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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25 views

Calculating uncertainties for histogram bins of experimental data with known measurement errors

I have a set of experimental data (with each data-point having its own measured uncertainty), and I wish to produce a histogram of it. The x values of the edges of each bin are already defined. The ...
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10 views

Estimating the uncertainty in the peak of a non-stationary poisson process

I have daily counts of observed disease cases for a single location. I am interested in the peak timing of the outbreak of the disease and want to assess the uncertainty in the peak estimate. In other ...
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38 views

calculating effect size of individual predictors in multiple regression and associated uncertainty

Lets say I have a multiple regression model, where I predict y from predictors x1 and x2. ...
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57 views

Non-direct measurement and degrees of freedom

Background and current intuition In statistics, degrees of freedom are used to characterise the number of independent observations after some statistic has been calculated. The most common example is ...
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11 views

Uncertainty of regression tree and regression tree terminal node values as function of the predictors

Model = as.data.frame(matrix1) train = sample (1: nrow(Model), nrow(Model)/2) tree.model =tree(y~.,Model ,subset =train) Prediction on the test set for unpruned tree yhat=predict (tree.model ...
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12 views

Calculation of vector norm uncertainty using covariance matrix

I have a vector $\mathbf{v} = [ v_x , v_y ] ^T$ whose PDF is Gaussian, thus it has an associated covariance matrix to represent its uncertainty (which is zero mean): $P = \begin{bmatrix} \sigma_x^2 ...
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25 views

Adaptive (variable) bandwidth in 2D Gaussian kernel density estimator to account for measurement errors

I have a 2D dataset composed of $N$ measured values for two discrete variables, $(x_i,y_i), i=1..N$, with associated standard deviations for each point $(\sigma_{ix}, \sigma_{iy}), i=1..N$. I want to ...
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22 views

how can I show in my model that a distribution function of demand forecast is more certain closer to the demand arrival?

I am using distribution function of future demand in my research. Assuming that this distribution comes from forecasting the demand. At the same time I want to capture the fact that this distribution ...
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41 views

Bayesian inference when observed variable contains uncertainty

I have a very simple graphical model to describe the relationship between two categorical variables $c \in \{0,1\}$ and $l \in \{A,B,C\}$: $$c \rightarrow l$$ I know all the conditional ...
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10 views

Combined measurement uncertainty for mass computation

Problem I would like to determine the combined standard measurement uncertainty for a mean mass $\bar{m}$ computed from a mean volume $\bar{V}$ and a constant density $\rho$ with $\bar{m} = \bar{V} ...
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11 views

Welch T-test between two populations of points with uncertainties

I have two populations of points and I want to assess if the difference between them is statistically significant. For now, I am using a Welch t-test (which only requires the knowledge of the mean, ...
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12 views

Can I propagate standard deviation and standard error together?

Can I mix standard deviation and standard error when propagating error? For example, if I multiply two values and one has error in terms of standard deviation and the other in terms of standard ...
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14 views

Variance of residual in propagation of uncertainties of variables

For a real and differentiable function $z\left ( v_{j=1},\cdot \cdot \cdot ,v_{j=N} \right )$ the estimated uncertainty in $z$ is $$\sigma^{2}_{z}=\sum_{i=1}^{N}\left [ \left ( \frac{\partial ...
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45 views

Is Monte Carlo uncertainty estimation equivalent to analytical error propagation?

If I have a deterministic, analytic model, $y=f(x)$, I can analytically calculate the uncertainty in $y$ from a known uncertainty in $x$, $\sigma$. Or I can do a Monte Carlo integration: sample from ...
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1answer
14 views

Uncertainty in Enumerated Data

I am interested in assessing possible uncertainty in enumerated data. To do this, I randomly pick 80% of the enumerated data to predict the remaining 20% through a regression analysis. I reapeat the ...
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1answer
25 views

Determine significant figures from a scale/weight reading

(Hope this is the right forum, otherwise please bear with me) This is not a homework assignment but just some of the stuff you come across and stop to wonder.. Either I forgot how to do it or my old ...
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7 views

Best way to report variability in a multiple measures from a single event?

Thanks in advance for any help - I am an MD doing research, no significant stats background. Though we have statisticians in my institution, they are expensive and hard to access without grants. Of ...
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99 views

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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24 views

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
13 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
37 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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17 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
107 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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23 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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52 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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101 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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2answers
29 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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5 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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42 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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28 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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43 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 $y$. ...
3
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1answer
379 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
44 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 ...
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1answer
34 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 ...
2
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1answer
48 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
32 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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48 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
71 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 ...
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136 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 ...
1
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1answer
31 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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36 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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18 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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18 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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122 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
58 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
66 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
53 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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50 views

Confidence interval for Repeatability from a lme mixed model

I have a (lme) mixed model of this type: ...
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28 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 ...