# What is Estimation: Definition and 206 Discussions

Estimation (or estimating) is the process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available. Typically, estimation involves "using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter". The sample provides information that can be projected, through various formal or informal processes, to determine a range most likely to describe the missing information. An estimate that turns out to be incorrect will be an overestimate if the estimate exceeded the actual result, and an underestimate if the estimate fell short of the actual result.

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1. ### I How to implement proper error estimation using MC

Hello! I have a situation of the following form. I have a function ##f = xy##. In my experiment ##y## is fixed, but it has some noise to it, such that at each measurement it is basically sampled from a Gaussian with the mean given by the fixed value and the standard deviation given by the known...
2. ### B Estimate the difficulty of a mountain route

Hello guys, I am not into this field and finished my college long ago. I am trying to find a formula to estimate the difficulty of a mountain route. The input is: D = linear distance between start and destination (as given by Google Maps) in m, km, whatever. Both points are considered at the...
3. ### I Monte Carlo for uncertainty estimation

Hello! This is tangentially also a follow up to this post. I have the following equation: $$A = \frac{0.2\frac{W}{\Delta}}{\left(\frac{W}{\Delta}\right)^2+0.1^2}$$ where ##\Delta## is an experimental parameter, ##A## is obtained by some measurements and it depends on ##\Delta## and the...
4. ### I Confused about using Monte Carlo for error estimation

Hello! I have 2 probabilities ##p_1## and ##p_2## which governs the probability of measuring some events. I measure event 1 N times and get ##N_1## counts and event 2 N times and get ##N_2## counts. Then I need to build the function ##A = \frac{N_1-N_2}{N_1+N_2}##. I am trying to estimate the...
5. ### A Minimum-variance bound for the extended maximum likelihood estimation

I am fitting a mass spectrum using pdf(M)=Ns×S(M)+Nb×B(M; a, b) to determine the yield with the extended maximum likelihood fit, where Ns and Nb are the number of signal and background events, S(M) is the function for the signal, B(M;a, b) is the function for the background with parameters a and...
6. ### Delay estimation using cross correlation

Hi Suppose there are two continuous signals of same frequency say 4 KHz. The time corresponding to its one cycle is around 250 us. If we delay one signal by 4010 us (i.e >> one cycle delay), can we use cross correlation techniques to estimate this delay accurately? Thanks
7. ### Help with random variable linear estimation

Hi all, I have a problem on linear estimation that I would like help on. This is related to Wiener filtering. Problem: I attempted part (a), but not too sure on the answer. As for unconstrained case in part (b), I don't know how to find the autocorrelation function, I applied the definition...
8. ### MSE estimation with random variables

Hello all, I would appreciate any guidance to the following problem. I have started on parts (a) and (b), but need some help solving for the coefficients. Would I simply take the expressions involving the coefficients, take the derivative and set it equal to 0 and solve? I believe I also need...
9. ### MSE estimation with random variables

Hello all, I am wondering if my approach is correct for the following problem on MSE estimation/linear prediction on a zero-mean random variable. My final answer would be c1 = 1, c2 = 0, and c3 = 1. If my approach is incorrect, I certainly appreciate some guidance on the problem. Thank you...
10. ### A Uncertainty estimation in pgopher

Hello! Can someone who used pgopher before (I am fitting a diatomic molecular spectra) help me understand how does it calculate the uncertainty on the parameters when doing a line fit. I found very little online and it is not totally clear to me. Mainly I am not sure how, just by providing the...
11. ### B Mean-Value Theorem, Taylor's formula, and error estimation

Hi, PF Taylor's formula provides a formula for the error in a Taylor approximation ##f(x)\approx{P_{n}(x)}## similar to that provided for linear approximation. Observe that the case ##n=0## of Taylor's formula, namely, ##f(x)=P_{0}(x)+E_{0}(x)=f(a)+\dfrac{f'(s)}{1!}(x-a)##, is just the...
12. ### A Quantum weak measurement parameter estimation vs Classical Estimation

I am not an expert in quantum theory. I want to carry out some parameter estimation on a set of data I have. I have a model for the data with the parameter(s) of interest as variable(s). The data available is sporadic, meaning non-statistical or techniques involving no prior knowledge on the...
13. ### Comp Sci Confusion on motion estimation block diagram-MPEG video compression-:

My doubts are as follows-: -> Why frame n is not segmented to blocks? -> Why no inputs from (n-1) side for block matching? -> What do we do in prediction error coding? Source-: https://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/AV0506/s0561282.pdf I have read this many times but that...
14. ### MHB Confusion on motion estimation block diagram-MPEG video compression-:

https://lh4.googleusercontent.com/g6wQjnQ6p3IVt86-_kwnNVwyOb_iUxUXWChyf0XZR5PO17uOnPbNhCxdpfUSScvU8sAR8Al2FNRMoeMEqLUUuJsvGOSnpFO94tutB2h-927rxVYRDUGzi-JF9FYs9hKivGdCvrAP My doubts are as follows-: -> Why frame n is not segmented to blocks? -> Why no inputs from (n-1) side for block matching...
15. ### I Estimation of E-field strength at a distance from dipole antenna

Hello everyone, I was asking myself about electric field strength estimation at a distance d from - in my case - a half wave dipole antenna. There are pretty much a lot of information about this on internet or in books but still, there are a few things that are confusing to me that I would...
16. ### I Notation of the approximation in quantum phase estimation algorithm

I'am interested in the notation of the approximation in quantum phase estimation algorithm. In the literature there are different definitions, which I divide into two cases here. Both different in their definition of the ##\delta##. In both cases I start with a quote of the source and show an...
17. ### I Quantum phase estimation - Question regarding rewriting the state

In Nielsen and Chuang p.223 we have the following situation: $$\frac{1}{2^t} \sum\limits_{k,l=0}^{2^t-1} e^{\frac{-2\pi i k l}{2^t}} e^{2 \pi i \varphi k} |l\rangle$$ Which results from applying the inverse quantum Fourier transform to state ##\frac{1}{2^{t/2}} \sum\limits_{k=0}^{2^t-1}...
18. ### A HHL quantum algorithm and the phase estimation

In HHL algorithm, does the controlled unitary (Hamiltonian simulation part of Quantum phase estimation) depend on Hermitian matrix coefficients and how?
19. ### I Measurement of a qubit in the computational basis - Phase estimation

Hello, I have a question about the measurement of a qubit in the computational basis. I would like to first state what I know so far and then ask my actual question at the end.What I know: Let's say we have a qubit in the general state of ##|\psi\rangle = \alpha|0\rangle + \beta|1\rangle##. Now...
20. ### Engineering 2D MAP Estimation with a Uniform Prior

Hi, I was attempting the following question, but got confused on this part: Question: Two radar tracking stations provide independent measurements ##x_1## and ##x_2## of the landing site, ##\mathbf{x} = (x, y) ##, of a returning space probe. Both have Gaussian sensor models, ##p(x_i|X_i ) =...
21. ### Question about Spectral Estimation using AR Models

Hi, I was recently reading about spectral estimation with parametric methods, and specifically auto-regressive models. I came across the statement: "An AR(p) model can provide spectral estimates with p/2 peaks" and I was wondering why this was the case. I do apologize if this is the wrong forum...
22. ### MHB Value of f(1/2) using estimation for the remainder

Hey! :giggle: Let $f(x)=e^{-x}\sin (x)$, $x\in \mathbb{R}$. a) Calculate the Taylor polynomial of order $4$ at $0$. b) Calculate the value of $f \left (\frac{1}{2}\right )$ using estimation for the remainder with an error not more than $\frac{1}{400}$.I have done question a) ...
23. ### What is a good estimation for the limit of what a person can know?

For example: A person who gains degrees in 5 different fields. Will this person be able to refer to information learned in all 5 fields and bring it up at will? Going by my own understanding of my self it seems to fade away when something new is learned and focused on. But once you revise over...
24. ### A Frequency estimation - Minimising the number of samples

I have a practical question about frequency estimation of a noisy sine In some of my experiments I need to estimate the frequency of a noisy damped sine. Currently I just use uniform sampling (sampling at times t=n*T) (making sure to exceed the Nyquist criteria) followed by an FFT. In the...
25. ### Estimation of the number of background events

The problem is; You are designing an experiment to search for a new particle. Based on some model, the number of expected signal events is estimated to be 10. In order to claim the signal with the confidence level of 3σ (or 5σ), how small the expected number of background events should be? I...
26. ### Cost Estimation capacity exponent formula

To estimate the cost of an item of equipment or plant from another of a known cost and size or capacity , we use a well known formula Cost B = Cost A * ( CapacityB/Capacity A)^n, where n is a factor usually around 0.5-0.8 depending on the plant or equipment involved. These exponents are...
27. ### MHB Squared Error of Estimation

I would like to estimate the magnitude of a radio signal received from a transmitter by first principles: Transmitter antenna length ##L=1## m Transmitter antenna area ##A=1\hbox{ cm}^2## Number of electrons per unit volume in antenna ##n_e=10^{28}## Radiation resistance of antenna ##R_R=10\...
29. ### Deterministic method for cost estimation

This is for my Engineering master project. I am doing a feasibility study on a couple of different designs of small gas fuelled power stations for remote areas. A big part of it is the CAPEX costs. Most companies hold that kind of info very closely. Does anyone have any insights on this kind...
30. ### MHB About ML and LMMSE Estimation - I

Can anyone help me for this question?
31. ### MHB Maximum Likelihood Estimation Formula Simplification and Solution for p?

Hey guys ! My mother language is not English by the way. Sorry for spelling and gramme. :) I'm curious to see if you can help me with my problem.I have already tried for almost a week and did not get to a solution. I also know, that the Maximum likelihood estimation is part of statistics and...
32. ### ARMA/GARCH estimation with standard errors

I want to estimate the parameters and standard errors of the following ARMA/GARCH model: ##y_t=a+b y_{t−6}+cy_{t−8}+dϵ_{t−1}+ϵ_t## ##σ^2_t=ω+αϵ^2_{t−1}+βσ^2_{t−1}##The code I use is: def main(): x0 = (0.01,0.01,0.01,0.01,0.01, 0.01, 0.01) b = minimize(garch_loglike, x0, R_bel, bounds...
33. ### Estimation of the Power Output of a steam turbine

Hoow can one estimate the amount of steam required to generate certain amount of electical power mathematicaly?
34. ### How to estimate a GARCH model in python (without standard function)?

Hi, I want to program an GARCH model for exchange rates. To do this, I calculated the residuals. Next, I did the following (in python) def main(): vP0 = (0.1, 0.05, 0.92) a = minimize(garch_loglike, vP0, eps, bounds = ((0.0001, None), (0.0001, None), (0.0001, None))...
35. ### I Fisher matrix - equivalence or not between sequences

I am currently studying Fisher's formalism as part of parameter estimation. From this documentation : They that Fisher matrix is the inverse matrix of the covariance matrix. Initially, one builds a matrix "full" that takes into account all the parameters. 1) Projection : We can then do...
36. ### Transition energy estimation based on bond length

I come across this question in a textbook. Somehow my result is way off from the solution answer. I used the energy formula for particle in a box with n(Initial) = 22 and n(End) = 23, the calculated box length is 732 pm. I arrived at an answer of 39.3 nm. The answer from the answer book is but...
37. ### I Maximum Likelihood to find the original data or estimation directly

I make confusions in the using of Maximum Likelihood to find (approximately) the original signal knowing the data observed and the using of Maximum Likelihood to find estimations of parameters of the PSF 1) Find (up to some point) the original signal : I start from this general definition (in...
38. ### A Estimation error from estimation quantile of normal distribution

Hi guys, For my (master) project I am trying to find the probability that a random variable, which is normally distributed, exceeds a quantile that is estimated by a limited number of observations. See attached for my attempt. - Is it correct? - How to incorporate the fact that the mean and...
39. ### Automotive Estimation of the damping coefficient of a suspenion

Hi all, I have a suspended seat with a scissor mechanism like the following: This seat is composed of coil spring and a hydraulic damper. My aim is to develop a multibody model of that seat. Actually, my model is quite complete, only the parameters of damper are missing (i.e. the damping...
40. ### Estimation and validation of water pressure at nozzle

ρ I am trying to estimate and validate the pressure of water exiting a nozzle. For an unknown reason, the validation is consistently twice as high as the estimation. Here the approach: Estimation: I am using the dynamic pressure equation for the estimation: q = 1/2 * ρ * u2 where, q = dynamic...
41. ### I What is the thickness of the atmosphere?

I was thinking of a Fermi-question: the thickness of atmosphere with diffusive equilibrium. And I estimated roughly 10^{5}m (where it should be ~10^{4}m). The difference of order of magnitude to real thickness is 1 (from Wiki). I had a lot of fun, and I am looking for interesting ways other...
42. ### MHB Convergence of Alternating Series and Estimation of Absolute Error

Hey! :o I want to determine the value of $n\in \mathbb{N}$ such that the absolute error $$\left |\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)\cdot k!}-\sum_{k=0}^{n}\frac{(-1)^k}{(2k+1)\cdot k!}\right | =\left |\sum_{k=n+1}^{\infty}\frac{(-1)^k}{(2k+1)\cdot k!}\right |$$ is less than $10^{-6}$. Do I...
43. ### A Error estimation in linear regression

I have a data set of 11 predictors and one response for 1000 observation and i want to do linear regression. I also have measurements errors of the predictors (also 11X1000 matrix) and i need to count for them in the total error estimation. how can i do that?
44. ### MHB Maximum of the Likelihood estimation

Hey! :o I am looking at the Likelihood function. I have understood how we define that function, but having find the maximum of the Likelihood estimation, what is the meaning of that? What information do we have, when we have found the $\theta$ so that the Likelihood function L is maximized...
45. ### Orders of Magnitude Estimation Problem

Hello, I'm sort of stuck with this order of magnitude question I have came across. Q: The annual global production of jet fuel in 2010 was approximately 783 million litres. An aeroplane consumes 0.03 litres of jet fuel per passenger for every kilometre it flies. Estimate the number of...
46. ### I Why is the maximum likelihood estimation accurate?

Hi I've been googling maximum likelihood estimation. While I do understand how to compute it, I don't understand why maximizing the likelihood function will give us a good estimate of the actual parameter. In some cases, like the normal distribution, it seems almost obvious. However, in the...
47. L

### I Problems that could occur in estimating n from a Binomial distribution

Hi, I am doing the following question: https://i.gyazo.com/f2e651334bcbd5f1dcb6d661e4160956.png I have estimated both n and theta. But the part that is throwing me off is what problem could you encounter in estimating n here? My only idea is that it might be something to do with the sample...
48. ### MATLAB Sample Code for Monte Carlo estimation of pi

Below is the partial code to plot the rejection/accept regions using monte carlo sampling. The context is to estimate pi and plotting is just one part of it. I'm not sure how the ~ symbol can work. scatter(samples(1,~reject),samples(2,~reject),'b.')...
49. ### A LTI Impulse Response Estimation with Point Process Input

Hello, I am trying to estimate transfer function of unknown LTI system, given output and assumed input as point process. I have measurement of output, while input, which is assumed to be point process, could be created synthetically using known times and amplitudes. My questions: 1. What is...
50. ### I Cosmological constant estimation in QFT

My question is about the interpretation of the large estimated value. In QM we are supposed to think in terms of measurement results and not of ontological properties. So, if QFT predicts a large vacuum energy what is the correct approach? 1. The predicted value is the result you get if you...