Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [interpolation]

Given a set of bivariate data (x, y), to impute a value of y corresponding to some value of x at which there is no measurement of y is called interpolation, if the value of x is within the range of the measured values of x.

Reference: Glossary of Statistical Terms from berkeley.edu

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Extrapolation v. Interpolation

What is the difference between extrapolation and interpolation, and what is the most precise way of using these terms? For example, I have seen a statement in a paper using interpolation as: "The procedure interpolates the shape of the estimated…
Frank Swanton
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How is interpolation related to the concept of regression?

Explain briefly What is meant by interpolation.How is it related to the concept of regression? interpolation is art of reading between the lines of a table and in elementary mathematics the term usually denotes the process of computing the…
Argha
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Why is the use of high order polynomials for regression discouraged?

I've read many times on this site that high order polynomials (generally more than third) shouldn't be used in linear regression, unless there is a substantial justification to do so. I understand the issues about extrapolation (and prediction at…
Marco Rudelli
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How do I find values not given in (interpolate in) statistical tables?

Often people use programs to obtain p-values, but sometimes - for whatever reason - it may be necessary to obtain a critical value from a set of tables. Given a statistical table with a limited number of significance levels, and a limited number of…
Glen_b
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What are the advantages / disadvantages of using splines, smoothed splines, and gaussian process emulators?

I am interested in learning (and implementing) an alternative to polynomial interpolation. However, I am having trouble finding a good description of how these methods work, how they relate, and how they compare. I would appreciate your input on…
David LeBauer
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Fitting multivariate, natural cubic spline

note: with no correct answers after a month, I have reposted to SO Background I have a model, $f$, where $Y=f(\textbf{X})$ $\textbf{X}$ is an $n \times m$ matrix of samples from $m$ parameters and $Y$ is the $n \times 1$ vector of model…
David LeBauer
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What does interpolating the training set actually mean?

I just read this article: Understanding Deep Learning (Still) Requires Rethinking Generalization In section 6.1 I stumbled upon the following sentence Specifically, in the overparameterized regime where the model capacity greatly exceeds the…
Samuel
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Is a spline interpolation considered to be a nonparametric model?

I am aware of the basic differences between nonparametric and parametric statistics. In parametric models, we assume the data follows a distribution and fit it onto it using a fixed number of parameters. With KDE for instance, this is not the case…
John Doe
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What is the statistical justification of interpolation?

Suppose that we have two points (the following figure: black circles) and we want to find a value for a third point between them (cross). Indeed we are going to estimate it based on our experimental results, the black points. The simplest case is to…
Developer
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Interpolation of influenza data that conserves weekly mean

Edit I have found a paper describing exactly the procedure I need. The only difference is that the paper interpolates monthly mean data to daily, while preserving the monthly means. I have trouble to implement the approach in R. Any hints are…
COOLSerdash
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Interpolating binned data such that bin average is preserved

Say I have this binned data as input. The average value $\bar{y}_i$ is given for each successive $\Delta x_i$ interval. For simplicity, let's assume sampling density is uniform within each bin. Now I want to estimate the underlying function $y$($x$)…
Jean-François Corbett
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Modern machine learning and the bias-variance trade-off

I stumbled upon the following paper Reconciling modern machine learning practice and the bias-variance trade-off and do not completely understand how they justify the double descent risk curve (see below), desribed in their paper. In the…
Samuel
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How Does Kriging Interpolation work?

I am working on a problem in which I need to use Kriging to predict the value of some variables based on some surrounding variables. I want to implement its code by myself. So, I've went through too many documents to understand how it works, but I…
Dania
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Fourier/trigonometric interpolation

Background In a paper from Epstein (1991): On obtaining daily climatological values from monthly means, the formulation and an algorithm for calculating Fourier interpolation for periodical and even-spaced values are given. In the paper, the goal is…
COOLSerdash
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Gaussian process - what am I doing wrong?

I have recently started to delve into Gaussian processes. During my review, I have found a book which states that one can interpret the mean of a Gaussian process as a combination of basis functions, i.e.: $$\bar{f}(x^*)=\sum_{n=1}^N \alpha_i…
J.Galt
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