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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.

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3k views

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 ...
22k views

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 ...
50k views

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 ...
29k views

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 ...
12k views

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 ...
2k views

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 ...
876 views

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 ...
4k views

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 ...
987 views

Confusion regarding kriging

I was reading this wikipedia article related to kriging . I didn't understand the part when it says that Kriging computes the best linear unbiased estimator, $\hat Z (x_0)$, of $Z(x_0)$ such that ...
2k views

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-...
1k views

Using ARMA when data is missing

I am using ARMA over a dataset with missing samples. How do I treat them? Would you suggest to make linear/nonlinear interpolation or just keep them out and consider two samples with missing data in ...
1k views

Stationarity - assumptions and examination

I am examining rodent captures on six permanent rodent trapping grids measuring 150 x 150 meters and consisting of 121 trap stations evenly spaced 15 meters apart. There are six such trapping grids ...
944 views

Averaging time series with different sampling interval

I have a few time series that were (for technical reasons) acquired with slightly different time intervals, ranging between 19 and 21 seconds. Now, I would like to average the values of these ...
1k views

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 ...
1k views

Explanation of cubic spline interpolation

Can someone explain to me what a cubic spline is, and how we could use it to interpolate a function? I have searched on the internet but I would like a simple explanation.
364 views

Connecting scatter plots with linear interpolation?

Given the decision that on a scatter plot the data points will be connected (just as an example, let's say we're talking about students attending class per week), is it more correct to connect the ...
332 views

In inverse theory, how do I transform the averaging kernel matrix to a new grid?

Rodgers and Connor (2003) describe how measurements by remote sounders can be properly compared, taking into account differences in averaging kernels and error covariances. They make the assumption ...
7k views

Bicubic/bilinear interpolation in R

I have a data set of x,y,z data and I'd like to do a bicubic interpolation. x and y are spatial coordinates and z is a temperature. Below there are two images. The ...
2k views

How to simplify a stretched exponential fit?

I have data from a Monte Carlo experiment that I was hoping to fit to a model of the form $$\log(x y) \approx \beta_0 + \beta_1 \log(z),$$ where I have many observations of triplets, $x, y, z$. This ...
3k views

Non-algebric curve-fitting along weighted pointcloud (if possible using python)

I have a list of weighted 2D points taken from symmetry analysis of a human back surface. I am supposed to find the "midline" representing the most likely path describing vertebrae location (actually, ...
243 views

Extrapolation of 2d movement

I have a problem with missing data in my dataset. My dataset is timeseries which contains x,y coordinates. I'd like to extrapolate missing values and use the assumption that I know speed and direction ...
4k views

Uncertainty propagation in linear interpolation

How do I calculate the uncertainties in linearly interpolated values from a given tabulated function? I am just coming back into the fold after a bit of a hiatus, and am having trouble ...
963 views

Difference between extrapolation and interpolation in higher dimensions

The most common distinction I've seen made between interpolation and extrapolation is that interpolation is within the range of the data, whereas extrapolation is outside the range of the data. This ...
1k views

Interpolation with radial basis functions (RBF) is failing for some reason

This is not a pure programming question. I am trying to understand what's going on when I try to use RBF with 5 centers. I am using R to exemplify, see below. My data set: ...
850 views

Assessing error of a spatial interpolation algorithm

I have a set of 3D points. The points have three components $x$, $y$, $z$. You can think of these points as the surveyor points that one collects from measuring a terrain for GIS purposes. I have a ...
956 views

What is the difference between (universal) kriging and spatial autoregressive models?

As part of a course on missing observations in social/survey statistics I am trying to explore existing methods of predicting either point pattern or polygon data. I got quite confused by all the ...
278 views

Spatial interpolation models: deterministic vs statistical

I am applying diferent methods to interpolate continuous spatial surfaces (kriging, splines, glm,etc). Most of the studies that have enough detail for me to follow usually focus on one specific method....
2k views

Resampling/Interpolating monthly rates to daily rate estimates in R

I'm really not sure what to search for. If the answer to this is googleable, I'd be happy to hear what I should google. I have a dataset of energy meter data. Readings are taken at roughly monthly ...
244 views

Interpolating/smoothing 8-bit data

(As a caveat, I think this belongs on this stack site, but I'm not 100% sure.) We have a time series that is physically sampled with only 8bit resolution, so we wind up with a "staircase" pattern, ...
222 views

Interpolation and Sample size when Visualizing distributions

Let's assume a stochastic simulation or test with a control variable. The task is to visualize the distribution to demonstrate the effect that is being researched. The objective is to get smooth plot, ...
791 views

Correlate bivariate Brownian bridges

Given two independently constructed Brownian bridges (from their marginal means and variances), is there a way to correlate the sample paths?
2k views

303 views

Multivariate Interpolation Approaches

Is there a good, modern treatment covering the various methods of multivariate interpolation, including which methodologies are typically best for particular types of problems? I'm interested in a ...