not a linear curve but a model I cannot estimate analitically. I know the uncertainy on Y (1 sigma) and there is no uncertainty on X. Due ...
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How can I estimate the uncertainty/probability of a single prediction (e.g., from a regression)?
I would like to create a statistical model (e.g., multiple linear regression) that i can apply to new data to get a prediction of an outcome; as well as an probability/likelyhood estimate on the (un)...
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K-fold cross validation based standard errors?
I have an expensive model (or class of models). My baseline approach to quantify uncertainty re the model parameters are hessian based standard errors, and I use k-fold cross validation for model ...
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Is a statistically significant difference within analytical uncertainty still valid?
The isotopic analyses of two tissues across 50 specimens showed a mean difference of 0.12 ‰. A Wilcoxon signed-rank test for paired samples indicated this to be statistically significant (Z: -2.515, P ...
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How do I combine probabilities from two different methods of calculating a single result?
I am doing a convergence analysis in on a finite element model. The converged result is the result when the element size is zero which is also when there are an infinite number of elements in the ...
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Ratios and proportions as predictors [duplicate]
I am interested in modeling a continuous variable (e.g., second language learners' English proficiency measured in TOEFL scores) as a function of a number of predictors some of which are continuous ...
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What is a good way to compare two data pre-processing methods e.g better predictions and/or narrower HPDs?
Given one dataset and two different data pre-processing pipelines, does it make sense to say that one of the processing pipelines is better if, given a regression model, it subsequently leads to a ...
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Bayesian model averaging when none of the models is well specified
Usually, from what I've read of Bayesian Model Averaging (BMA), a typical assumption is that one of the models is well specified...
However, what will happen when all models are misspecified? What ...
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Monte Carlo uncertainty analysis of actual and predicted data in R?
I am a need of Monte Carlo uncertainty analysis of actual and predicted data in R I used a regression AI model to predict and now I would like to conduct Monte Carlo uncertainty analysis of actual and ...
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How can the prediction of a model be assessed?
I just played around with the VGG16 and ResNet56 model trained on the ImageNet dataset and realized, after running some tests, that the prediction confidence of both networks is really high even if ...
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Difference-in-difference: fixed effect vs. clustered standard error
I am trying to run a difference-in-difference regression. I have one country in the treatment group and two countries in the control group. I believe there is a need to account for fixed effects to ...
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Uncertainty propagation in ODEs
I want to see the effect of parameter uncertainty in the Euler method for ODEs.
For a differential equation:
$dx/dt=f$
with initial condition $x(0)=xo$ and a function $f$ (that has uncertain ...
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random forest regression with uncertainty output [closed]
For a Bayesian optimization problem, I wish to use a random forest regressor in Python, able to predict for unseen data a probability distribution, like in the paper Decision Forests for ...
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error propagation for derivatives
I have the following problem:
I have some data of a function f(x) with a set of 300 values of it associated to the same number of values of x including corresponding standard deviation σ(f) for each ...
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Computing the average of measurements with an associated uncertainty
I think this might be a silly (or a really basic) thing to ask, but I have not been able to see this clearly. Suppose I have $N$ measurements of a certain magnitude $x$, each with an associated ...
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Incorporating experimental uncertainty into prediction interval
I have the following data
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Uncertainty of parameters estimated by maximum likelihood
For different sample sizes we will get different estimate of parameters by MLE. Can this size(n) be related to uncertainty in those MLE estimated parameters?
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How do you know when you are 90% sure or 99% sure?
The problem is a follow up to my previous one, so a lot of contextual data can be found at:
how to find 10th, 50th, 90th percentile of a uniformly distributed data for all cases?
But this is a very ...
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Uncertainty analysis using Bayesian bootstrap
I am trying to use Bayesian bootstrap to asses uncertainty in a model, but I'm having difficulty to conclude my analysis.
I am independently training many randomly initialized instances of the model ...
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What is the best way to report the results and uncertainty from a Monte Carlo simulation?
I am fitting data to a model that has ~30 input parameters, each with their own uncertainty levels, and which can interact with each other in the model. I therefore decided the best way to fit the ...
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How do I properly include systematic uncertainty of x and y values correctly into fitting parameters (y=ax+b)?
I am doing a simple experiment that involves measuring the resistance of a wire. To do this, we measure the voltage across a wire as we increase the the current going through it with two Fluke Digital ...
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How to estimate the uncertainty in the zeros of a fitted function?
I have fitted points with a polynomial. I now have the coefficients and the covariance matrix.
For a given y (in this case y=0; that is, x is a root of the polynomial) what is the uncertainty of that ...
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Beta-Binomial regression or Poisson-Gamma model to account for uncertainty in (empricial Bayesian) prior? Explained in simple terms?
I have a dataset of $m$ individuals. For each individual $m$ I have $n_m$ (binomial ) observations with $s_m$ corresponding to the number of 'successes'.
I use this data to fit a beta-binomial ...
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How does uncertainty of observations propagate through linear regression fits [duplicate]
I'm quite new to statistics, so please bear with :)
I'm trying to estimate the uncertainty of a variable which is predicted using a linear equation. The linear equation is estimated with a series of ...
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How to model the likelihood of an inhomogeneous Poisson process with "uncertain" event values
Using the example of an inhomogeneous Poisson process in 1 dimension for simplicity, with a varying rate parameter $\lambda (t)$.
Let's say I am trying to find the form of $\lambda (t)$, using data ...
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Including model uncertainty in non-linear least squares minimization
The problem
I have experimental data $Y$ with heteroscedastic and normally distributed uncertainties characterized by covariance matrix $C_{exp}$. I want to fit the data using model $F(X, \beta)$ ...
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Randomness in parameters per se captures the incomplete knowledge on the phenomenon: analysis in Bayesian models
I have been studying some books on uncertainty quantification for stochastic systems: Numerical Methods for Stochastic Computations: A Spectral Method Approach and Spectral Methods for Uncertainty ...
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Determine if point is in 2 sigma error
I have a two dimensional space in x and y coordinates. I have a point (5,5) representing the mean and two sigma error is 2 for x coordinate and 3 for y coordinate. How do I determine if any (x,y) ...
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Calculate the ideal mix give data with uncertainties [duplicate]
I have a sample (C) with a given elemental isotopic ratio. It is the mixture of elements from two different populations (A and B) which have different isotopic ratios. For each population A and B I ...
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Quantify the output variance of a neural network classifier
Lately at work we are dealing with a theoretical problem concerning the output variance of a neural network classifier. To set the scene, suppose you have an image classifier, which takes an image as ...
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Percents of Random Samples
I have three sets $A,B,C$ of sizes $N_A=2508$, $N_B=36211$ and $N_C=2296$ respectively, containing binary values. I took 200 samples of each set to produce point estimates of the averages: $\hat p_A=0....
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Accounting for uncertain information (few observations) in a prior (empirial Bayes)
I did not really know how to choose an adequate title for this question, so please feel free to change it.
I have a weird case wherein frequentist and Bayesian philosophies come together. I am ...
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Estimate size of each group with uncertainties from a KDE plot
I want to know the percentage of individuals in the "low-squeak" and "high-squeak" groups with uncertainties. How do I calculate it given the following bimodal distribution?
For example, I need to ...
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Bootstrapping for time series modeling
I am developing a model to decompose a univariate time series dataset into three components: seasonal, trend, and a piecewise semi-linear component with a sawtooth pattern (repeated gradual decline ...
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How to perform regression on data with uncertainty?
There are many resources for linear and polynomial regression, but I have not seen any material where the data comes with its own uncertainty as it appears in the real world. I have n data points, {...
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Uncertainty Quantification in Time Series Analysis
The stock market value of the data point connected by the red line is predicted by linear regression using market values as well as Twitter sentiment data and more in a certain period of time (red ...
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How to calculate uncertainty of probability derived from random samples?
I'm running many simulations based on random samples, each of which produces a True or False result. The goal is to calculate the probability that the result will be True, which I can easily ...
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Can the correlation between uncertanties on variables be used to evaluate the correlation on variables?
Consider two variables $X$ and $Y$ correlated with a coefficient $\rho$. If associated to each measurement of $X$ and $Y$ we have independently estimated uncertainties $\epsilon_X$ and $\epsilon_Y$, ...
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Why do Uncertainty Quantification using a Bayesian Perspective?
Besides the reasons stated in this article, Stuart(2010) (chapter 2) - related to equivalence between using a certain prior on the observation error and defining which norms to use when doing a ...
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Uncertainty so small it rounds to 0.0?
So I was refreshing my physics knowledge and someone gave me a question about uncertainty. I figured it would be easy, right? So I calculated the uncertainty from the error bars of raw data, and got ...
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Quantifying a reduction in prior uncertainty over several experiments
I am interested in how to quantify reductions in uncertainty about the size of an experimental effect over a series of studies which, for hypothetical reasons, preclude the merging of data. I would ...