Questions tagged [statistics]
The statistics tag has no usage guidance.
444
questions
-1
votes
0answers
17 views
Sensitivity of a function [closed]
Let's say I am drawing a six-sided dice 600 times. For every six times, I am recording six different values I have got. I will be getting something like:
1 -> 4,3,6,2,4,3 2 -> 1,4,5,3,6,3 3-> ...
0
votes
0answers
24 views
Sensitivity of the parameter for the measurement [closed]
Thank you for the feedback! Let me explain.
Let's say I am drawing a six-sided dice 600 times. For every six times, I am recording six different values I have got. I will be getting something like:
1 ...
0
votes
0answers
19 views
How to average two numbers with error bars?
I am trying to fit a function with two different data sets. Each data set gives me the fitting parameter with its error bar. How can I use these two fitting values of the fitting parameter to get its ...
2
votes
1answer
24 views
What is the tension of the Hubble constant in standard deviations?
Depending on the data, the tension in the measurement of the Hubble constant H0 is up to 9 percent. This corresponds to about 5 sigma. I am interested how this standard deviation is calculated.
0
votes
5answers
81 views
What is meant by frequency = 0? [closed]
When I say that an event has frequency =0, does that imply that the event is impossible?
0
votes
1answer
23 views
What metrics can be used to quantify underestimation of uncertainties?
Suppose an experiment measures a quantity to be $5 \pm 0.3$ and another measures it to be $9 \pm 0.3$
What metrics can be used to emphasize and quantify the error in the estimation of uncertainties by ...
0
votes
0answers
26 views
In experimental particle physics: Why and when can a combinatorial background be modeled with exponential functions?
A common model for the combinatorial background in an invariant mass distribution in experimental particle physics is an exponential distribution. Is there a physical reason why this is a good model ...
1
vote
0answers
27 views
Is it always possible to infer photon distribution from photon statistics?
Say we are detecting light in the time interval $(t,t+T)$ that is described by the intensity $I(t)$. Let the integrated intensity in this interval be given by:
$$U=\int_t^{t+T}I(t’)dt’$$
Since $I(t)$ ...
3
votes
2answers
96 views
Different forms of Heisenberg Uncertainty Principle
The Heisenberg Uncertainty Principle is often written in two forms:
$$\Delta x \Delta p \geq \frac{\hbar}{2} $$
and
$$\sigma_x \sigma_p \geq \frac{\hbar}{2}. $$
Are these two equivalent? I've been ...
0
votes
1answer
26 views
Uncertainty from variable to derivative in data fitting
If I have a system of differential equations, say $x' = f(x,p)$ and a set of data $(t_n,x_n)$, where $p$ is the set of constant parameters. I can then use a fitting method like least squared to obtain ...
22
votes
9answers
5k views
Why does a collection of radioactive atoms show predictable behaviour while a single one is highly random?
Well, we know that it is impossible to say exactly when a radioactive atom will go on decay. It is a random process. My question is why then a collection of them decays in a predictable nature (...
0
votes
2answers
39 views
Relationship between physical scale and certainty
Partially motivated by this question, I get the impression that it is generally more difficult to make accurate statistical predictions in Physics about "the small" (microscopic phenomena) ...
1
vote
1answer
32 views
Error estimation over multiple instruments readings [closed]
A cable factory ships cables in spools of 100 km each. The overall length of each spool is known with great precision, it's 100 km sharp.
In order to speed up the sale process, distance markers are ...
4
votes
2answers
38 views
Examples of macroscopic systems with exponentially distributed lifetimes?
I was considering the statistical lifetimes of various light bulbs at first. However, upon further reading it seems that they tend to be approximately Weibull distributed with a shape parameter $k \...
2
votes
5answers
268 views
Is the Uncertainty Principle a mathematical consequence or a physical consequence or both? [duplicate]
I am currently exploring the mathematical structure of Quantum Mechanics on an introductory level. A couple of books and online sources (including this website) stated how the Uncertainty Principle is ...
0
votes
1answer
38 views
Question about temperature limit to infinity
I want to find the limit of T to infinity for a specific function:
$$\frac{a^{2}L^2}{4kT^2}\frac{e^{aL/2kT}}{(e^{aL/2kT}-1)^2}$$
When T approaches infinity, the e on the top becomes 1. Furthermore I ...
3
votes
4answers
99 views
Error propagation for quadratic
I have a very simple question I am struggling with. Lets say I want to propagate the error for some expression $$ y = x^2$$
Lets say I known that $x = 0 \pm 100$. Using standard error propagation I ...
1
vote
0answers
14 views
Bayesian error propagation: How to get probability of event given many outcomes and many realizations of process?
Imagine that a point is space x can be characterized by either A,B,C,D,E,F,G in the c_A, c_B .. classifications of x as A,B,C,... My data gives:
P(x = A | c_A) = f_A(x)
P(x = B | c_B) = f_B(x) and so ...
0
votes
0answers
24 views
About regularization cost function present in Hasselman's 91 (Retrieve wave spectra)
Good morning,
What I'm trying to understand is the part of minimizing the functional present in HH91 ("On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image ...
2
votes
0answers
87 views
How can we calculate autocorrelation?
In a Markov chain Monte Carlo (MCMC) algorithm, autocorrelation is a measure of correlation between subsequent measurements. This is in many cases quantified by considering the correlation between ...
1
vote
1answer
29 views
Relation between moments and cumulants in Kardar
I've been going through Kardar's book and, in the chapter on probability, I found this expression (numbered as $2.13$ in the book):
$$
\sum_{m=0}^\infty \frac{(-ik)^m}{m!} \langle x^m \rangle = \exp ...
0
votes
0answers
18 views
Statistical tension between two measurements [duplicate]
If we have two measurements of the same quantity, say, $m_1=a\pm c$ and $m_2=b\pm d$, how many sigma away are these values? In other words, when we say that two measurements are in e.g. $3$ sigma ...
0
votes
1answer
56 views
Is this $CL$ or $CL_S$ method?
I have already posted this problem here, closed for asking too many questions. I will reproduce the introduction and contextualization here, and try to ask a more specific one that I hope will be ...
2
votes
1answer
31 views
Quantum vs Classical estimation using Fisher Information
Is it possible to have a different estimated value of a parameter by Classical Fisher Information (CFI) compared to Quantum Fisher Information (QFI)?
Say, for example, I am plotting, $\mathcal{F_{\...
3
votes
1answer
52 views
Quantum Fisher Information vs Classical Fisher Information
I am currently studying about Fisher Information and have a rather simple doubt which I can't figure out.
Is it possible to have Quantum Fisher Information (QFI) more than Classical Fisher ...
0
votes
2answers
41 views
I don't understand how to interpret “Events/MeV” in plots like this
I was reading a paper regarding electron excess events in MiniBooNE data and I came across the following plot:
I don't understand how to interpret the meaning of "events/MeV". This is a histogram and ...
1
vote
4answers
94 views
Uncertainty in Quantum Mechanics
In Quantum Mechanics, as we know, the uncertainty is defined as
$$\Delta x=\sqrt{\langle x^2\rangle-\langle x\rangle^2}.$$
My question is - Why is uncertainty equal to the standard deviation?
-1
votes
1answer
37 views
Correlations vs. negligence of correlations in covariance matrix
Suppose I have a model composed of two parameters $(a,b)$ that I want to describe a set of data points with. In CASE A, I fit the model taking into consideration the correlations between the data ...
0
votes
1answer
18 views
I am studying fragmentation warheads and this formula of 'numbers of fragments hitting the target' is just not making sense
What is parameter 'p' in the formula? If somebody knows any better source to study this part... welcome to suggest. Thanks a lot.
Probable Number of Fragments Hitting the Target
It can be ...
0
votes
0answers
21 views
In parameter estimation, how does one obtain an estimator?
To estimate the value of a parameter $\theta$, we require an estimator $\hat{\Theta}(\epsilon)$, the estimator associates a particular measurement value $\epsilon$ with an estimate of the parameter $\...
1
vote
2answers
39 views
Number of microstates for a simple object
For the sake of argument let's say an object is made from 4 atoms where 3 atoms have 1 quanta of energy and 1 atom has two quantas of energy. Something like this:
Where a pair of curved lines ...
1
vote
1answer
59 views
Variance of an Overlap Between States: Bra-Ket Notation?
Imagine two eigenstates of a system $|0\rangle$ and $|1\rangle$, and suppose you manage to prepare your system in the superposition $|\psi_{in}\rangle = (|0\rangle + |1\rangle)/\sqrt{2}$. After some ...
1
vote
1answer
80 views
Data analysis on particle physics: what am I formally doing in this specific case? [closed]
I have performed an analysis of the exclusion(discovery) perspectives for a BSM particle at the LHC. However, my focus of study (and understanding) was until little time ago the purely theoretical and,...
0
votes
2answers
25 views
Understanding error analysis terminology
I'm working in a lab, and the terminology in error analysis is confusing me. Lets say I have a theory that claims the fine structure constant is exactly 1/137. My current reference tells me that the ...
0
votes
0answers
17 views
Correlation function definition in hear transfer (statistical theory of turbulence)
I am trying to reproduce the approach in the paper by Nikishov. Since the paper is not easy to get I will just write out the statements here. They write the heat transfer equation for averaged ...
6
votes
2answers
244 views
How to incorporate the uncertainty of the model coefficients in the prediction interval of a multiple linear regression
I'm dealing with the modeling of small experimental physics data sets (specifically the stickiness of glue-compounds). As most of this experimental work does not generate thousands of samples, but ...
0
votes
0answers
46 views
General question about Galton Board
I’m new here, and most notably NOT a Scientist, but I do have a question about
the Galton Board (which I happily stumbled upon today, thanks to YouTube and ‘the quarantine’)
So, as I understand it, ...
1
vote
1answer
48 views
Significant Figures in functions
How to extend the idea of significant figures to operations like $\sin\theta$, $\log x$, $\sqrt{x}$, $\cos^{-1} x$, $e^x$ etc. Is there a general rule or method to find/define the no. of significant ...
0
votes
1answer
38 views
Can I add individual kWh measurements to get the total?
I have a time series file showing kWh electricity use measurements from a building every 15 minutes. For example:
...
0
votes
0answers
28 views
Model fit error pinching
I am performing a model function fit, $f=f(x,a,b)$, with the two parameters $\left\{a,b\right\}$ to be determined from the best fit to a set of data. In my determination of the resulting $1 \sigma$ ...
0
votes
2answers
46 views
How is the root-mean-square error related to the confidence interval?
If the car's speed is calculated as V = 100 km/s, and the RMSE of V is 20 km/s.
Does that mean V = 100 +/- 10 km/s, or V = 100 +/- 20 km/s?
4
votes
2answers
173 views
A Maxwell-Boltzmann distribution, written as a Gamma distribution [closed]
Introduction
I have read that a Maxwell-Boltzmann distribution can be written equivalently as a Gamma distribution, however I have not managed to find or derive the parameters used to do so.
The ...
0
votes
0answers
31 views
Error in FWHM of photo peak
I have spectra for different sources I need to find the FWHM of to determine energy resolution of a scintillation detector.
I have taken spectra and then fitted a gaussian to the photopeak:
The scipy ...
3
votes
1answer
36 views
Why traditional turbulence theory concerns so much about statistics such as correlations?
I have been wondering why the traditional turbulence theory, e.g., Kolmogorov's 1941 theory, concerns so much about things like two-point correlations, structure functions, their scalings, and so ...
1
vote
1answer
54 views
Connecting Heat and Statistical definitions of Entropy
My Question:
Thanks for reading.
I understand that when entropy was first defined, in an attempt to explain which processes happened and which didn't, it was defined as:
$$\Delta S=\frac{Q}{T}$$
...
-1
votes
2answers
50 views
Calculating errors based on other variables
I am trying to calculate the mass and respective error of a star in kg. I have the numbers in units of $M_{Sun}$,in the form $M_{star}=(a\pm b)$ $M_{Sun}$.
Given that I have the mass (with error) of ...
1
vote
2answers
74 views
Propagation of error for difference of values
I think there is a simple answer out there but I have hit a silly mental block.
Say I have two values, each with their own error (precision):
$845.9 \pm 0.3, 845.6 \pm 0.3$
Now, I understand that ...
0
votes
1answer
26 views
Are the measurement outcomes of an observable gaussian distributed?
Suppose in an experiment we perform $n$ independent measurements to find the true value of an observable $X$. Let the outcomes of $n$ measurement are denoted by $x_1,x_2,...x_n$. If $n$ is ...
0
votes
0answers
40 views
Difference between Fuchs-Hansen and Fuchs-Nordheim model of reactor excursion?
I was using both models to fit experimental data of a reactivity insertion (more specifically, a power vs. time plot). Both models produce almost the same fit, with slight difference in peak power. ...
1
vote
2answers
136 views
Propagating uncertainty in logarithmic calculation
I have a calculation using the following pseudo-formula:
$ y = -ln(X/X_o)$
where both $X$ and $X_o$ have an associated error with them. I have propagated the error out simply using:
$ \delta y = y\...
