Questions tagged [statistics]

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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 ...
Harikrishnan M's user avatar
1 vote
1 answer
51 views

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 ...
Anchal Kumar Sharma's user avatar
-1 votes
0 answers
32 views

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 (...
Paula Portela's user avatar
1 vote
1 answer
92 views

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, ...
MsTais's user avatar
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0 answers
17 views

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 $n$ ...
dariom's user avatar
  • 1
1 vote
1 answer
42 views

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 ...
Physicist_285's user avatar
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 ...
TomS's user avatar
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0 votes
1 answer
50 views

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 ...
gatsu's user avatar
  • 7,082
4 votes
1 answer
526 views

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 ...
Merci chao's user avatar
1 vote
2 answers
101 views

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 ...
mertvy's user avatar
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0 answers
40 views

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 ...
Collector101's user avatar
0 votes
1 answer
177 views

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 ...
Govind Prajapat's user avatar
0 votes
1 answer
53 views

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: $$\...
Ulshy's user avatar
  • 143
2 votes
0 answers
38 views

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 $N$ ...
Ricardo Ochel's user avatar
2 votes
1 answer
120 views

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 ...
iwab's user avatar
  • 145
1 vote
2 answers
92 views

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 ...
Isaac Holst's user avatar
0 votes
1 answer
54 views

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. ...
vreithinger's user avatar
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" ...
Govind Prajapat's user avatar
0 votes
1 answer
50 views

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 ...
SurfaceIntegral's user avatar
21 votes
7 answers
2k views

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 ...
Luke Pritchett's user avatar
1 vote
2 answers
105 views

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 ...
radioactive.fade's user avatar
0 votes
0 answers
45 views

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 ...
Ignis Idea's user avatar
0 votes
2 answers
125 views

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)...
user21390097's user avatar
0 votes
0 answers
59 views

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 ...
Matthew D.'s user avatar
0 votes
1 answer
99 views

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 $g=0$, ...
Noobgrammer's user avatar
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, ...
wos's user avatar
  • 123
0 votes
0 answers
15 views

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 ...
Aaron Hendrickson's user avatar
1 vote
0 answers
76 views

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 ...
probablysid's user avatar
4 votes
2 answers
507 views

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 ...
Mitsuko's user avatar
  • 1,429
1 vote
1 answer
58 views

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)...
Charlie's user avatar
  • 11
2 votes
1 answer
89 views

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 ...
Wil's user avatar
  • 43
2 votes
2 answers
159 views

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 ...
BoundaryCondition's user avatar
-1 votes
1 answer
71 views

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 ...
probablysid's user avatar
0 votes
2 answers
155 views

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 ...
m_1265's user avatar
  • 51
0 votes
1 answer
31 views

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.
matutinal procyonlotor 's user avatar
1 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 ...
gemini's user avatar
  • 35
1 vote
0 answers
33 views

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 ...
Usual_Learner's user avatar
1 vote
0 answers
14 views

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 \...
aivmh's user avatar
  • 11
3 votes
0 answers
30 views

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}}.}$...
Rui Sun's user avatar
  • 31
0 votes
1 answer
74 views

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 ...
Nick Lee's user avatar
  • 103
0 votes
3 answers
57 views

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 ...
Muhammad Ikhwan Perwira's user avatar
0 votes
1 answer
43 views

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 ...
Gagan's user avatar
  • 195
1 vote
1 answer
113 views

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 ...
user35952's user avatar
  • 2,935
0 votes
1 answer
98 views

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-...
Chris Touk's user avatar
1 vote
1 answer
256 views

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 ...
Matteo Brini's user avatar
-5 votes
1 answer
165 views

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 ...
user avatar
0 votes
2 answers
564 views

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 ...
Rena W's user avatar
  • 1
0 votes
1 answer
50 views

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 ...
Shikhar Arora's user avatar
2 votes
1 answer
81 views

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 ...
StackExchanger's user avatar
1 vote
1 answer
40 views

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})^...
Andrew Tom's user avatar

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