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0answers
15 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 ...
2
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1answer
13 views

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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0answers
21 views

Correcting for sampling in arbitrary distributions

Let's say I've got a series of Gaussian random variables $^{1}x_{i} \sim N(x_i,\sigma_i)$, with each $\sigma_i$ different, but known a priori. I've got another identical series of Gaussian random ...
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1answer
30 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 ...
4
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3answers
73 views

Kernel density estimation incorporating uncertainties

When visualising one-dimensional data it's common to use the Kernel Density Estimation technique to account for improperly chosen bin widths. When my one-dimensional dataset has measurement ...
6
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1answer
99 views

How to measure uncertainty of a parameter when false positives exist?

The main goal of my research is to measure the percentage of brown dwarf stars in the Pleiades star forming cluster that are actually double stars (i.e. the brown dwarf star has a companion brown ...
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0answers
32 views

Uncertainty in gradient of data

So I have a set of 9 x,y values, and I need to find the gradient/slope of the data, AND its associated error. Without the error, I would've used Excels LINEST function, but as the errors in my y ...
1
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1answer
46 views

Uncertainty in Genetic Algorithm output

I'm applying a simple genetic algorithm to an optimization problem (I need to find a 4-parameter function's global minimum) I start the generations run with say ...
0
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1answer
42 views

Is there a way to measure the viability of an experiment?

Is there a way to calculate a number that evaluates the viability of an experiment? By that I mean the probability that the observed probability is just chance. I read about the $p$ value, but it ...
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0answers
33 views

Incorporating systematic uncertainty in interval estimation

I am trying to fit some binomially distributed data to a model. There is a reasonable systematic error associated with the measurements. This uncertainty comes from imperfect theoretical knowledge of ...
1
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2answers
77 views

standard error of the estimated p-values from simulations

This might be a question in general: due to computational burden, I have to use a subset of my complete data (say, 1,000 out of the complete 10,000 observations) to get a p-value of a test. The test ...
1
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0answers
41 views

how the uncertainty of the coefficient in the model affect the uncertainty of the fit

I am wondering how to estimate the uncertainty of the fit if the coefficients in the model have uncertainties as well. for example: I try to use model y=exp(-(a+b)*x)+c to fit a data set x and y to ...
3
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2answers
102 views

How to get asymptotic covariance matrix when observed information matrix is singular

I'm fitting different models by Maximum Likelihood. To do this I'm using a stochastic version of Newton-Raphson algorithm, where both the gradient and the Hessian of the likelihood are estimated at ...
6
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4answers
201 views

Classifier for uncertain class labels

Let's say I have a set of instances with class labels associated. It does not matter how these instances were labelled, but how certain their class membership is. Each instancs belongs to exactly one ...
2
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2answers
57 views

Parameter confidence intervals which include errors in data

My question seems to be very basic one but my search has not given any similar question. I have small dataset of 8 $(x,y)$ values with uncertainties for $y$ (dependent variable) and the theory ...
1
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0answers
27 views

Monte Carlo by time or by interval

Say I compute monte carlo output from input scenarios. Input are discrete time series. I choose time series as an example to make the problem more obvious - this could be also any curve. Computation ...
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3answers
1k views

Calculate uncertainty of linear regression slope based on data uncertainty

How to calculate uncertainty of linear regression slope based on data uncertainty (possibly in Excel/Mathematica)? Example: Let's have data points (0,0), (1,2), (2,4), (3,6), (4,8), ... (8, 16), but ...
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0answers
57 views

Determining uncertainty propagation for an overdetermined set of equations

I have this problem of the following format. \begin{align*} x_L &= X\left(\frac{dx_L}{dX}\right) + Y\left(\frac{dx_L}{dY}\right) + Z\left(\frac{dx_L}{dZ}\right)\\ &\\ x_R &= ...
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1answer
131 views

Simulating Monte Carlo with different standard deviations and interval confidence

I have a question regarding Monte Carlo simulation (direct simulation), applied to propagation of uncertainties. From what I understand Monte Carlo accepts random numbers of each input variable of ...
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0answers
40 views

Calculating point AND uncertainty estimates for IRT factor scores

I have a survey dataset that includes items designed to measure several latent variables. There are around 3-5 items per latent variable. The items generally use 5-point response sets, so I would like ...
4
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0answers
238 views

Uncertainty propagation in linear interpolation

How do I calculate the uncertainties in linearly interpolated values from a given tabulated function? I am just coming back into the fold after a bit of a hiatus, and am having trouble ...
3
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1answer
179 views

Adding uncertainty range to probability density function using bootstrapping

I'm hoping this isn't a ridiculous question! Here goes... I would like to visualise the range of uncertainty in a probability density function fit to observed data using Maximum Likelihood ...
0
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1answer
156 views

What is the difference between the Monte Carlo (MC) and Monte Carlo Markov Chain (MCMC) method?

The goal of both methods seems to be to derive an estimate of a posterior/target distribution. If a process model exists which links some input parameters (which are themselves uncertain and can be ...
1
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1answer
76 views

Modelling uncertainty with probability distributions

Suppose we’re building a system with certain qualities that we’re interested in, e.g. response time, battery usage, etc. Each of the system’s qualities depends on our decision about components we use ...
4
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1answer
166 views

Confidence error bars and “central point”: Should we emphasize the median?

Say I want to plot summary data with a point and a 95% confidence interval around that point. What should my point really be? Mean, mode, or median? I know that mean = median for any symmetrical ...
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0answers
16 views

Covariance of function uncertainty, why (J^T)*S*J? [duplicate]

As I understand it; to get the uncertainty of a function that is based on some measurements, the derivative of this function with respect to this measurment has to be calculated, and multiplied by ...
3
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1answer
180 views

how to estimate CTR (ctr-click-through-rate)?

How many times should a banner be shown to estimate its click-through-rate (CTR)? For example, if a banner was shown $x$ times, and was clicked $y$ times. $$\text{CTR} = \frac{y}{x}$$ How could I ...
0
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1answer
187 views

Mean of means -> error propagation or uncertainty or both?

my problem is as follows. I have a simulation of a neural network which creates activity patterns, learns them and then tries to retrieve previously learned patterns one by one. The performance of ...
6
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2answers
400 views

How to find +/- uncertainty with a least squares regression

I have a set of data points with an uncertainty on each point. From these data points I can fit a line, who's which the slope is a significant value. How do I use the information I have to get an ...
3
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1answer
102 views

Can someone explain this uncertainty estimation technique to me

I have been trying to understand a method of finding parameter uncertainties resulting from maximum likelihood estimation. Unfortunately the document I have is not in the public domain however I have ...
1
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0answers
21 views

Calculate a monthly uncertainty from an annual uncertainty

Given a normal distribution of annual mean values (sunny days per year), I know the P50 and the annual uncertainty. Is there any method to calculate the monthly uncertainty? Thank you very much.
5
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2answers
517 views

Histogram of uncertain data

I have a set of values, each of these values has its own mean and variance. I want to be able to account for this variance when I plot the histogram of the means. Something like an error bar on the ...
4
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1answer
1k views

Can I convert a covariance matrix into uncertainties for variables?

I have a GPS unit that outputs a noise measurement via covariance matrix $\Sigma$: $\Sigma = \left[\begin{matrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\ \sigma_{yx} & \sigma_{yy} ...
1
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1answer
200 views

Propagation of uncertainty through an average

I have a set of distance measurements that are all accurate to +/- 0.01 M. {1.00,2.00,3,00} We can obtain the distance moved ...
5
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3answers
229 views

What is the preferred way to give asymmetric uncertainties?

I have seen something like $4.1^{+2.1}_{-1.5}$ or $4.1 [+2.1, -1.5]$ but I would like to know, what is the preferred way or something like a standard in scientific work (especially in ...
2
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0answers
152 views

Linearity in local sensitivity analysis

As it is know local sensitivity analysis attempt to quantify the local impact of input factors on the model, through partial derivatives: a derivative of the outputs accordingly to the inputs, when ...
1
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1answer
71 views

Level of uncertainty when measuring a period of time?

I need to create a raw data table for my science experiment, but I'm unsure what the level of uncertainty would be when measuring days. How would I determine the level of uncertainty when measuring a ...
3
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1answer
529 views

How to determine calibration accuracy/uncertainty of a linear regression?

To determine organic carbon concentrations in a water solution from UV spectroscopy I made a calibration curve with known carbon concentrations and measured the UV absorbance. I used R for the data ...
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0answers
183 views

ANOVA with uncertain values - attempt to redefine node

I'm trying to do one-way ANOVA on uncertain (latent) input value YReal[i] (each input value is not exactly known, but it is given as normal distribution with mean ...
2
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1answer
78 views

Uncertainty modeling for samples

I have instances of data that are composed of 6 attributes. Each attribute takes values between 1-10. Any instance has a utility calculated by some utility function: Example: {1,1,2,5,5,2} , utility ...
3
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2answers
336 views

Uncertainty and sensitivity analysis

I have the following problem: Given inputs $x$ ($n$-dimensional vector) of scalars, ordered integers and unordered integers (i.e., labels) and one or several outputs $y$, I would like to ...
2
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2answers
282 views

Fitting distributions and comparing tails

Suppose I have some data points (0.6695, 0.5968, 0.7641, 0.7252, and 0.7779) and want to fit different distributions to this dataset, say, log-normal and log-t (with different df), and then compare ...
0
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1answer
92 views

Expected deviation and uncertainty for a number of environmental measurements

I have a couple of measurements for an environmental variable on different locations (7 measurement stations) as time series with averages for every year. For the single locations I have calculated ...
1
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0answers
432 views

Uncertainty of extrapolation (curve fitting)

I have estimated (MC simulated) some probability values y, that each depends on a value of x between 0 and 1. Say, for instance, that the vector x contains $x_{1} = 0.1,\ \ x_2 = 0.2,\ \ x_3 = ...
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3answers
359 views

How best to communicate uncertainty?

A massive problem in communicating the results of statistical calculations to the media and to the public is how we communicate uncertainty. Certainly most mass media seems to like a hard and fast ...
4
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2answers
229 views

How do I handle measurement error in sparse data?

Under-educated non-statistician seeks short-term relationship for very one-sided benefit. System in question involves rocks and physical properties. Modelling bits of the earth typically means few ...
1
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3answers
132 views

Learning measurement uncertainty; could not find any online resources

I'm currently writing a lab report on Atwood's machine, and the gist of it is that $a=a_{g}\tfrac{\left ( m_{2}-m_{1} \right )}{\left ( m_{2}+m_{1} \right )}$. We're holding $\left (m_{2}+m_{1} ...
1
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0answers
54 views

Correlation of elevation data and elevation uncertainty as a function of range in a DEM

I would like to ask a question to experts on spatial statistics: I have a gridded Digital Elevation Model (DEM) which provides terrain elevation (z) at cartesian coordinates (x,y). Together with the ...
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1answer
187 views

Correlation under uncertainty

I've got two sets of measurements whose uncertainty has been quantified: $x_1..x_n$ and $y_1..y_n$. For each $x_i$ and $y_i$, I have not only a point estimate but also an interval that expresses my ...
0
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0answers
107 views

Error amplification in linear regression with uncertainties in design matrix

I am running a least squares regression, and I am trying to estimate the uncertainty on the fit solution. The problem is, I have an uncertainty in my design matrix coefficients as well as in my ...