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3
votes
1answer
31 views

PDF from number of standard deviations plot

I must consider plots like these where the bounds on $x$ (in this case $\sin^2\theta_{12}$ or $\delta/\pi$) are shown in terms of the number of standard deviations $N\sigma$ from the best-fit value. ...
0
votes
2answers
46 views

Least Squares Fitting - 68% Confidence Interval

I am fitting a linear polynomial to some data and I have derived the errors for each of the best-fit parameters from the covariance matrix. I would expect these errors to correspond to a $1\sigma$ 68% ...
0
votes
2answers
376 views

Is there a fundamental difference between the statistical methods of science, comparing medicine to physics?

Is there a fundamental difference between the statistical methods of science, comparing medicine/biology with small sample sizes(n < 10^2 or 10^3) to the statistics applied in Quantum Mechanics (h: ...
3
votes
2answers
59 views

Best way of calculating average acceleration in lab experiments

I am doing a lab experiment that works as follows. An object moves along the $x$ axis with an initial acceleration and then moves with a pretty constant velocity that may slightly vary within $20\%$ ...
0
votes
0answers
18 views

Statistics: combining independent observables for the same quantity, how to check independence

Let's assume we have a set of observations $\{x_i\}$ and that I have a physical models aimed to describe the observations, and that this model has a parameter $y$. Let's assume that I have two ...
1
vote
1answer
198 views

Error calculation for experimental data

I have the list of experimental values: $$\{w_i \pm \Delta w_i\},$$ where $w_j$ is a mean value and $\Delta w_i$ is an error. I want to calculate the second list $\{a_i \pm \Delta a_i\}$ according to ...
0
votes
1answer
87 views

Thermal average, thermal fluctuations

I've a doubt concerning the physical meaning of "thermal average" and the "thermal fluctuation" in the canonical ensemble. Let's consider a very simple thermodynamic system: N particles, at fixed ...
11
votes
2answers
18k views

How do you find the uncertainty of a weighted average?

The following is taken from a practice GRE question: Two experimental techniques determine the mass of an object to be $11\pm 1\, \mathrm{kg}$ and $10\pm 2\, \mathrm{kg}$. These two ...
0
votes
0answers
18 views

Total uncertainty of multiple stereo camera depth measurements

I have a stereo camera that measures depth for a rectangular area of pixels in a single image. Each depth measurement is obtained independently (this goes back to the stereo matching algorithm used). ...
4
votes
0answers
45 views

Calculating statistical significance of peak over background in counting experiment

I histogrammed the invariant masses of particular events in a counting experiment. There is a specific peak which towers over the expected exponential background. How can I give the statistical ...
2
votes
2answers
31 views

How do I find uncertainties in an intensity plot created from a photograph?

I have a photo of a laser beam (taken by sending the laser into a CCD). I then took the image and ran it through an image reader that gave an intensity surface plot. I then took a single cut from that ...
0
votes
1answer
55 views

Error propagation estimation [closed]

I have a physical quantity A defined as $A=(74.5 B^2*(M+N))^{1/3}$ where B, M, N and relative uncertainties are given. And M and N are dependent on B: $log M=(0.755 \pm 0.059)*log B+(0.416\pm ...
2
votes
0answers
20 views

Dispersion parameters for Pasquill–Gifford stability class G (extremely stable)

Gaussian plume models are often used to model atmospheric dispersion because they are simple and computationally efficient. When not constrained by the ground or by inversion layers, the Gaussian ...
1
vote
0answers
21 views

Goodness of fit for two different properties of the same model?

This is a question about statistics and optimisation. I have a model which produces two different distributions of the same dimension. Let's say they are the mean velocity distribution $\langle v(r) ...
1
vote
0answers
39 views

Relevance of pure mathematics vs statistics to physics [closed]

For someone currently studying physics, with an interest in experimental physics, would pure mathematics or statistics be more relevant?
0
votes
1answer
35 views

Derivation for the most probable macrostate for distinguishable particles using lagrange's method of undetermined multipliers

We have an expression for $\Omega$ (occupation of each macrostate) in terms of $n_i$ (occupation numbers) . We want to find the $n_i$ which maximises $\Omega$. We now that ...
0
votes
0answers
14 views

Counting the accesible microestates compatible with the macrostate conditions

Let be a system consisting of $N$ magnetic dipoles with magnetic dipole $\vec{\mu}$ in a magnetic field $\vec{B}$. I want to count the micro states accessible to the macro estate defined by $E=-\mu B$ ...
4
votes
0answers
54 views

Appropriate fit function for $\phi$ meson mass from $K^{+}K^{-}$ pair

I am attempting to measure the mass of the $\phi$ meson using the decay mode $\phi \to K^{+}K^{-}$. I have isolated the $\phi$ meson candidates using this decay mode, and have constructed the graph ...
11
votes
2answers
316 views

Modeling non-quantum objects (in finance, sociology etc) using fermionic fields?

Please provide (if any) applications of fermionic field theory in non-physics macro contexts (finance, sociology etc). I see only bosonic fields being used mostly. The only (minor) application of ...
1
vote
1answer
46 views

Are residuals supposed to have error bars?

Hopefully I'm asking this in the correct section. So I've got a graph with a linear trend of data and a best fit line plotted. The data points on the main graph obviously each have their own error ...
1
vote
0answers
30 views

The central limit theorem from a path integral?

On https://en.wikipedia.org/wiki/Path_integral_formulation it is noted that the central limit theorem can be interpreted as the first historical evaluation of a statistical path integral. Is this ...
1
vote
1answer
20 views

How to find the error of all the counts within the Full Width Half Maximum (FWHM)?

We've been doing Gamma ray spectroscopy and have peaks from various sources. We'd use Poisson statistics, but obviously the detector doesn't have a resolution of zero, thus we are summing the counts ...
1
vote
0answers
55 views

LIGO detection statistic, SNR formula

According to B. P. Abbott paper published in Physical Review Letters, "Observation of Gravitational Waves from a Binary Black Hole Merger" ...
0
votes
0answers
36 views

Does the gravitational wave community plan to lower the threshold for claiming detections by 2000x?

I've read: To investigate the impact of reducing the parameter space for GRB searches, we will deliberately avoid the question of first gravitational wave detection - where a "5-sigma" ...
6
votes
3answers
226 views

Meaning of $5.1\sigma$ significance with regards to GW150914

I couldn't find any publication by LIGO that explains how we should interpret this value. The closest I have found is the following quote: This means that a noise event mimicking GW150914 would be ...
0
votes
0answers
25 views

Statistical analysis of random variable with finite mean and infinite variance

Given a measurement that (we know from theory) has a finite expected value, but infinite variance, is it possible to have some statistical information? Can I get the significance of such data? Can ...
1
vote
0answers
21 views

Why are isoprobabilty contours circles for uncorrelated functions and ellipse for correlated functions? Kindly explain.

I would like to know how to understand these and to learn how to go from a scatter plot to the isoprobabity contour plots. Thanks is advance!
2
votes
4answers
119 views

Why is the Pythagorean Theorem used for error calculation? [duplicate]

They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then $$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$ I can't ...
1
vote
0answers
28 views

Does a set of eigenvalues in QM correspond to a random variable in statistics? [duplicate]

In quantum mechanics the possible outcomes of a measurement of a quantity corresponding to a linear hermitian operator $A$ are only the eigenvalues $a_i$ of $A$ (see e.g. ...
2
votes
4answers
172 views

Is what statisticians call a “random variable” what physicists call an “observable” in QM? [duplicate]

I read at http://www.statlect.com/fundamentals-of-probability/random-variables that A random variable is a variable whose value depends on the outcome of a probabilistic experiment. Its value is ...
5
votes
4answers
852 views

How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?

$$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$ What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
0
votes
2answers
111 views

Calculate the probability that a radioactive nucleus will have decayed after the passage of three half-lives

This is a problem given in my Physics Textbook and I've been trying to solve it for the past hour. It's not something exceptionally challenging, but more conceptual in nature. Not much, connections ...
3
votes
0answers
59 views

What is the physical meaning of the parameter of a Poisson distribution?

I have done a laboratory session at my university where I had to check that the disintegration of nucleii follows a Poisson distribution. $$P(n)=\frac{\lambda^n}{n!} e^{-\lambda}$$ Where $P(n)$ is ...
0
votes
1answer
66 views

Combining errors. Gamma spectrometry, Poisson distribution

I have run an experiment 3 times and measured the results by gamma spectrometry. For example I get values like this (1 $\sigma$): $100 (10)$ $90 (8)$ $110 (12)$ The above 1 sigma error is based ...
3
votes
0answers
71 views

Remove measured distribution from another distribution [closed]

Take a particle beam as an ensemble of many particles. Assume two independent random variables $X_\beta$ and $\delta$ that add up to the horizontal position $X$ of a particle: $$ X = X_\beta + D_x ...
3
votes
2answers
84 views

What exactly is an arbitrary parameter?

I was reading the article Turning Points: A meeting with Enrico Fermi by Freeman Dyson (available e.g. here), and I had a question about Dyson's use of the term 'arbitrary parameter'. More ...
1
vote
1answer
671 views

Why is uncertainty divided by $\sqrt{3}$?

Why do we have to divide uncertainty of the measurement by $\sqrt{3}$? For example we have the uncertainty of the measurement with a ruler being the smallest scale of 0.01cm, and it is not our ...
2
votes
0answers
34 views

Comparing $X_\text{red}^2$ statistics for cosmological models

I'm evaluating a cosmological model which competes with ΛCDM. I have charted the $Χ_{red}^2$ and $R^2$ statistics for the sample of galaxies from McGaugh et al (2001) for my model and ΛCDM. Each ...
0
votes
1answer
25 views

Random partitioning of single-mode thermal light

While studying Fundamentals of Photonics by Saleh and Teich, I find it difficult to prove that the photon-number distribution of randomly partitioned single-mode thermal light retain its Bose-Einstein ...
5
votes
1answer
314 views

Advanced data analysis in Physics experiments

I know that regression, chi-distribution, covariance, error propagation, etc. are frequent tools for experimental physicists. So, I'd like to know if advanced statistics topics are used in data ...
0
votes
0answers
11 views

What is the distribution of a battery transmission?

I have an energy-harvesting battery attached to a node, transmitting data over Rayleigh flat fading channels. Energy in the battery is used, and simultaneously energy is harvested and stored. I want ...
0
votes
1answer
80 views

How should I interpret a Chi-Squared Result?

I've got a Model A with a reduced chi-square of 1.28. I've got a Model B with a reduced chi-square of 0.70. Which is a better model? The model closest to 1 or the model closest to zero? (Yes, I ...
1
vote
1answer
104 views

Can binary sequences generated from ergodic maps be chaotic?

Briefly, the way symbols are generated is: Consider a one-dimensional chaotic map $T: [0,1]→[0,1]$ and a time series $\{x_n\}_{n=1}^N$ generated with this map. Define a threshold $A$ and a ...
2
votes
1answer
57 views

Any fractal physical model that generates time series which demonstrate heavy-tailed (non-Gaussian) behavior in some form?

I know that fractal structures have power-laws in various forms "hidden" in them. I am looking for the most simple fractal model that I can find that generates time series with, say, ...
0
votes
0answers
31 views

Reduced Chi-Square - How to compare values?

I've got two models of velocity curves fitting a Low Surface Brightness (LSB) galaxy: one is MOND-like, the other ΛCDM. I've fit them both with Chi-Square minimization. I understand the winning ...
1
vote
2answers
305 views

Use of normal distribution in measurement error theory

When you study an experimental results you assume that normal distribution describe random error, specially in lab courses in K12. Is this true for every random component error treatment in physics? ...
1
vote
1answer
39 views

Residuals are normally distributed

I did not know whether to post this question in the Physics or Statistics section of StackExchange, but the question involves the application of statistics to the analysis of experimental results. I ...
1
vote
1answer
72 views

Error in total counts

I'm performing a radioactivity experiment where I measure a specific number of counts in some time period t. Later on I take the total count rate. (Number of counts/time: $N/t$) I'm supposed to find ...
8
votes
2answers
417 views

Arrhenius Fit: Linear or exponential form?

I have a seemingly easy question about performing an Arrhenius fit to the equation $$y = A \times \exp \left( -\frac{E_A}{RT} \right)$$ I can either fit this in the exponential form using a ...
8
votes
3answers
421 views

How does uncertainty/error propagate with differentiation?

I have a noisy temperature (T) vs. time (t) measurement and I want to calculate dT/dt. If I approximate $dT/dt = \Delta T/\Delta t$ then the noise in the derivative gets too high and the derivative ...