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Questions tagged [statistics]

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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
27 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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14 views

Is the standard deviation of thermal energy in a crystal lattice at room temperature well defined?

It is well known that the mean thermal energy available in a crystal lattice at room temperature is approximately equal to 0.026 eV. I'm curious if there is a well defined corresponding standard ...
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0answers
23 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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26 views

Is there correlation in these pictures? [closed]

Is correlation in these pictures please? Thank you.
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0answers
7 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 ...
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0answers
12 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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0answers
17 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
18 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
31 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
32 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
89 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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38 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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23 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
45 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
27 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
40 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
54 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
49 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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39 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 ...
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1answer
33 views

Interpretation of a CLs exclusion plot

I have some trouble with the interpretation of this plot. The plot on the right shows the CLs values for the SM Higgs boson hypothesis as a function of the Higgs boson mass in the range 110–145 GeV. I ...
2
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1answer
45 views

Error propagation and data linearization

I am fairly new to teaching error propagation to students but came across a question I couldn’t answer myself. Say we have a set of data that produces a parabola. In order to linearize the data and ...
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0answers
28 views

How can I determine, in what extent the fit to experimental data is good in Matlab?

I have experimental spectrum in which y-axis is intensity values, and x-axis is frequency values. Int - array of experimental intensities (y-axis). w - array of frequencies (x-axis). I know the view ...
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7answers
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When to average in the lab for indirect measurements?

I am measuring distance and time to calculate the velocity. I repeat the experiment 10 times. What is better, to first calculate the average of distance and time and then the velocity, or to calculate ...
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0answers
35 views

How to fit mean squared displacement data from nanoparticle tracking analysis?

I am trying to independently analyze raw nanoparticle tracking analysis (NTA) data, but my diffusion coefficients calculated directly from x and y pixel values only moderately correlate with reported ...
0
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1answer
57 views

Reduced Chi-Squared values of 5?

I have plotted a linear plot, all errors seem to be on the line yet my chi squared value is 5. What does this mean for my results? Could there perhaps be a problem with how they were calculated? I ...
2
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2answers
72 views

How to calculate the error when multiple measurements are made, each of which has an error?

So if I have made three measurements, measuring the same physical quantity $d$: $a \pm \Delta a$ $b \pm\Delta b$ $c \pm\Delta c$ and I want to take the average of $a, b$ and $c$ to get the ...
2
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2answers
164 views

The mean of Langevin equation

I have a very basic question regarding the mean of the Langevin equation. So we have an equation of the form: $$\dot{v}(t)=-\beta v(t)+ \xi (t)$$ Where $\xi (t)$ is a Gaussian white noise with an ...
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2answers
43 views

Definition of continuous distribution (intuitively understanding)

Def: A continuous random variable is not defined at specific values. Instead, it is defined over an interval of values, and is represented by the area under a curve. The probability of observing any ...
3
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1answer
102 views

Propagation of asymmetric error bars [duplicate]

I have two (fully independent) measurements of the same quantity X. Each of them reports a measurement $X_{\sigma_L}^{\sigma_R}$, where $\sigma_L$ and $\sigma_R$ are the left and right uncertainties (...
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2answers
89 views

Notation in Heisenberg Uncertainty Relation: greater than with tilde: $\gtrsim$

In "The Road to Reality" (pg. 523), Roger Penrose writes: Heisenberg's uncertainty relation tells us that the product of these spreads cannot be smaller than the order of Planck's constant, and ...
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1answer
40 views

Using probability of camera flash interval to get the probability density equation in Griffith's Quantum Mechanics book

In Griffith's QM, example 1 chapter 1, what is the intuition behind using the probability of camera flash interval to get the probability density equation in terms of "dx". Griffith says that ...
18
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1answer
197 views

Are the masses of merging black holes correlated?

LIGO/VIRGO recently released data on observed "gravitational wave transients", mostly BH-BH mergers. The data includes a plot of the primary and secondary mass (the primary mass is defined as the ...
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0answers
45 views

Calculate variance of number of photon counts in detector with second coherence function

Knowing the second coherence function of the light beam that's normally incident to a detector how do can you find the variance of the number of counts $n$ received in the time interval $T$.
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1answer
35 views

How should I find an average for data that randomly fluctuates?

I have data for the temperature of a flame at a given height above the burner. The temperature fluctuates quite a bit (see figure), but there is definitely an "average" value that it tends to ...
2
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1answer
25 views

Propagation of uncertainty for a mean value

During an experiment I had to measure the speed of light $c$ (it's an indirect measurement, because i had $c(x,y,z)$ as a function of some quantities $x,y,z$ I could measure). I took several measures $...
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1answer
73 views

Problem in measuring uncertainty

While performing an experiment involving a bar pendulum, we had to measure the time period of one oscillation by measuring the time taken for 30 oscillations. There is some confusion regarding ...
2
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1answer
160 views

Estimating standard deviation of radioactive decay [closed]

I recently did a laboratory exercise where we had an amount of silver containing two isotopes. Silver with 108 and 110 neutrons, respectively. Using sensors and software, we measured the amount of ...
2
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2answers
136 views

Formula for combining relative uncertainties [duplicate]

Different sources are giving me different formulae for combining relative uncertainties. One tells me to simply add the relative uncertainties together to get the combined uncertainty while another ...
0
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0answers
24 views

Correlation function and power spectrum of discrete time Gaussian noise summed with a time delayed version of itself

Suppose we have a process $\zeta(n) = \xi(n) + \xi(n + 1)$ Where $\xi(n)$ is discrete time white noise process, where the values taken at different times are from identically distributed Gaussian ...
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1answer
45 views

Is it possible to estimate the average time until entropy decreases a certain amount?

We all know the classical Joule free expansion experiment for an ideal gas: we trap an ideal gas inside half of a cylinder. Then, we open the door and the gas expands to the whole cylinder. After ...
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1answer
40 views

Random walk with Ammonia molecule [closed]

This question is from Keith Stowe's Introduction to Thermodynamics book under Random walk. The question is something like this: I am aware that I am not supposed to post homework questions like this ...
6
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2answers
81 views

Why are the Lyapunov and Lindeberg Central Limit Theorem conditions often satisfied in the real world?

Some background for the question. I've been trying to understand why so many things have a Gaussian Distribution. There are a lot of questions about this on StackExchange but none of them were ...
0
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1answer
122 views

Why does taking more readings reduce random error? [closed]

So I was tossing a coin And I did two experiments Experiment 1: Tossing same Coin with no fan with different torque each time and did'nt much care about orientation of the coin, 8 times I got 5 ...
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3answers
81 views

What happens to a radioactive material's atom when it disintegrates?

Suppose you initial had radioactive $2^n$ atoms (where $n$ is an integer). Now after a number of halflives the number of left out atoms becomes 1. Now what will happen to it will it disintegrate and ...
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1answer
86 views

What causes Lorentzian broadening of X-ray diffraction peaks?

In X-ray diffraction, the pseudo-Voigt model is a combination of Gaussian and Lorentzian distributions, and is often used to model peaks. The form of the peak is often described as $V(x)$ = (1-$\...
0
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1answer
86 views

Significant figures in a practical experimental problem [duplicate]

Here is a question that combines uncertainties in measurements and significant figures. Consider the following results to measure the value of g: $$g={9.7,9.8,9.7,10.0,10.1,10.3}$$ Then to four ...
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2answers
353 views

Why aren't Maxwell-Boltzmann statistics used in general cases?

From Probability Theory Vol. 1 Feller Section 2 Chapter 5: Maxwell-Boltzaman distribution: consider $r$ indistinguishable balls and $n$ cells. Assuming that all $n^r$ possible placements are ...
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1answer
50 views

What is the significance of a $\chi^2$ analysis?

What is the merit of $\chi^2$ analysis in the laboratory experiments? Why is so much emphasis put on it?
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1answer
50 views

Modelling the Z mass

I'm interested in approximating (analytically) the mass distribution of the Z boson, as shown below (numerically/MC): On-shell, you obviously have a Breit-Wigner distribution; but what about to the ...