Questions tagged [statistics]
The statistics tag has no usage guidance.
642
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Errors when the quantity is an exponent
Errors add up in addition or subtraction.
Relative errors add up in multiplication or division.
When a quantity is raised to a power, the error is increased by times of the exponent.
Now what if the ...
1
vote
1
answer
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How to use error propagation formula in equation with inseparable variables?
$$
R_i(t) =
\frac{\mu_{s,E_i}+\mu_{s,E_0}}{\mu_{s,E_i}-\mu_{s,E_0}}
\cdot
\frac{e^{-\rho\sqrt2\mu_{s,E_0}}-e^{-\rho\sqrt2\mu_{s,E_i}}}{1-e^{-\rho\sqrt2(\mu_{s,E_0}+\mu_{s,E_i})}}.
$$
How do I can find ...
-1
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0
answers
32
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Propagation of error from statistical error [migrated]
We have done the determination of protein abundance in two fractions (M and P) in one condition (SP).
We've done three biological replicas.
The data obtained are:
\begin{align*}
&\text{SP (...
1
vote
1
answer
92
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Ising model and the axiomatics of Statistical Mechanics
I am revisiting Statistical Mechanics to better understand models of spin glass and was wondering to what extent axiomatics of Stat.Mech. applies to an ensamble of spin configurations. In particular, ...
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Central Limit Theorem for subsamples [migrated]
I observe a set/realisation of $n$ i.i.d. $\{X_1, X_2, ..., X_n\}$.
Because of the Central Limit Theorem, I know that repeating such an observation enough times, the pdf of the mean of such $n$ ...
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1
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1
answer
42
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What is the optimal measuring time split for limited measuring time between signal+background and background in a Poisson counting experiment?
I’m trying to figure out the best split of time between measuring either background or signal+background in a counting experiment in the case where we have no prior knowledge about the mean signal ...
0
votes
1
answer
68
views
Curve fitting and error propagation for non-independent quantities
I have measurement values $y_\mu$ at times $t_\mu$; the should follow a function $y(t) = f_t \, \cos (\Omega_t\cdot t - \delta)$ where $f_t, \Omega_t$ are slowly varying functions (currently I am ...
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1
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50
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Distribution sampling from a trajectory
Consider a sequence of random variables $\{X_1, X_2,.., X_n\}$ corresponding to regular measurements of a single observable over time obtained from a laboratory or computer experiment.
Assume that the ...
- 7,082
4
votes
1
answer
526
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How large a closed system does the 2nd law of thermodynamics require?
Does the second law of thermodynamics apply to a single electron in deep space? Or two electrons? Or 100? (assume the electrons are restricted in a finite area)
From which point we can start to talk ...
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vote
2
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Mean squared displacement of a particle on a biased random walk [closed]
Given a particle on a 1-D random walk with some drift velocity $\nu_d = \frac{\Delta x_d}{\Delta t}$, the position in at some time step j is given by $$x_j=x_{j-1}+k_j L + \Delta x_d$$ where $L$ is ...
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40
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Which statistical methods are better than basic random scans for studying and exploring the parameter space of extensions of the standard model?
Given a lagrangian of a new model beyond the standard model, and given a set of constraints, say the oblique parameters for instance and the decay of the higgs boson and some signal strengths and ...
- 55
0
votes
1
answer
177
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Measurement Error Analysis in Gaussian distribution
I am new to statistics and recently learned about ISO guidelines for Accuracy & Precision and Uncertainty & Error. But there are some graphs of probability distribution I found on internet ...
- 109
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1
answer
53
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From where does the uncertainty formula come from? [duplicate]
The uncertainty formula is the one used in the laboratories to find the uncertainty of a variable. Say $X$ is a function of $Y$ and $Z$ such that $X=X(Y,Z)$ then it's uncertainty can be found with: $$\...
- 143
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0
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Integral over rapidly randomly fluctuating function [closed]
As a part of my bachelor thesis on cosmic structure formation I have been dealing with a sum of many randomly distributed phase factors, so in principle with a pearson random walk. If there are $N$ ...
2
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1
answer
120
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Why don't I get a whole number when determining the vibrational energy level of F2?
So I was playing around with some data and formulas and wanted to calculate the index for the wave number of the vibration of F2 that I got from here, i.e. which allowed energy level n this ...
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2
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Median Uncertainty propagation
I have a data set of values each with a different associated error. If I take the mean, I can use standard error propagation to calculate a much smaller error. This will therefore incorporate the ...
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1
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54
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Error analysis for counting experiments
i am trying to refresh my knowledge in error analysis and stumbled over an interesting question.
Suppose i have a radioactive compound and i want to measure the standard deviation of the decay count. ...
- 66
4
votes
2
answers
511
views
Error analysis via two different methods
We have a quantity $a$ expressed in terms of two quantities $b $ and $c$ as $a = b/c$.
It seems to me that there are two ways of estimating the error on $a$, the "physics" ...
- 109
0
votes
1
answer
50
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Correct Way to Calculate Uncertainty [closed]
Given a function $f(x_1,x_2,...,x_n)$ of $n$ uncorrelated variables $x_1,x_2,...,x_n$, each of which has some small absolute uncertainty $\Delta x_1,\Delta x_2,...,\Delta x_n$, I know that the ...
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7
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Line of Best Fit with or Without Constant Term
Some other physics teachers and I were discussing an AP problem about a potential experiment for measuring $g$ and disagreed on the best way to use a line of best fit to analyze the data.
The ...
- 6,899
1
vote
2
answers
105
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Units in a Poisson probability mass function
I'm trying to calculate a likelihood ratio test, but some of the units in the calculation don't make sense to me.
I have a toy 1-dimensional X-meters-long photon detector, and I'm trying to calculate ...
0
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0
answers
45
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How should I normalize the histograms for signal vs background study?
I am currently working on a signal vs. background study for some particle physics detector.
I am having a hard time understanding how I should normalize the signal/background histograms such that my ...
0
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2
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125
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Can the standard errors in the slope and the intercept of a linear regression be used to get the uncertainty in the dependent variable?
I have bought a resistor that works as a heater when a voltage is applied to it, and the seller provided me these $ \left(V (\mathrm{V}), T (\mathrm{°C})\right)$ points: $(6.20$, $200)$, $(7.75$, $250)...
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0
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Why on the ATLAS Higgs discovery paper there are uncertanties on the expected cross section upper limits but not on the observed upper limits?
I was reading the ATLAS paper on the Higgs discovery and a question came to my mind. In the plot I attached, there are uncertainty bands on the background only hypothesis upper limits, and not on the ...
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votes
1
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99
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Level spacing statistics of the quantum Ising model
Consider the quantum Ising model defined by the Hamiltonian
\begin{equation}
\hat H=-\sum_j\hat\sigma_j^z \hat\sigma_{j+1}^z-h\sum_j \hat\sigma_j^x-g\sum_j\hat\sigma_j^z.
\end{equation}
For $g=0$, ...
2
votes
1
answer
451
views
Significant figures and angles
We measure an angle to be -55 degrees (2 sigfigs).
Let us take the sine of this angle. We get sin(-55) (2 sigfigs). Now, since sin(-55)=sin(305), then we can also take the sin(305) (3sigfigs). Now, ...
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0
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What is the quantum effect that makes the quantum annealing expectation maximization algorithm robust to local maxima in the likelihood function?
The Expectation Maximization (EM) algorithm is a classic method of maximum likelihood estimation for problems involving missing (latent) variables. This method is particularly useful in estimating ...
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0
answers
76
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Wilson Coefficients in the Standard Model
I'm not particularly knowledgeable in this area of physics. From my understanding as an undergraduate, Wilson coefficients are sets of parameters that arise from an effective field theory which ...
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2
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507
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How can I resolve this apparent paradox about the average age and the average lifetime?
I've got very much confused about distributions and am looking for quick help. Distributions are common in physics, so I humbly hope to receive an answer that will resolve my confusion.
Let's suppose ...
- 1,429
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1
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Uncertainty measurements done with multiple devices
so I need to calculate the volume of a cylinder. I have measured both the radius and the height with three different devices (ruler, calipers, micrometer), each of them 10 times (total 90 measurements)...
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2
votes
1
answer
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Problem with the Fisher information matrix in case of $N$ measurements of two observables
Let consider two observables, $x$ and $y$. Suppose that $y$ depends on the independent variable $x$ through the model $m(x; \boldsymbol{\theta})$, where $\boldsymbol{\theta}$ is a vector of model ...
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2
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Uncertainty Calculation: Applying Product Rule instead of Power Rule
I use $\delta$ to represent absolute uncertainty. The power rule for the calculation of relative uncertainty in $t^2$ is
$$\frac{\delta (t^2)}{(t^2)}=2\left(\frac{\delta t}{t}\right).$$
But if I treat ...
-1
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1
answer
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Is there sufficient "content" in the field of econophysics to write a substantial undergraduate thesis/project on? [closed]
Okay, maybe the title is somewhat misleading. My university calls this a BSc Project, but it is limited to between 4000 and 6000 words, so it isn't particularly long. Anyhow, one of the projects ...
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How are the standard deviation, expectation value, and uncertainty related for a wave function?
In my introduction to Quantum Physics class we're learning about wave functions and uncertainties (with a great deal of it being shown through graphical means). However, in the notes from my lecture I ...
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1
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Failure distribution for florescent lights. Is the failure per unit time constant or does it increase with bulb age? [closed]
what is the distribution for the statistic:' time to failure' for florescent light bulbs. does the probability of failure per unit time stay fixed as the bulb ages, or does does it increase.
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vote
2
answers
82
views
Significance of continuity of normal vs. Poisson distribution in central limit theorem
Say I have an experiment where we have a radioactive source, and we measure the particles detected. At the start, we use a thin metal sheet to cover the detector such that the mean number of counts ...
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0
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Physical interpretations of covariance and correlation in Statistics [closed]
(I was directed to this site from Mathematics SE!)
From what I know, theoretically, covariance is a measure of the degree to which two variables change together. A positive covariance indicates that ...
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0
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14
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Uncertainty on a mean with individual measurement uncertainties [duplicate]
Let's say I measure the diameter $(x)$ of five checkers pieces, using a ruler with a precision of $\pm 0.5mm$, and get the following results:
$x_1 = 50 \pm 0.5mm, \; x_2 = 51 \pm 0.5mm, \; x_3 = 48 \...
- 11
3
votes
0
answers
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Motivation of $p$-spin glass model
In general, the $p$-spin glass model focuses on $p$-body interactions like
$${\displaystyle H({\boldsymbol {\sigma }})=\sum_{i_1,...,i_p} J_{i_{1},\ldots i_{p}} \sigma _{i_{1}}\cdots \sigma _{i_{p}}.}$...
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Geiger tube counts-per-minute Poissonian, but counts-per-hour not. Why?
I am testing a Geiger tube and counting its pulses. Because the pulses are random, I expect the counts-per-minute (cpm) to follow a Poisson distribution. That's indeed what I found:
mean cpm = 38.39
...
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3
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Distribution result of flipping coin with same initial conditions repeteadly
Still related with that question Flipping a coin with same initial conditions.
While it was asking about flipping coin with same initial conditions and the chosen answer said it's impossible to toss ...
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votes
1
answer
43
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Statistical significance for longer measurement
I recently read that icecube neutrino detector measured neutrinos emmitted from the direction of NGC1068, which is a nearby Active Galactic Nucleus which has reported an excess
of neutrinos from that ...
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1
answer
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Higher order (order > 2) derivatives of free energy - higher cumulants in statistical mechanics
The first derivatives of free energies generally give relationships between thermodynamic conjugate pairs, like
entropy $S$ & temperature $T$
pressure $P$ & volume $V$
and so on.
The second ...
- 2,935
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98
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Fitting histograms and error propagation
I am new to fitting histograms and as a result i have an issue understanding what to consider as error propagation when calculating a quantity. The following diagram shows entries for 4 different x-...
- 11
1
vote
1
answer
256
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Accidental coincidence formula
Suppose you have a setup with $n$ scintillators coupled with $n$ PMTs. These signals are passed to a discriminator. I am observing some signal, let's say this signal is coming from cosmic rays and I ...
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Does the difference between the definition of probability in physics and probability in mathematics really matter?
The realistic definition of transition probability in physics is well defined and constrains the probability to rational numbers.
The abstract definition of probability in mathematics is also well ...
user349605
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564
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Error propagation for a constant divided by the value
I have a value (let's just call it $x$) and am given its uncertainty. However, how would I find the uncertainty of $2/x$? I know that for other constants, if it was something like x/2 or 2x I would ...
- 1
0
votes
1
answer
50
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Is there any continuous distribution (except Gaussian) that can be characterized by their first and second moments only? [closed]
I am trying to figure out why Gaussian distribution is uniquely significant in random physical processes. I think the answer lies in its characterization by only two moments. In a way it is the ...
2
votes
1
answer
81
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Post-fit distribution
In experimental particle physics papers, often one reads "pre-fit" and "post-fit" distribution as the caption of some kinematic distribution of data and simulation.
What is meant ...
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1
answer
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Getting different uncertainties for the same variable [closed]
I was given frequency and wavelength of a wave and asked to find the period and uncertainty in the period.
I first found the uncertainty by doing $$\Delta T = \Delta (1/f)=T\sqrt{(\frac{\Delta 1}{1})^...
- 11