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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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Are the standard errors in the coefficients of a linear regression corellated?

Lowly physical scientist here so please excuse my ignorance. I have a data set of thermal expansion coefficient, $\alpha$, against temperature, $T$ that I fit with a linear regression. From this, I ...
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8 views

Binary classification with uncertain class

Suppose we have a two-class problem (C1 and C2) where in C1 the label is certain, that is, you know 100% sure of the label but in C2 you don't. To be more precise, observations from C2 may have a ...
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7 views

Uncertainty in Fit Parameters from R^2 and/or Independent Variable Uncertainties

Suppose that I am using a least-squares method to fit experimental data $(x,y)$ to the equation $$y = m x + b.$$ In order to determine $\sigma_m$ and $\sigma_b$, the uncertainty in the parameters $m$ ...
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13 views

Propagating Uncertainties on Interpolated Data

I have a data set of 2000 $[x, F(x), \delta F(x)]$ triples, where $x$ is exact and $F$ is a measured value with an uncertainty $\delta F$. I can interpolate/fit the function however needed, and this ...
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36 views

Uncertainty in Linear Regression Coefficients

Suppose I do linear regression for data $y \in \mathbb{R}^n$ and design matrix $X \in \mathbb{R}^{n \times m}$, with $n \gg m$. I seek $$ \hat{\beta} = \operatorname*{argmin}_{\beta \in \mathbb{R}^m} ...
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23 views

Regression via neural network on training data with uncertainties

I have a regression task where all my training data that I want to predict is of the form ($y$, $\sigma$), where $\sigma$ is the Gaussian noise corresponding to $y$, i.e. I want to be able to predict ...
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21 views

Should the predicted variance in Gaussian process regression include experimental error?

Suppose I have an experiment where I measure the temperature of water in a cup, $y$, as a function of time, $x$. My measurement is normally distributed with an experimental uncertainty given by $\...
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6 views

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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1answer
57 views

Uncertainty in measurement error

Imagine having a list of positions $\mathbf{x}$ and two different systems trying to estimate $\mathbf{x}$. One system is more precise than the other, and it will be used as ground truth. When ...
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8 views

Uncertainty quantification in both model and parameters of the model

In engineering analysis in my domain (civil engineering), we have many models based on partial differential equations. We predict the behavior of the system based on the parameters we measure from ...
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49 views

Handling negative variances on the derivative of Gaussian processes

The variance of the derivative of a Gaussian process, $f$, is given by (9.1): $$ Var(\frac{\partial f}{\partial x}) =\frac {\partial ^2 k(x,x)}{\partial x^2},$$ where $k(·, ·)$ is both a positive-...
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28 views

Statistical uncertainty in average of continuous variable, where values are not expected to be the same

I have been trying to understand statistical uncertainties on measurements made, I have found many partial sources, but they seem to either deal with simply counting whether something happened or not ...
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12 views

What are some approaches in online decision making under uncertain input data?

For example, I observe a set of measurements $n=\{n_1,n_2,n_3,n_4,....,n_k\}$. Here, a subset of measurements $\{n_1,n_2,n_3\}$ are assumed to be uncertain and are not trustworthy. As a decision maker,...
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14 views

Covariance of measurement uncertainties

So I have a sample of data points call them $X_1$ and $X_2$, these are derived quantities based on measured values and each has a mean $\mu_{X_{1,2}}$ and variance $\sigma^2_{X_{1,2}}$ which can be ...
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72 views

What are some of the approaches of defining joint pdf under sum constrain?

For example, we have three random variables, $x_1 = Uniform(10,20)$ $x_2 = Uniform(20,40)$ $x_3 = Uniform(50,150)$ which follows the condition $x_1+x_2+x_3 = 100$ I am looking for a joint ...
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How to account for experimental errors when computing the derivative of a Gaussian process?

When applying Gaussian process regression upon training data, the covariance function can be generally given in the form: $\Sigma_{i,j} = k(x_i, x_j) + \sigma(x_i) \delta_{i,j}$, where $k$ is a ...
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19 views

Expected value for max weight of two stones (given independent uncertainty in each) [duplicate]

If I have two stones A and B with estimated weights (and associated uncertainties) of A=100 +/- 5kg B=102 +/- 2kg Is there any formula (or good approximation) to compute the expected value of ...
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32 views

Central limit theorem and statistical uncertainities

I am unable to understand the statement that the statistical uncertainties associated with measured data are have to be gaussian distributed because of the CLT theorem. What I know about CLT is that ...
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20 views

Error on distribution of values with uncertainties

I'm currently analysing a measurement which results in a high number of values, each having a slightly different uncertainty. These values are following a gaussian distribution, so I wrote a python ...
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20 views

Uncertainty associated with area of under curve (integrated) estimates

Say I have a set of data points (y) measured at different times (hence a time series) which I know the uncertainties (in the form of standard error). I connect them to form a line graph and find the ...
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6 views

Combined uncertainity given probability measurement belongs to one of two classes

I have two classes of measurements $A$ and $B$ characterized by different uncertainty distributions. I also have a probability $P_A$ that a given measurement belongs to class A and not B ($P_A = 1 - ...
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27 views

Uncertainty from equation involving fitted parameters [closed]

I want to estimate the uncertainty of a calculation which involves a quantity from a fitted mathematical model. More specifically, the end calculation would be something like: P = x / A_tot where I ...
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2answers
249 views

Uncertainty estimation in high-dimensional inference problems without sampling?

I'm working on a high-dimensional inference problem (around 2000 model parameters) for which we are able to robustly perform MAP estimation by finding the global maximum of the log-posterior using a ...
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1answer
26 views

Statistical analysis of two same experimental measurements

Say I have two blood samples (Sample A and Sample B). Now, I want to do a measurement (dependent variable, let's call it D) on both samples, at 5 different levels of mechanical stress (independent ...
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39 views

How to plot error bands (uncertainty) for different available x values?

Question: how to plot uncertainty bands where each set of (x, y) data points has different x-values to be available. Context: The use case here is training neural network experiment (reinforcement ...
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36 views

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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19 views

how to incorporate individual-level classification uncertainty into population-level uncertainty (via Poisson distribution)?

How do I incorporate uncertainty in an individual-level predictive model into the prediction of a population-level variable? To give a specific example: Suppose I have a binary classification model ...
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12 views

Convert regression parameter standard error estimates to standard deviation estimates

Lets say I fit a linear model (in R), of y ~ x: x <- runif(100,0,5) y <- x*0.5 + rnorm(length(x)) summary(lm(y~x)) The summary output returned is: ...
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29 views

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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63 views

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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1answer
26 views

Reporting model uncertinty

I hope I'm using the right terms here. I've generated a statistical model (PLS regression) based on LWIR (8-10.5 micrometer) spectrum from some lab samples. This model predicts the concentration of a ...
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43 views

Data binning with error bars

I've got some measured data where each data point has an uncertainty associated with it i.e, Data $\mathbf{x} = (x_1,x_2,...,x_n)$ with uncertainties $\mathbf{\alpha}_x = (\alpha_1,\alpha_2,...,\...
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1answer
26 views

How to handle measurement inaccuracy? [improved]

This is based on my old question but the question was too confusing. I've tried to make it clearer this time. This is the kind of data we're dealing with: ...
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45 views

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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93 views

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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23 views

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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1answer
35 views

Uncertainty of the dispersion parameter

I am trying to retrace the steps that Gary King and colleagues suggest in their article "Making the most of statistical analyses: Improving interpretation and presentation" to calculate quantities of ...
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1answer
53 views

Why, *intuitively*, in regular parametric problems, does uncertainty go down at a $\sqrt{ n }$ rate on the SE/posterior SD scale?

consider the simplest regular statistical inference problem: $( y_1, \dots, y_n | F ) \sim$ $\text{IID}$ from a cumulative distribution function $F$ on $\mathbb{ R }$ with mean $\mu$ and finite ...
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60 views

Determining the uncertainty in regression parameters

I want to regress crop yield against total rainfall collected over many years. For each year, rainfall could be computed for different time periods i.e. total rainfall can be calculated between 1st ...
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1answer
37 views

Counterintuitive mass versus probability in Dempster-Shafer

I'm trying to understand Dempster-Shafer, the part before the combination rule. example Say I have a hypothesis space $H = \{x, y, z\}$, which describes three things that might be true about the ...
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20 views

Quantify the uncertainties around the regression parameters

I need some advise of how to quantify the uncertainties around the regression estimates. I have collected crop yield data across multiple locations and multiple years. The crop broader cultivation ...
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1answer
183 views

Bootstrap intervals for predictions, how to interpret it?

I want to come up with a way to get how confident I am in my predictions. I am not using a Bayesian model so I was thinking a bootstrap confidence interval would be good: I would re-sample my ...
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22 views

Bootstrapping quantiles from an estimated binary outcome

I am trying to predict a binary outcome that is unobserved but I have made bootstrap estimations of its value. As a result I have bootstrapped training data where the outcome for the same observation ...
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1answer
25 views

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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1answer
39 views

Can taking into account all observations composing few data points help to mitigate small-sample problems?

I conducted a pilot study in which I measured a variable on 20 different days in order to document how time passage affects this variable. I want to plot the uncertainty for each day, but I have a ...
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1answer
52 views

Which type of distribution is associated with a continuous variable that can take values between zero and a constant?

I'm working in descriptive statistics of a variable that is the duration of an animal's response given an 8 s interval window. Thus, this variable is bounded between 0 and 8 s. I want to estimate ...
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1answer
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How can I estimate uncertainty for a small sample of proportion data?

I'm not an expert on this topic. I'm working on a poster for a conference. I need to plot SEMs, confidence intervals, or some measure of uncertainty around a measure of central tendency (e.g., median)....
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1answer
71 views

In Bayesian, what is the effect of prior on the curvature of posterior?

Just wonder about the simplest example, I have a simple Normal prior on my scalar parameter $w$. $$P(w|D) \sim P(D|w) P(w)$$ $$P(w) = \mathcal{N}(0,\alpha^2)$$ When I increase $\alpha$ from 0 to $\...
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675 views

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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Multi-tiered (nested?) uncertainty & confidence bands - subset populations

I have a current and historical dataset of likelihood that a population gets into a car accident. I have my predictions for a rare event - say the % chance that a given driver gets in a car accident ...