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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how to find the aleatory uncertainty in parameter using Bayes?

Generally, the uncertainty can be categorized into aleatory and epistemic according to whether it can be reduced or not. In Bayesian statistics, one "true fixed parameter" is presumed as discussions ...
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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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Propagation of uncertainties in functions not continuously differentiable

According to the Guide to the Expression of Uncertainty in Measurement as published by the Bureau International des Poids et Mesures (BIPM), the combined standard uncertainty $u_c^2$ for a function $y ...
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1answer
50 views

Disadvantages of uncertainty in modeling

I am preparing a presentation, my work mainly concentrates on uncertainty and sensitivity analysis. I was wondering if I can convince my audience by the importance of studying uncertainty in modeling. ...
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How to evaluate uncertainty estimates in regression?

Some regression algorithms (e.g. Gaussian process regression) can produce uncertainties along with point predictions at test time. These should also be evaluated. How about calculating the Pearson ...
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14 views

Back propagation of Uncertainty

I am recently working on the subject of uncertainty. I read that uncertainty analysis and sensitivity analysis are important topics in this domain(the first is ti do a forward propagation of ...
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Uncertainty propagation in open equations

I don't know if this is the proper place for asking this kind of questions and I apologise in advance if it isn't, but anyways: is there a way to propagate linear uncertainties (i.e. through ...
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hypothesis testing with uncertainty in variables

This is one of those questions that are easier to be explained with an example. Suppose we have the following data (made in R) ...
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How can we calculate the standard deviation of multiple values with different uncertainties each?

For example, if I have a set of readings, like: 13.4 +/- 0.5 14.5 +/- 0.7 12.8 +/- 0.6 13.9 +/- 0.4 14.8 +/- 0.5 How do I calculate the standard deviation of ...
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What determines the precision of uncertainties?

What limits the precision with which you can describe the uncertainty of a measurement? I will describe two examples that feel qualitatively different, but I am not sure if they are quantitatively ...
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60 views

Does it make sense to generate prediction intervals for the estimates of a logistic regression?

Say I have a binary outcome of 0 or 1 and suppose I were to use logistic regression model to estimate the probability a new sample will have an outcome of 1. I have read answers (for example here: ...
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Local Sensitivity Analysis

I am tring to have a comprehensive idea about sensitivity analysis. I found numerous papers, books, and serves about global senstivity analysis methods. Coming to the local sensitivtiy Methods, I try ...
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81 views

Can you reduce the risk involved in an uncertain event?

I'm not sure if this is the right Stack Exchange site but I felt it came closest. Based on Knights 1971 definition of risk uncertainty is defined as a situation where factors exogenous to the ...
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44 views

How can one resolve an apparent paradox regarding the uncertainty of the product of two measured quantities?

Suppose one has three quantities $X$, $X_1$ and $X_2$, such that $X = X_1X_2$. Since percentages uncertainties of products just add up we have: $$\frac{\delta X}{X} = \frac{\delta X_1}{X_1} + ...
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1answer
68 views

Construct the likelihood with asymmetric uncertainties

I want to study the correlation between 2 parameters, this is done by fitting a straight line. I have uncertainties on both parameters. I want to solve my problem using the Bayesian approach, i.e. I ...
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31 views

How best to communicate uncertainty due to data quality and measurement issues

This question is coming from a business background. I want to focus here on issues that occur within a business (or perhaps academic) background which are usually difficult to quantify but it is ...
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2answers
85 views

Visualising uncertainty in slope and offset for a regression line?

According to a least squares fit I have performed to my data, my slope is $-0.1038±0.033$, and my offset $0.1065±0.032$. My first idea was to visualise this by drawing three lines: $0.1065-0.1038x$, ...
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1answer
62 views

Errors vs measurement errors

I'm reading about how to fit a straight line with measurement errors in both coordinates ($x$ and $y$). Let the true unobserved variables be $x_{t,i}$ and $y_{t,i}$ and the observed variables be ...
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17 views

How to visualise the uncertainty of the classification?

I used SVM to do some classification, and SVM can output some probabilities (likelihood) value measuring how likely each data to be one particular class. For example, Data point 1: 90% (class 1) 5% ...
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Can a forecast that reaches further into the future be less uncertain?

In Austrian television there is a weather show that gives temperature forecasts for the coming 15 days. They usually also provide uncertainty bands around that forecast which naturally makes the ...
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Uncertainty on ratio of integrals (correlated)?

I have a histogram, and a quantity defined as the integral of a subrange of that histogram (int_sub) divided by the integral of the full range (...
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31 views

Inferring the bias of two types of coin

I would like to find the bias of a type of coin, when there is uncertainty about which kind of coin I am testing. The scenario is as follows, there are 2 mints in my neighbourhood that produce ...
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2answers
54 views

How might Google go about estimating and updating traffic speeds?

This is, I guess, a specific example of a wider class of problem, one to which there must be a well-established solution, but which I, as a relative layman when it comes to statistics have thus far ...
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Under what assumptions can parameter estimate uncertainty be estimated from the Hessian?

Given a model with some parameters, some data it's attempting to reproduce, and a distance function to quantify how well the predictions correspond to the data, I can fit parameters via a general ...
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Usage of standard deviation in random forests regression (for expected improvement)

It seems to me that the awareness of this problem is not high enough. Often the standard deviation (so the sd from each prediction of each tree in the forest) from the random forest regression is ...
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47 views

Which kind of “uncertainty” is this?

I'm a bit confused about all the different "definitions" of uncertainty? One can calculate "uncertainty" of a single measurement by simply checking how accurate the tool that is being used to do the ...
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Propagation of uncertainty: entropy of multinomial

My goal is to estimate the entropy of a multinomial distribution, based on a single observation (a set of counts for each possible outcome). I also want to calculate the uncertainty in my estimated ...
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39 views

cumulative uncertainty with time series predictive model

So I have a time-series with a set of variables a, b, c... and another measured variable y. What I do is using the initial state of a,b,c and y (at t0), I predict what y "should" be at the next time ...
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Squared uncertainties: what may it be used for?

If the squared standard deviation of a set of values is the variance of this sample, then, what is the squared standard error of the mean of this sample ? and what may it be used for ? A quick search ...
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estimating model fit parameters using simulations

I'm trying to fit 2D ellipticals gaussians to an image (with correlated background noise) using prewritten fitting software. I'd like to know about the uncertainty in the fit parameters with this ...
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17 views

Classification under uncertainty in observations

I am tackling a multiclass classification problem where the values of the independent variables are not known with certainty. Instead, each observation is represented by a multivariate Gaussian pdf ...
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48 views

Intuitive and Formulaic Justification for the Rao-Blackwell Theorem

I've tried looking online and I can't seem to grasp the Rao-Blackwell theorem. Could someone please give an intuitive explanation backed up by formulae.
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Error Propagation

I come from a physics background where the only error propagation I've dealt with was in the lab using the simple formulas found here: ...
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Should additional crime reports about someone change our level of doubt about an initial crime report?

Edit: Note that this question is not about multiple unreliable witnesses to the same incident, but rather multiple incidents with only one witness each. Should the accumulation of separate alleged ...
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47 views

Shape uncertainty of a 3D point cloud

Given a point cloud of a 3D object, how to calculate the shape uncertainty in this discrete sample set? and what factors maximize or minimize this uncertainty?
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How to properly consider uncertainty propagation in random variables

I have 34 input random variables and one output random variable, named R. From 33 input random variables and some dataset I determined the best predictive ...
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Power law fitting of data with uncertainties

I need to fit data points on a power law and each one of these carries an uncertainty. I've been using Python, more precisely scipy.optimize.curve_fit to get the job done but I don't know how to ...
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1answer
43 views

In OLS is it methodologically correct to use the variance of a variable as an explanatory variable?

Are some OLS assumptions not satisfied if I use the variance of a variable as a proxy of uncertainty in a regression? For instance, would it be methodologically correct if I use moving averages of ...
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Power to detect significant correlation given measurement uncertainty

First of all, apologies if some of the technical terminology in here is not accurate - my experience with statistics is fairly limited. To illustrate my problem, let's say I wanted to design a study ...
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1answer
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To use or not to use a variable that contains information w.r.t. uncertainty

The data I'm looking at is concerned with percentages of people who would recommend a hospital. ...
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Uncertainty consistency?

The problem statement, all variables and given/known data I am given a set of x and y values x: (1,2,3,etc.) y: (1.2,2.2,3.1,etc.) with a given uncertainty and am asked a) find the best fit b) ...
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1answer
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Uncertainty analysis

Here is my situation. I am trying to predict the 'entire' distribution of the dependent variable, not just the mean( or conditional mean). Does it then make sense to seprateley predict quantiles of ...
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Combining sources of uncertainty/variation in a multi-layered linear model

I’m having trouble understanding how to combine parameter uncertainty and interannual variability from various levels in a bootstrapped linear model. Specifically, this model is designed to generate ...
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229 views

Principal component analysis with known uncertainty varying across both samples and variables

I want to do dimensionality reduction on a data set $X_{ij}$. In this case, $i$ indexes samples and $j$ indexes a large number of variables (densities at different locations in space). The units of ...
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59 views

Cheaper/faster method to estimate uncertainties than bootstrap

I'm using a genetic algorithm (GA) to estimate the minimum value of a likelihood function $L[x]$ which is too complicated to evaluate mathematically. This likelihood function quantifies the goodness ...
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72 views

Derivation of uncertainty propogation?

For a function $$ y =f(x), x=\left(x_1, x_2, ..., x_N\right)$$ the law of propagation of uncertainty, see GUM sect 5$^{[1]}$ (pdf), is generally given as $$ u_y^2 = \sum_{i=1}^N \left(\frac{\partial ...
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132 views

Determining the uncertainty of an exponential fit

My problem should probably be built up from the beginning, so lets start there. I performed a certain experiment 25 times. Every time, the experiment consists of 5000 measurements, and each ...
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1answer
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Uncertainty formula if measured “best” value is zero

If the uncertainty of a function $f(x,y)$ is given by: $$\delta f = |f_{best}|\sqrt{ \left( \frac{\delta x}{x_{best}} \right)^2 + \left( \frac{\delta y}{y_{best}} \right)^2}$$ what do we do if ...
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139 views

How to sum uncertainties, systematic and random

I apologize for the simplistic questions. I have a retrieval process that has a set of random and systematic uncertainties associated with it. I'm assuming that these are all independent. The goal is ...