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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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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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27 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
26 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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17 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
108 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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13 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
21 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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28 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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44 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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24 views

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
48 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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113 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 ...
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17 views

Is it more accurate to measure an object with 4 scales, or 1 scale?

If I know the relative uncertainty of an instrument, and I take multiple measurements of the same thing with that, how do I know my new relative uncertainty? For example: Does my relative uncertain ...
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1answer
151 views

Working out error on fit parameters for nonlinear fit

I am struggling to find a concrete formula for the Hessian or Jacobian in respects to fitting parameters. I have implemented some fitting in Java using the Apache Common Maths package for the ...
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22 views

Individual data point variance and covariance

In the paper, "Data analysis recipes: Fitting a model to data" (Hogg, Bovy, Lang), individual data point variances are found and used for subsequent statistical analysis. The data and corresponding ...
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1answer
14 views

How does the unit affect the propagation of uncertainty?

Say I'm measuring two lengths, $L_1$ and $L_2$, with a measuring stick in cm. For concreteness, let's say that $L_1 = 10 \pm 1$cm and $L_2 = 20 \pm 1$cm. I now want to compute the ratio of those two ...
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49 views

Optimal subset from training data used in Random Forest

I have a set of say 10,000 spatial locations with associated values of a soil property (e.g. soil clay). In addition, I have 100 spatial covariates (e.g. elevation) which cover entirely my study area. ...
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24 views

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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1answer
39 views

Comparison of Bayesian Neural Network with Multilayer Perceptron

I have a machine learning project with not so much data, so I have the following reasons to use Bayesian neural network (not Bayesian network / directed graphical models) for my work: There are ...
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7 views

Calculation of the acceleration correction for BCa bootstraps for data with known errors

I have paired measures for a set of data, and these measures have associated uncertainties. I'm attempting to correlate them using Kendall's tau-b (as we have reason to believe that while they are ...
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72 views

Linear Fit with uncertainty on data [closed]

I read a lot about the argument but I found a lot of different opinions and ways to act. I have a set of data that theoretically should lie on a straight line. Experimentally I have data with their ...
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53 views

Conditional Distributions for continuous sets using bnlearn

I created and fitted a Gaussian Bayesian network using the bnlearn package in R. I am able to make predictions on my test set but I'm only getting point estimates of the predicted values. I would ...
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51 views

Metrics for uncertainty estimates in steering angle prediction

I am working on steering angle prediction for self-driving cars. Assume the model has an output $\{\hat{y},\hat{\sigma}^2\}$ for the (continuous) steering angle $\hat{y}$ and variance $\hat{\sigma}^2$ ...
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117 views

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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Log-measure of uncertainty

I would like to investigate if the following quantity has already a well-known meaning in statistic: $$G_{\eta}(X) =\frac{1}{\eta} \log\Biggl[1 + \lim_{N\to +\infty}\sum_{n=2}^N\frac{\eta^n}{n!}\...
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Fisher Matrix of best-fit parameters when modelling a time series

I have a time series dataset and a best-fit model. I want to calculate $1\sigma$ uncertainties in my model parameters using a Fisher matrix. My model is a linear combination of sine waves. For ...
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42 views

Confidence intervals for bilinear interpolation

I have 4 data points which I am using to interpolate a query point using bilinear interpolation. Each of the 4 data points is obtained from the average of several observations (typically 10-16 for ...
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27 views

survival analysis, censoring endpoint unknown

I writing a study on migration. I have census data from one particular year (1900) and information who has emigrated and when exactly from years (1900–1910). I was thinking about doing survival ...
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1answer
50 views

Prediction error in Neural Networks

With Random Forests, one can estimate the prediction error using out-of-bag simulations. So for every sample in the training/test-set, one can estimate the predictive uncertainty. What would be the ...
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131 views

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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22 views

Sine-Wave Fit To Time Series: Confidence Limits For Non-Normal Data

I have a time series that I know to be made up of several sine waves: $F(t)=C + \sum_{i=1}^NA_i\sin(2\pi f_it+p_i)$ Where $C$ is a normalization constant, and $(A_i,f_i,p_i)$ are the amplitude, ...
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2answers
265 views

Accounting for uncertainty in a mixed-effects regression

I have calculated an effect size along a dataset of experiments distributed worldwide through a mixed-effects meta-regression. The effect size in the dataset depends on climate (y ~ temperature + ...
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Uncertainty propagation with unsuccessful curve fits

I have a set of measurement results and their uncertainties that I need to fit to an implicit nonlinear function of four parameters. If the uncertainties are large enough, this works like a charm. If ...
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80 views

How to quantify uncertainty in nonparametric regression models

I'm trying to get a handle on what the current state of things is when it comes to quantifying uncertainty in nonparametric regression models. It seems like the options are Use a Bayesian model and ...
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49 views

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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20 views

Confidence interval of a mean when single measurements have uncertainty

I have following problem: There is a process in which I would like to determine exposure of sample irradiation (in Lux*hours). I measure illuminance every 10 min over 24 hours, getting 144 data ...
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Nested cross-validation and quantifying uncertainty

Background: I'm working on a ML project to predict a continuous target and am comparing different models using nested cross-validation, where I don't have access to the test set for which my model ...
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52 views

How to estimate confidence interval for weighted correlation

It is my understanding that the confidence interval for a Pearson correlation is asymmetric. (Confidence interval for correlation, for example.) r’s command ...
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51 views

Propagation of uncertainty

I have a problem to understand the concept of propagation of uncertainty. To be honest there are two issues am confused about. (1) Do we need to use sum of uncertainties or sum of squares? (2) ...
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44 views

Conveying uncertainty in accuracy measurements for machine learning models

I've noticed that depending on how I sample training and test samples I can get a range of model accuracies, but the mean of those accuracies is reasonable. Also for methods like random forests and ...
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53 views

Uncertainty associated with a multiple linear Regression model

I am using a model for some part of my research and in that I am using a multiple linear model. I have a dependent variable (y) and 4 independent variable(y1,y2,x1,x2). So my model looks like below ...
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1answer
109 views

Bayesian updating with discrete priors + possibly unknown classes

I'm following along with some lecture notes on Bayesian updating with discrete priors. They give an example problem to illustrate some of these concepts, which I briefly restate here: Someone tells ...
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13 views

Is my uncertainty estimate good?

Given is a forecast method that predicts time series $X_t$. Method returns state estimate $\hat{X}_{t+1}$, as well as uncertainty $U_{t+1}$ (let's think of it as "expected error"). What are ways to ...
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28 views

Confidence interval from monte carlo realizations of linear regression

I have a simple linear model where my y variable has associated measurement uncertainty. To determine the effect of that measurement uncertainty on my model predictions, I used a Monte Carlo approach ...
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1answer
46 views

Uncertainty of the fitting parameters and the function using Monte Carlo methods

We have a set of measurements with known uncertainty both in dependent and independent variables. The uncertainties follow Gaussian distributions. The model function is known and nonlinear. How can ...
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23 views

How do I calculate the predictive uncertainty on an average of multiple predictions?

I have two time series (10 minute intervals) of wind measurements at two locations quite far from each other. These are so far away from each other that they have quite different wind speeds, but they ...
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21 views

Comparing the efficiency of confidence interval regression methods

I'm trying to compare the performance of various regression methods that can produce confidence intervals (CIs) for their predictions. Examples include quantile regression and CIs for linear ...
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24 views

How to interpret uncertainties in interpolated and smoothed timeseries?

I have a years worth of surface reflectance data, collected daily via satellite. However, some days are totally cloudy, so there were no observations. That being said, I use linear interpolation to ...
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17 views

Estimating variance/predictive posterior from quantiles

Quantile regression methods allow us to get a measure of uncertainty for our predictions by computing a quantile estimate for the dependent instead of a point estimate. For example I could perform a ...