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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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28
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4answers
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 ...
20
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2answers
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 ...
19
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1answer
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 ...
16
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8answers
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 ...
16
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4answers
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 ...
16
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2answers
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 ...
13
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4answers
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 ...
10
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1answer
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 ...
9
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2answers
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 ...
9
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1answer
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-...
8
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1answer
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 ...
8
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1answer
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 ...
7
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1answer
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 ...
7
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3answers
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 ...
6
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1answer
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.
6
votes
1answer
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 ...
6
votes
1answer
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 ...
6
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3answers
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 ...
6
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1answer
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 ...
6
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2answers
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, ...
6
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2answers
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 ...
6
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1answer
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 ...
6
votes
1answer
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 ...
6
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0answers
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: ...
5
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2answers
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 ...
5
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1answer
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 ...
5
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1answer
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....
5
votes
2answers
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 ...
5
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3answers
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, ...
5
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0answers
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, ...
5
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0answers
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?
4
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3answers
2k views

Interpolating the empirical cumulative function

The empirical cumulative distribution function of a random variable, given observations $x_\left( k \right) > x_\left( k-1 \right)$, $k \in \mathbb N$, $k \le n$, is defined as $F_{emp}(x_\left( k \...
4
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1answer
400 views

Looking for an unbiased version of the empirical cumulative distribution function that I can interpolate

Most definitions of the ECDF define it as (#elements <= threshold) / #elements. Matlab and R both implement their ecdf() functions using this formula. In my testing, however, I find that there is ...
4
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1answer
1k views

How to interpolate (spline, LOESS, etc.) with a mix of critical and non-critical points

The data we are interpolating is monotonically increasing (for example, a car's odometer reading). We have two types of points we'd like the solution to interpolate through. The solution surface must ...
4
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1answer
274 views

How can I estimate the tail of a distribution with a truncated distribution?

The broadband speed data I'm working with have all values over 30Mbps placed into a >30 category. The distribution is thus truncated. This leads to the final column in the histogram below being a ...
4
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1answer
142 views

Parametric Surface Reconstruction from Contours with Quick Rescaling

I'm looking to construct a 3-D surface of a part of the brain based on 2-D contours from cross-sectional slices from multiple angles. Once I get this shape, I want to "fit" it to another set of ...
4
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1answer
1k views

How to interpolate independent variable over five-year period?

I have panel data on income and population for the years 1990, 1995, 2000 and 2005. I would like to interpolate these two variables (both independent variables), so that I have data for every year ...
4
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1answer
176 views

Interpolation of spectra: uneven sampling to even sampling

I have a spectrum. Specifically, my data is relative intensity $[I_{\tilde{\nu}}]$ versus wavenumbers $[\tilde{\nu}]$. The wavenumbers are equally sampled so that ${d\tilde{\nu}} = c$, where $c$ is ...
4
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0answers
92 views

Estimating Spline curve by OLS. Is a good idea to fix the knots at Chebyshev sites?

I am writing my master's degree thesis on a novel method for fixing knots in an adaptive way and while reading the literature I've found many references to the so-called Chebyshev sites. This sites or ...
4
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0answers
276 views

Spatial interpolation of vectors in vector fields

Statistical modeling is new to me and I would appreciate some thoughts on my project. I am trying to model the spatial (and possibly temporal as well) relationships within vectors in vector fields. ...
3
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4answers
3k views

Software for making semi variograms and analyses?

Our lab used to have a program called GS+ that let us make semi variograms on our data and analyse them. Unfortunately, the licence has expired. Is there another piece of software that lets you do ...
3
votes
1answer
555 views

Kriging without covariance?

I am trying to krige monthly snowfall totals using data from weather stations and elevation. When I use a linear variogram model (set using a GUI and appears to be a good fit), the resulting layer ...
3
votes
2answers
157 views

Coefficient estimated with a binary predictor $\in \{0,1\}$, but making predictions with values between $0$ and $1$ - is this OK?

Let's say I have a variable $x_d$ that, in the estimation data, is a simple indicator ($x_d \in \left\{0,1\right\}$). I estimate a coefficient for it, $\beta_d$, along with several other coefficients ...
3
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1answer
558 views

How to display concentration data in space?

I have a data frame of chemical concentrations that are measurements taken from 12 locations all in the same vicinity. I have manually assigned x and y coordinates to each location (on a 0 to 20 scale)...
3
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2answers
2k views

Kriging on log transformed rainfall data

I am beginner in R. I had found in the literature that prior to performing kriging on the data, the distribution has to be investigated to check if it is Gaussian. So, in order to check if the data ...
3
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1answer
177 views

Centroid of nearest-neighbours on a hypersphere as a method for applying crossover in genetic algorithms

I am currently building a genetic algorithm to tune n parameters where n will probably be in the range of ...
3
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1answer
285 views

Density estimation with scaled sinc-like kernels

Given data points $x_i$ in $\mathbb{R}^d$ with function values $f_i$, one can estimate the function at a given $x$ by $\ \ \ \ \text{f}_{est}( x ) = \frac {\sum { w_i f_i }} {\sum { w_i }}$ with $w_i ...
3
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1answer
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 ...
3
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1answer
704 views

Interpolation of missing values using results produced by arima

I would like to know if anyone knows how to apply the arima results to calculate missing values in the observation period. I am looking for something similar to <...
3
votes
1answer
432 views

Interpolation in multivariate time series

I have a problem in multivariate time series. The data consist of three time series related to foreign trade. Although my client is still doing research and attempting to find monthly data for all ...