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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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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1answer
8 views

How to target data gathering to minimize loss-function?

I have a data-set, a model (single variable) and a loss function. I can collect more data but each data point requires significant analysis to obtain. Hence how can I target the data collection to ...
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1answer
33 views

Independent and conditionally independent

I was wondering if two variables can be independent and conditionally independent. For example, A and D are independent. But are they also independent given the evidence C? I think they are, because ...
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15 views

Applying an uncertainty to a prediction

I am estimating/predicting the numbers of students who will pass on an exam at a school this year. My method is very simple: Each student give me a guess of their own grade one month before the test. ...
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2answers
60 views

Can I use bootstrapping to estimate the uncertainty in a maximum value of a GAM?

I have data from an experiment where I look at the development of algal biomass as a function of the concentration of a nutrient. The relationship between biomass (the response variable) and the ...
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16 views

Propagation of uncertainty when both axes depend on same variables

I have a data set y as a function of t measured at a distance L. Both t and L have a known standard deviation (i.e. the relative error on t changes with t). What I am now trying to do is to define a ...
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29 views

Uncertainty in Peak Value of Spectrum (Standard Error or Parameter Error)

I want to extract the position of a peak from a spectrum (energy spectrum of scattered photons). To do so, I am using scipy.optimize.curve_fit to fit a Gaussian to the region of the spectrum that ...
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65 views

Gaussian-Process (scikit-learn) Prediction Confidence Interval Oddities - Stats Question

I'm doing some particle physics analysis and was hoping someone out there could give me some insight on a Gaussian-Process fit I'm trying to use to extrapolate some data. I have data with ...
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1answer
16 views

Error propagation in a linear model

I am currently interested in learning more on error propagation. At the moment I am trying to find out how to calculate the uncertainty of a value that is obtained from a linear model. For the linear ...
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3 views

Suitable (Bayesian) panel data model, allowing for nonlinear effects of certain variables and incorporating model uncertainty

I've got a panel data set and I'm looking for a suitable (Bayesian) model, which allows the effects of certain variables to be nonlinear (more than just U- or inverse-U-shaped) and additionally also ...
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19 views

How does a curve fit accuracy depend on the number of points?

The accuracy of a curve fit must increase with the number of points (perhaps like sqrt(N)), but I haven't found an equation for it. Trying estimate accuracy of a 2nd order poly fit. Thanks.
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17 views

Uncertainty in pixel intensity value due to the spatial uncertainty of phenomena

Assume we have image of point object (I use Gaussian PSF). Let's assume that position of this point object is not precisely known due to some phenomena. Spatial position of point source can be ...
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27 views

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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1answer
130 views

Uncertainty in random forest imputations from R missForest package

I am in the process of imputing missing values for my data set that contains approximately 20 variables and 3,000 observations. Most of the missing data values are contained in 2 of the variables (one ...
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1answer
33 views

Calculate the area of a Gaussian process kernel

I am thinking about a problem using Bayesian optimization with a Gaussian process. Bayesian optimization is explained well elsewhere; briefly the idea is that we sequentially evaluate a function where ...
3
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1answer
27 views

Propagate uncertainty of a parameter through a function

Suppose I have a probability distribution (in fact I've got a nice case where that distribution is Gaussian) on a parameter value. e.g. the parameter $x$ has $\mu = 3$ and $\sigma^2 = 1$. Now suppose ...
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1answer
39 views

Making use of the uncertainty of a sample proportion

I would like to understand more about how to use the uncertainty in a sample proportion. Imagine I need to offer a warranty for a product against individual sold items failing to work as ...
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0answers
25 views

Obtaining uncertainties from an errors-in-variables machine learning algorithm

In my field, every value reported comes with a 1-sigma uncertainty value. I'm using random forest regressors to estimate a value. All of my inputs have 1-sigma uncertainty information with them. ...
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22 views

Propagation of uncertainty through a linear system of equations - rectangular matrix, pseudo-inverse

I refer you to this post as I have very similar problem: Propagation of uncertainty through a linear system of equations Can the same technique, proposed by Glen_b, be used to find uncertainty in ...
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15 views

Proof for uncertainty mixing intuition

Could somewone give me a mathematical proof for this 'intuitive' result? I have a random vector $\mathbf{Y}$ related to another random vector $\mathbf{X}$ with the equation $\mathbf{Y} = ...
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1answer
69 views

Including errors in perpendicular off-set determination of points from a line

I have a set of lines and some data points which have errors for the x and y components I would like to see which one of these ...
2
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0answers
79 views

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 ...
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1answer
30 views

Regression on Inferred Variables

Given a set of labels $y$ and design matrix $X$ we often compute a linear regression to find a set of parameters $\hat{\beta}$ such that $E[y|X] = X\hat{\beta}$. However, how does one perform ...
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29 views

Standard deviation in cumulative displacements reconstructed from noisy velocities

By solving an overdetermined problem one gets velocities at different time intervals with known standard deviations. The cumulative displacement is then reconstructed from computed velocities as ...
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16 views

How to estimate uncertainty in the slope when by chance the sample variance is pathologically low?

Let's say I have a hundred trillion data sets, each of which having measurement $y$ at time $t$. In each data set, I regress lm(y~t) and find both the slope $\beta$ ...
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17 views

Testing if slopes differ using data with different uncertainties?

I have two data sets that each have the following form: x y sigma 13 1495.00 0.07 15 1700.91 0.09 ... basically where $x$ and $y$ are given, but also ...
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93 views

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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1answer
44 views

How to generate probability function for uncertain data based on euclidean distance?

I am calculating pairwise distances between some points. The obtained distances can either be accurate, over-estimated or under-estimated. The respective probability is 80%, 5% and 15%. And the error ...
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1answer
50 views

How do I obtain the uncertainty of a value generated from a known distribution?

I wish to semi-randomly generate values from the known distribution of a particular quantity. The distribution is represented in my data as a list of values with a probability for each value, where ...
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1answer
36 views

Distance between Vectors with Confidence Intervals

I have a machine learning application where I extract numerical features $a_{i1}, a_{i2}, \dots, a_{ik}$ for each object $a_i$ to study. Objects are then compared using standard euclidean distance. ...
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39 views

Confidence interval for Repeatability from a lme mixed model

I have a (lme) mixed model of this type: ...
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0answers
23 views

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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253 views

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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20 views

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
78 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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25 views

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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15 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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1answer
27 views

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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24 views

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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58 views

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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0answers
124 views

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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2answers
107 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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1answer
28 views

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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1answer
151 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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1answer
48 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
123 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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2answers
41 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
138 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
95 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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26 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% ...