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Questions tagged [statistics]

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24 views

How to obtain a relationship between variance and resolution?

In general, resolution can be expressed as a function of the variance of a measured variable. For example the resolution of measuring $x$ can be proportional to $\sigma_{x}$ or $\sigma_{x}/x$ or some ...
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1answer
40 views

Uncertainty about the ensemble average?

Does an uncertainty in momentum of $\Delta p$ mean that the actual momentum is in the range $\langle p \rangle - \Delta p\space <p< \langle p\rangle+\Delta p\space$ ? Or does it mean that the ...
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3answers
45 views

Use of significant figures in lab report calculations

I am currently doing a lab report that involves multi-step calculations. The values σ(mean, visual) and σ(mean, auditory) are calculated to be 0.004051s and 0.004917s. Since the number of trials (27 ...
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1answer
33 views

What is a free parameter?

Soft question here, but I was wondering just what exactly free parameters are? I have a murky understanding on the concept but I would much appreciate someone shedding some light on the matter. Is ...
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2answers
42 views

Error propagation in sine

Having little experience teaching uncertainties and error propagation to high school students I am learning a lot of new things this year. One thing in the textbook we use states that the uncertainty ...
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1answer
36 views

How to build a particle detector, given a desired probability of detection [closed]

Suppose that the average flux of cosmic rays at sea level on an horizontal surface is $$\varphi = 1\, {\text{cm}}^{-2}\,{\text{min}}^{-1}$$ and that we can take this value without error. What should ...
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3answers
168 views

Why nature rejects 100% accuracy in experiments? [closed]

I have never heard about any experiment performed which is 100% accurate (Sorry,if there is any).By the term accurate I mean accurate measurements involved in the experiment.Is it every time that an ...
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0answers
23 views

Question about the cumulant expansion in Kardar's book

I have one question relating to cumulant expansion when learning statistical mechanics using Kardar's textbook.To calculate the partition function for intertacting system, it runs as following The ...
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0answers
28 views

Propagation of an experimental uncertainty through a function without an inverse

I have a function, $y=f(x)$, which cannot be solved for $x$ analytically. For an experimental value of $y$ with an uncertainty, $y_{exp.}\pm\sigma_{y}$, how could a value of $x$ and its $\pm1\sigma$ ...
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2answers
40 views

Accurate measurement using inaccurate tools

Is there a good way to systematically increase the accuracy and precision of a measuring tool using only mathematical means? For example, average 10 measurements can create a better one. Or using two ...
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0answers
25 views

Correct method for error propagation in pseudo-data approach using model

I want to compute the error on the integral over experimental data $(y_i,\delta y_i)$ in a pseudo-data approach using model ($x_i$ are assumed to be known error-less numbers). If I were using direct ...
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5answers
3k views

What triggers a nuclear decay?

I am not a physicist but I have been wondering about this: I understand that the decay of a nucleus is a random event and one cannot predict exactly when it will happen for a particular nucleus. ...
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2answers
67 views

Why do we don't get exact answers to our experiment but rather an approx value to it?

Why do we face a problem of not getting to the exact answer but to an approx to it, mostly everything we come through in practical physics is a approx but not the exact one.
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1answer
44 views

Why do we subtract least count in measurement? Trying to understand intuitively

With respect to the following situation, it is quite clear that our true reading has to be at least 21degC. It can be more than that such as 21.4, 21.5. 21.7 etc. We can also see that the maximum ...
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1answer
34 views

Meaning of standard deviation

If two measured values of the Hubble Constant differ by 4 standard deviations, what does this mean in plain language or in probability terms?
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0answers
30 views

What should be the real error band of a fit function?

This is a question concerning data analysis. It could relate to particle/nuclear physics or other field. Please note that this question has nothing to do with technical problems, and is more of a ...
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1answer
25 views

How to optimize the significance for my neural network with the purpose of classifying detector events?

For my Bachelor's thesis, I've created a neural network with the task of classifying FCNC tz-production events. It was trained on data from a Monte-Carlo simulation, and tries to output 0 when ...
1
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1answer
32 views

Calculate uncertainty of a measurment given several measurments and uncertainties

I have several simulations of the same quantity (such as displacement $x$ after a simulated annealing run). Then I average the quantity over $N$ runs of the simulations and calculate the mean $\bar{x} ...
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0answers
17 views

Rebinning experimental data

I am working on a spectroscopy experiment and for each wavelength of a laser I have some counts. For the purpose of my question I will make up some data to illustrate my problem, in the table below (...
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3answers
60 views

How to fit the data for the asymptotic limit?

Suppose we have a pretty good experiment data with very small random error. But our theory is limited, which makes the systematic error significant. Sometimes we do have a nice theory for the weak ...
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0answers
39 views

Likelihood, posterior, prior interpretation and credibility/confidence_level with bayesian/frequentist approaches [closed]

I try to understand the following article : testing general relativity from curvature and energy contents at cosmological scale I don't understand the title of figure 1 : where it is indicated ...
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1answer
74 views

Are longer lives more likely in Everettian multiverse?

There are some interesting statistical thought experiments related to observers and the Anthropic Principle such as the Doomsday Argument formulated by a physicist Brandon Carter and later improved by ...
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1answer
81 views

Does Fisher Information quantify only the precision of the instrument?

Looking at perspective from estimating the actual value from a set of data measured by the instrument. Does Fisher information just quantify the precision of the measurement? What does it say about ...
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1answer
65 views

How to calculate the uncertainty of a fit function? [closed]

I'm doing research on nuclear physics. What I will be asking is actually some general question. Suppose that I have a set of data with 8 points x={x0,x2...,x7} (in my example, x-axis is transverse ...
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0answers
37 views

Error in the derivative of Poisson Distribution [closed]

I have a Poisson Distribution $N(x)$ and so I know the error in the $N(x)$. But I want to find the error in $N'(x)$. How to do this?
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0answers
25 views

Winner-takes-it-all algorithm in particle decays

How does the winner-takes-it-all algorithm work for two competing processes, specifically in particle decay processes? What are its advantages against veto algorithm, for example?
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0answers
53 views

What do marginalised or marginalised error mean? Contours and posterior

I am curently working on Forecast in cosmology and I didn't grasp very well different details. Forecast allows, wiht Fisher's formalism, to compute constraints on cosmological parameters. I have 2 ...
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1answer
44 views

Propagation of Uncertainty vs Dividing Uncertainties

I have a quick question! When I’m calculating the uncertainty of a formula, like $v = d/t$ . . . What method do I use? Sticking with my example ($v = d/t$). Do I convert the uncertainties of ...
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0answers
21 views

Signal-to-noise (SNR) in a quantum network

I'm studying dynamics of a quantum network of coupled oscillators driven by an external force. Am I doing right, if I calculate signal-to-noise ratio by dividing the expectation value of oscillator ...
0
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1answer
21 views

What does averaging over time means in literature?

Disclaimer: This question is cross posted in here because the answer might be field dependent. Let $h: [0, L]\times \mathbb{Z}^1 \to \mathbb{Z}^1$ be a function, called the height function, and lets ...
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2answers
58 views

What software programs are recommended for background extraction and peak fitting?

I have an energy spectrum for various gamma sources. What software programs are recommended for background extraction and peak fitting in this case?
3
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1answer
69 views

Fisher Information in Statistical Mechanics

I am studying the canonical ensemble and it seems to me there is an analogy between derivatives of the partition function, which can extract energy momenta for the system and Fisher score /information....
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0answers
31 views

Signal parameter estimation in PyCBC

I have a gravitational wave signal (strain vs. time). And I want to find out the corresponding parameters of the compact binary. But I do not know how to create injection for this signal in PyCBC. ...
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1answer
32 views

Relation of Corresponding principle and law of large numbers

Is it possible that Corresponding principle can be derived from the law of large numbers? Also is the principle a postulate of Quantum Mechanics?
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0answers
30 views

Averaging over outgoing radiation in the firewall argument

Following the AMPS paper, the Hawking radiation can be divided into an early and late part, decomposed as follows: $$ |\Psi\rangle=\sum_{i}|\psi_{i}\rangle_{E}\otimes |i\rangle_{L},$$ where $\lbrace|...
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0answers
15 views

Looking for ways to transform time-series data recorded from object movement into equation describing the movement direction of the object

Looking for some time-series data transformation advice! I want to know what's the best way to transform data of 9-tuples time series data of IMU (Inertia Measurement Unit) sensor, recorded from a ...
1
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0answers
16 views

Compatibility of two bi-dimensional measures

As my last chance I try to post this question here, it seemed like a simple one but I have so much trouble finding an answer. While doing the PET experiment, one needs to reconstruct the original ...
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1answer
34 views

Veto algorithm in particle decays and Monte Carlo techniques

What is the main concept behind Veto algorithm and how does it contribute to efficiency in Monte Carlo methods like when used in designing a parton shower?
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0answers
20 views

Which statistical distribution could be assumed for the mobility of Silicon substrate material?

Mobility is a key parameter for Hall elements or in transistor models. If we measure the mobility on Si wafers, then we can expect some variation from die to die or sample to sample. Which statistical ...
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1answer
33 views

Poisson statistics & ratios

The rule of thumb I know for the error on a count for random sampling is that it goes as the square root of the count. For instance, if I observe a radioactive source for $1$ minute and measure $100$ ...
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0answers
39 views

Bayesian approach for setting upper limit

In the presentation by Cowan, on slide 18, he explains the baseyian approach of setting upper limit in parameter estimation. What I didn't get is the formula written. Bayes's theorem is like $P(a|b) \...
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2answers
93 views

Are all discovered normal distribution in the physical world a result of central limit theorem?

Apart from the wave function in a harmonic well. Are all discovered normal distribution in the physical world a result of central limit theorem? If it is the case, it may allow some reverse reasoning ...
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0answers
43 views

Error in histogram measurements

I ran into the following statement here and here but I believe it's more general. Let's suppose we're running a simulation of a system and we are interested in the distribution of a quantity (say $M$...
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0answers
31 views

Maximizing mutual information with Restricted Boltzmann Machines and Monte-Carlo sampling

So I've been reading through Koch-Janusz and Ringel's, "Mutual Information, Neural Networks, and the Renormalization Group" (check it out here). I'm currently trying to reimplement some results from ...
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1answer
76 views

Monte Carlo importance sampling in statistical physics finite approximation question

I am trying to understand a formula found in "Topics in Current Physics: Monte Carlo Methods in Statistical Physics Springer-Verlag" attributed to L. D. Fosdick methods comp physics 1963. I can't get ...
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0answers
28 views

Probability In a Nuclear Transmutation Question

How much cobalt will form into zinc when you add a mole of the set (3 protons, 3 electrons and 5 neutrons) to the cobalt? I cannot figure out how to find the probability of creating a certain ...
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2answers
60 views

What's “bimodal” about BEC velocity distributions?

I was just reviewing some papers discussing Bose-einstein condensation, specifically "Creation of a Bose-condensed gas of 87Rb by laser cooling" by Hu et al., and I saw repeated references to the ...
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2answers
86 views

What is the proper way to combine two different errors for the same measurement?

We did an experiment in the lab (regarding magnetic domain walls) that yielded some pictures that we later on analyzed and manipulated in Matlab (we took an RGB image made it into grayscale one and ...
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1answer
58 views

How does the expectation value of a partial derivative of a random variable make mathematical sense in QM?

In probability theory, I'm familiar with the definition of the expectation value of a random variable $X \colon \Omega \rightarrow \mathbb{R}$ being: $$ \langle X\rangle= \int_{-\infty}^{\infty} x ...
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0answers
48 views

Landau Theory of fluctuations

With respect to chapter 12 in the book Statistical Physics(Part 1) by Landau and Lifshitz, I am currently stuck at the intepretation of Fluctuation theory that Landau provides. In the neighbourhood of ...