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.
272 questions with no upvoted or accepted answers
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Empirical Prediction interval for time series forecast based on quantile regression
As Gardner notes "almost all point forecasts are wrong", so prediction intervals (PI) are necessary to quantify uncertainty and help us make informed decisions. There exists theoretical PI, and in ...
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Confidence Intervals with Propagation of Uncertainty
Lets say I'm trying to make a measurement of the area, $A$ of an object imaged in a large number of noisy gray-scale image, and I want to include uncertainty quantification to some confidence interval,...
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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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Quantifying uncertainty when fitting a statistical model to partial effects/dependencies from a random forest (or other machine learning model)
Question: I estimate the partial dependence of $y$ on one predictor in a fitted random forest (RF). I want to now fit a parametric model to this partial dependence. How can I estimate my uncertainty ...
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Can fuzzy numbers be used to propagate uncertainty?
I don't know if this is the right forum to ask this, but I'm currently reviewing a paper that uses arithmetic on fuzzy numbers to propagate uncertainty.
As I understand the authors, they claim that ...
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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 ...
4
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Loss function for probabilities with uncertainties
I have a problem for which I want to build a model that predicts probabilities with uncertainties.
As an example, let's say I want to predict the probability that it's going to rain today. My model ...
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Calculating the standard deviation of the mean of average rates of speed
Is it possible to determine the mean value of a point by averaging the average rate of ranges that contain that point, and if so, how can the uncertainty of that value be accurately determined?
I ...
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How to calculate uncertainty in bacterial growth rates (or in the slope of any local regression)?
I'm using a plate reader to measure optical density of different bacterial
strains so I can compare their responses (growth rates and changes in them over
time) to stress conditions. The growth curves ...
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4
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Uncertainty of extrapolation (curve fitting)
I have estimated (MC simulated) some probability values y, that each depends on a value of x between 0 and 1.
Say, for instance, that the vector x contains
$x_{1} = 0.1,\ \ x_2 = 0.2,\ \ x_3 = 0.3,\...
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Confidence Informed Confusion Matrix (Threshold Free)
I am using the normalized confusion matrix to aid in quantifying the uncertainty in related observations over time. More specifically, I have a classifier that returns the confidence of each class via ...
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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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3
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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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Model or State Uncertainty in Queueing Model due to uncertain arrival rate
$\textbf{Introduction}$
I am currently modelling a scenario where two queues need to be served by a single server in a non preemptive discipline. I am quite sorted on generating the optimal policy ...
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Using Bayesian formula to apply uncertainty to topic probability given length of document
After computing topics ($z$) over a word network, I'm assigning topic probability to documents, following:
$$p(z|d) = \sum_{w_i}p(z|w_i)p(w_i|d)$$
with $d$ being a document composed by $w_{i...n}$ ...
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Quantifying uncertainty of predictions for new data in the regression tree
I used Regression Learner to train my data. I held out 25% of the input for validation and ran different models for training. Based on the results using RMSE and R-squared, I decided to go for the ...
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How to incorporate uncertainty and noise information in training and prediction of neural networks?
I am trying to use RNNs to perform state estimation on noisy sensor data. The readings are from a GPS dataset and it provides $[longitude, latitude, n_{satellites}]$. The last column, which is the ...
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3
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What is the correct parameter range to choose when conducting a sensitivity analysis?
When conducting a (variance-based) sensitivity analysis, should I set the range of a specific parameter to its maximum allowable range, or restrict it to something more appropriate for my specific ...
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How to choose resample size when drawing without replacement?
Say I have some second-order statistic $m(x)$ where $x$ is a data vector of length $n$. Let's also assume that the limiting distribution of $x$ is gaussian-ish, but generally unknown, so that the ...
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Non-linear fitting with uncertainty in dependent and independent variable
This is related with this question.
What is the best strategy/package in R/python/Mathematica to fit a non-linear model to data with uncertainty measures in both variables?
Elaborating:
For every ...
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3
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187
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Propagating uncertainties using random forest out-of-bag accuracy estimates
Let's say I train a random forest on some data and get an out-of-bag accuracy estimate of 90%. I then predict a quantity using this trained forest. What should be the uncertainty I give to that ...
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Do Monte Carlo perturbations capture all the uncertainty in prediction?
I have a model $M$ that I use to predict a value $y = M(\vec x)$. I have known one-$\sigma$ error bars on each input $x_i \in \vec x$. I want to know the one-$\sigma$ error bar on my prediction $y$.
...
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How to estimate uncertainty on the prediction from a linear model with errors in the variables?
I have a theoretical model that I am feeding various inputs (initial conditions) and using to generate various outputs (observable quantities). Now I want to take real observations, which have known 1-...
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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 ...
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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-...
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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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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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Can be the output distribution non-normal using the moment method?
I want to study the uncertainty propagation through a nonlinear function $Y = f(X)$. I am assuming that $X$ is normally distributed and I am using the moment method approximating $f(X)$ by its first (...
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Statistical terminology for the "difficulty" of an estimation task
I am looking for the proper statistical terminology to express the fact that one estimation task maybe intrinsically harder to solve than another task. Intuitively, I would characterize this property ...
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560
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Uncertainty score from Monte Carlo dropout
When using a neural network for multi-class classification, there are situations where it is useful to estimate the uncertainty of the network's predicted class. One leading method for estimating ...
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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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2
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Gaussian process regression on a graph
I am looking for a way to do Gaussian process regression on a weighted graph. Analogously to the prototypical GPR plot, I made a drawing to make it more clear:
The filled nodes have a training point ...
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2
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228
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Uncertainty calculation for mean of spatially gridded data
I have data on a spatial grid. For each cell of the grid there is a best estimate ($x_i$) and an uncertainty ($\sigma_i$) which is specific to that grid cell. I'd like to calculate the mean for the ...
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If a zero entropy distribution implies high information a priori, what does it mean ex posteriori?
The following counteracts the statements made for the maximum entropy principle case in order to posit a pseudo "minimum entropy principle" case that is simply the polar opposite of the ...
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Help with Difference in Difference Variance Estimator (SEO Experimentation)
I found the following article https://medium.com/airbnb-engineering/experimentation-measurement-for-search-engine-optimization-b64136629760 regarding search engine optimization (SEO) frameworks. It ...
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Compute standard-error/deviation for an aggregated/ fractional metric
I have a dataset, where I want to visualize an aggregated efficiency over time (t), while also showing the variation/ uncertainty in the data.
The target metric is computed as the fraction of the ...
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56
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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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391
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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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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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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 ...
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287
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Confidence intervals and uncertainty estimation of classified polygon map
I am not mathematician, neither statistician, but I try to use statistics in my work, so I do my best here to explain the problem I have.
I have a map of millions of hectares that consist of nine ...
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Exponential errors in variables model with known uncertainties
I have $N$ data points that I am trying to fit using a function of the form
$y_i = \prod_j {X_{i,j}}^{b_j}, \quad j=1..N$
where $\mathbf X$ and $\mathbf y$ are measured values. The form of this ...
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Uncertainty in calibration/curve-fitting parameters
Let me preface with saying I have an idea of a solution, but I am interested in other ones
I am interested in the a way to quantify the uncertainty in a calibration/curve-fit parameter. For all ...
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Accounting for errors in independent variable through Gaussian process regression
In Gaussian process regression (GPR), one applies a kernel (i.e. covariance function) to describe the similarity between observed and predicted data in the domain. The diagonal of the covariance ...
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How to quantify the uncertainty in a single value obtained from a large number of simulations
Im a physics student working on a project in which I have to simulate a machine that would order a bunch of molecules according to their mass. I want to get a quantitative measure of how well the ...
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653
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Cross-Correlation Propagation of Uncertainty
I would like to calculate the uncertainty of the cross-correlation of two functions (in two dimensions but even one-dimension is a great start). Experimentally, I have discrete values of f and g, and ...
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Uncertainty of earthquake location
Maximum of the so-called image function in the figure below interpreted as earthquake location (in XY plane in this case). The shape of this function will depend (upon other things) on frequency of ...
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Predictive Uncertainty in classifiaction
I want to plot the predictive uncertainty for a binary classification problem. I have 30 observations and for each observation, I have 50 probability values predicted by the model. When I plot mean ...
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Uncertainty of a least squares fit with uncertain data
I often find myself with questions that vary along this theme, but the internet is so full of simpler cases that I can never find what I'm looking for. So this question is two-fold: a) what's the ...
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Uncertainty Calculation when measurements are subject to a constraint
I would like to know how to properly propagate the errors on measurements where I know a constraint on the sum of these measurements.
Lets say I have a rod of length exactly 1 metre which I have drawn ...
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