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0answers
17 views

Uncertainty on ratio of integrals (correlated)?

I have a histogram, and a quantity defined as the integral of a subrange of that histogram (int_sub) divided by the integral of the full range (...
0
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0answers
20 views

Inferring the bias of two types of coin

I would like to find the bias of a type of coin, when there is uncertainty about which kind of coin I am testing. The scenario is as follows, there are 2 mints in my neighbourhood that produce ...
2
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2answers
45 views

How might Google go about estimating and updating traffic speeds?

This is, I guess, a specific example of a wider class of problem, one to which there must be a well-established solution, but which I, as a relative layman when it comes to statistics have thus far ...
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0answers
14 views

Under what assumptions can parameter estimate uncertainty be estimated from the Hessian?

Given a model with some parameters, some data it's attempting to reproduce, and a distance function to quantify how well the predictions correspond to the data, I can fit parameters via a general ...
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0answers
16 views

Usage of standard deviation in random forests regression (for expected improvement)

It seems to me that the awareness of this problem is not high enough. Often the standard deviation (so the sd from each prediction of each tree in the forest) from the random forest regression is ...
1
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0answers
42 views

Which kind of “uncertainty” is this?

I'm a bit confused about all the different "definitions" of uncertainty? One can calculate "uncertainty" of a single measurement by simply checking how accurate the tool that is being used to do the ...
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0answers
21 views

Propagation of uncertainty: entropy of multinomial

My goal is to estimate the entropy of a multinomial distribution, based on a single observation (a set of counts for each possible outcome). I also want to calculate the uncertainty in my estimated ...
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0answers
22 views

cumulative uncertainty with time series predictive model

So I have a time-series with a set of variables a, b, c... and another measured variable y. What I do is using the initial state of a,b,c and y (at t0), I predict what y "should" be at the next time ...
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0answers
19 views

Squared uncertainties: what may it be used for?

If the squared standard deviation of a set of values is the variance of this sample, then, what is the squared standard error of the mean of this sample ? and what may it be used for ? A quick search ...
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0answers
15 views

estimating model fit parameters using simulations

I'm trying to fit 2D ellipticals gaussians to an image (with correlated background noise) using prewritten fitting software. I'd like to know about the uncertainty in the fit parameters with this ...
0
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0answers
11 views

Classification under uncertainty in observations

I am tackling a multiclass classification problem where the values of the independent variables are not known with certainty. Instead, each observation is represented by a multivariate Gaussian pdf ...
3
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0answers
32 views

Intuitive and Formulaic Justification for the Rao-Blackwell Theorem

I've tried looking online and I can't seem to grasp the Rao-Blackwell theorem. Could someone please give an intuitive explanation backed up by formulae.
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3answers
34 views

Error Propagation

I come from a physics background where the only error propagation I've dealt with was in the lab using the simple formulas found here: ...
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1answer
138 views

Should additional crime reports about someone change our level of doubt about an initial crime report?

Edit: Note that this question is not about multiple unreliable witnesses to the same incident, but rather multiple incidents with only one witness each. Should the accumulation of separate alleged ...
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0answers
37 views

Shape uncertainty of a 3D point cloud

Given a point cloud of a 3D object, how to calculate the shape uncertainty in this discrete sample set? and what factors maximize or minimize this uncertainty?
0
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0answers
22 views

How to properly consider uncertainty propagation in random variables

I have 34 input random variables and one output random variable, named R. From 33 input random variables and some dataset I determined the best predictive ...
1
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2answers
149 views

Power law fitting of data with uncertainties

I need to fit data points on a power law and each one of these carries an uncertainty. I've been using Python, more precisely scipy.optimize.curve_fit to get the job done but I don't know how to ...
2
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1answer
42 views

In OLS is it methodologically correct to use the variance of a variable as an explanatory variable?

Are some OLS assumptions not satisfied if I use the variance of a variable as a proxy of uncertainty in a regression? For instance, would it be methodologically correct if I use moving averages of ...
1
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0answers
13 views

Power to detect significant correlation given measurement uncertainty

First of all, apologies if some of the technical terminology in here is not accurate - my experience with statistics is fairly limited. To illustrate my problem, let's say I wanted to design a study ...
2
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1answer
32 views

To use or not to use a variable that contains information w.r.t. uncertainty

The data I'm looking at is concerned with percentages of people who would recommend a hospital. ...
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1answer
34 views

Uncertainty consistency?

The problem statement, all variables and given/known data I am given a set of x and y values x: (1,2,3,etc.) y: (1.2,2.2,3.1,etc.) with a given uncertainty and am asked a) find the best fit b) ...
0
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1answer
14 views

Uncertainty analysis

Here is my situation. I am trying to predict the 'entire' distribution of the dependent variable, not just the mean( or conditional mean). Does it then make sense to seprateley predict quantiles of ...
1
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3answers
57 views

Combining sources of uncertainty/variation in a multi-layered linear model

I’m having trouble understanding how to combine parameter uncertainty and interannual variability from various levels in a bootstrapped linear model. Specifically, this model is designed to generate ...
2
votes
1answer
164 views

Principal component analysis with known uncertainty varying across both samples and variables

I want to do dimensionality reduction on a data set $X_{ij}$. In this case, $i$ indexes samples and $j$ indexes a large number of variables (densities at different locations in space). The units of ...
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0answers
11 views

Influencing scores with level of uncertainty when sample is small

I am doing a thesis research on fraud in a review dataset and have a hard time solving the following problem. I created a feature that calculates the disagreement between two types of users (new and ...
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0answers
63 views

Estimation of percentiles in multivariate posterior distribution

Background: I am using Bayesian inference to find a posterior density. The parameters are change points in a piecewise Wiener process, and I wish to calculate the hitting time of some threshold $a$. ...
2
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0answers
51 views

Cheaper/faster method to estimate uncertainties than bootstrap

I'm using a genetic algorithm (GA) to estimate the minimum value of a likelihood function $L[x]$ which is too complicated to evaluate mathematically. This likelihood function quantifies the goodness ...
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0answers
56 views

Derivation of uncertainty propogation?

For a function $$ y =f(x), x=\left(x_1, x_2, ..., x_N\right)$$ the law of propagation of uncertainty, see GUM sect 5$^{[1]}$ (pdf), is generally given as $$ u_y^2 = \sum_{i=1}^N \left(\frac{\partial ...
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0answers
32 views

Upper Bound of Measured Data

HW question I am having trouble on: My attempt at solving it: I thought part (a) was pretty straight forward until I worked it out and got the same value of K for K_upperbound which I assume is ...
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0answers
84 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
18 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 ...
0
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0answers
27 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 ...
1
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1answer
101 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
222 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
105 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
43 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
110 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
46 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 ...
1
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0answers
44 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
95 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
43 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
259 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 ...
7
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4answers
508 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
88 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 ...
6
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3answers
4k 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 ...
0
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1answer
202 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 ...
5
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0answers
552 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
votes
1answer
318 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
votes
2answers
377 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
94 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 ...