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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4
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1answer
173 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 ...
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 ...
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

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 ...
13
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4answers
863 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 ...
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2answers
777 views

2d interpolation method for coarsely sampled image

I'm looking for a general method for 2d interpolation of a coarsely sampled image. I'll use an example, taken from the scipy.interpolate (Python) page. http://bit.ly/10lHXma Say, I have this image, ...
1
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1answer
302 views

Backfilling ARIMA data with exogenous variable

I have time series data for a set of cities that goes back for about 10 years. I also have the data at the state level for almost 30 years. There was an event that occurred about 20 years ago, that is ...
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0answers
219 views

Should we always do interpolation polynomially or fill the gaps with the average value?

I have a series which takes values as 1,2 and 3. It also has some ...
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 ...
5
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1answer
277 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....
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, ...
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0answers
525 views

Sparse matrix representation of a spline interpolation

I use spline interpolation within a statistical model, and the transpose of the operator turns up in the gradient of the log-likelihood. Let me set up some notation first. If $x_1 \ldots x_n$ are a ...
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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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1answer
557 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)...
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1answer
171 views

Sampling an interpolated model with MCMC

Is it safe to run a MCMC by interpolating in tabulated data of a model? For background, I have output of a model that involves a set of coupled non-linear differential equations. Calculating models ...
3
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1answer
283 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 ...
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1answer
700 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 <...
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0answers
786 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?
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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 ...
2
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1answer
785 views

Derivation of equations in kriging

I have some confusion regarding some derivations of the equations for kriging in the wiki article. $\newcommand{\Var}{\rm Var}$ It says that kriging error is given by: \begin{align} \Sigma_k^2(x_0) &...
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 ...
9
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2answers
981 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 ...
3
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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 ...
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1answer
669 views

Ordinary kriging stationary case

I am trying to understand ordinary kriging. Say I have 3 elevation measurements: Z1, Z2, and Z3 taken at X positions: X1, X2 and X3. I am also assuming some semivariogram: g(h) and that the process ...
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1answer
427 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 ...
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2answers
496 views

Adjusting data for missing observations

I have an unbalanced panel data set of 40 cities and 20 years. It is unbalanced because the data are not collected for certain cities for every year. The data are then balanced after these 20 years. ...
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0answers
836 views

Similarities between different size matrices, rescaling problem

Given a series of matrices {$M_i$($m_i\times n_i$),i=1...k,$m_j,n_j \in$random} if we rescale (resize) all matrices into a ...
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1answer
976 views

Correlated brownian interpolation

I would like to generate conditional correlated random variables. I have a correlation matrix between normal variables, and these variables are modeled through SDEs. What are the algorithms to ...
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0answers
83 views

Consistent ranked list for ROC interpolation

For classifiers with binary outputs, their performance is summarized by a true positive rate and false positive rate. To interpolate the performance between two classifiers $A$ and $B$ with their ...
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1answer
260 views

Interpolating between models in ROC space

Suppose I have two models $A$ an $B$ that predict class labels. If these give binary predictions, these will appear as pairs of (false positive rate, true positive rate) in the ROC space. We should be ...
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0answers
113 views

How to determine the number of nearby samples for spatial estimation?

In many applications e.g, in mining engineering when we need to generate a map of dispersion of an element (e.g., copper) over the field of study, to depict depletion and concentration regions we have ...
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 ...
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0answers
33 views

Accessing errors of 3D surface generation algorithm [duplicate]

Possible Duplicate: Assessing error of a spatial interpolation algorithm This is a similar question to this and this one. I have a set of 3D points that are sampled from a terrain. The points ...
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2answers
848 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 ...
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 ...
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 ...
2
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1answer
93 views

How to design a study and test the effect of dosage level on cure probability?

My goal is to quantify dosage impact on cure probability for different patients. Let's suppose I have N patients with their charateristics such as age, gender, weight.... Also let's assume there is a ...
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 ...
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1answer
108 views

How to present a empirical study when using econometric models?

I've got a (probably easy) question in how to handle empirical studies, when there are a lot of effects involved. I have a whole bunch of variables and I'd like to analyze just a few of them. But 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 ...
3
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2answers
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 \...
7
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1answer
943 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 ...
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 ...
3
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1answer
301 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 ...