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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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Propagating Uncertainties on Interpolated Data

I have a data set of 2000 $[x, F(x), \delta F(x)]$ triples, where $x$ is exact and $F$ is a measured value with an uncertainty $\delta F$. I can interpolate/fit the function however needed, and this ...
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SAS Proc expand, how does it go from lower to higher frequencies [closed]

Proc Expand is quite useful for interpolating values, however sas help is not clear how it does when we want to spread the time series from a lower frequency (say year) to a higher frequency (say ...
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What is the best way to represent uncertainty from linear interpolation?

A little background to this question: Part of my job is to conduct flood risk appraisals to help determine the viability of flood defence construction. There is a standardised way to do this, which ...
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Word for data-series comprised from resampled, interpolated and merged data-series

Two series of data-points for a specific curve are given: $x$ as a function of $y$ (high resolution, low range) $y$ as a function of $x$ (low resolution, high range) The two series are merged and ...
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Is there a method to approximately predict a 3D curve given two plane view of the curve?

Let's say the original data contains three variables, so it is a list of (x,y,z). In the figure, the blue and red curves are the lists of (x,z1) and (y,z2), respectively. These two lists are obtained ...
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Covariance matrix for a 2D state vector

I'm performing Optimal Interpolation (which in fact is a simplified Kalman filter with constant $\mathbf{K}$). My state variable is a 2D concentration field with a size of 370 x 400 on which I try to ...
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44 views

How to handle multiple points at the same location in spatial interpolation?

I am new to the topic of spatial interpolation and would appreciate your opinion on a general question which has arisen. Suppose I have a data set containing rental rates for different apartments in ...
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50 views

Regression for curve fitting

For a curve generated from dataset points, split the curve into parts and obtain the best-fit degree of polynomial,coeffcients and the interval/range of the split through implementation in python.I am ...
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Piece wise Polynomial Regression [duplicate]

It's wide known that for polynomial interpolation Chebyshev sites (as knots) are almost optimal, we can show that using those the Lebesgue constant is near to the lower bound. Is that claim also ...
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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 ...
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Estimation of function using Spline Interpolation

My problem is the following: Estimate the function from given data (below) and show that the estimated function has the following properties: (i) $f(0)=0$ (ii) $f(x)>0, x>0$ and $f(x)<0, x<...
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How to interpolate/resample both dense and sparse points?

Suppose I have data like red points below I would like to interpolate/resample these points at black ticks. At right the points are sparse and it is obvious to interpolate them linearly or with ...
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Nonparametric Bayesian estimation of several black-box functions of different variables from their noisy sums

In order to introduce my problem, let’s start with the nonparametric estimation of a single unknown/black-box function $f:{\Omega _f} \to \mathbb{R}$ of a discrete variable $x$ in a finite domain ${\...
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How does Excel interpolate / imputate missing values in time-series when fitting a line to a plot?

I have a scatter plot in Excel (upper part of the screenshot) of time-series data. In-between the values that I plot (to the left), are some missings. I fit a (linear) line to those values and display ...
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Spatio Temporal Interpolation of Vector Fields

I'm looking around for interpolation methods for vector fields, and RBFs seem to be a recommended approach. I've seen ALGLIB specifically mention that it is not suitable for spatio-temporal ...
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Interpolating between consecutive weather radar images

I have a series of rainfall intensity images from a weather radar taken every 10 minutes. My goal is to generate intermediate frames in order to create a slow motion video. I've tried using the ...
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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 ...
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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 ...
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Poor regression results of neural networks on 2d benchmark data (compared to spline interpolation)

I try to understand for which regression tasks neural networks might be useful. One benchmark for me is to reproduce the ability of scipy.interpolate.griddata: ...
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Can I say Holt-Winters Method is an example of interpolation?

I believe it fits under the definition from wiki: In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of ...
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265 views

Disaggregating averaged monthly data (into daily) using linear splines

Let's say I have a series that represents averaged data for each of the following five monthly periods. So each data point below is the average of that month. (Python code) ...
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Minimize function curve 'length'

Given a set of points $(x_i, y_i)$, how can I find the serie of $ C^\infty $-functions for which the sum passes through all points and for which the length of the resulting curve is minimal; i.e. if ...
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198 views

Interpolate covariance matrix

I have measurements $z_i$ and associated covariance matrices $R_i$ separated in time by some sampling interval, and I want to interpolate between measurements. For example, I have a measurement at ...
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Estimating distribution of sound features based on speed

I am currently working on creating a model of sound of inside of a car based on speed. To be specific, making a Gaussian distribution of MFCC(13 dim) for each speed, i.e. car running at 30kmph, 60kmph,...
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reducing 2 variables of a function into one

I have an experiment where I'm measuring some physical quantity Q as a function of 3 variables which I can physically control (x,y,z). I'm collecting many samples of Q and (x,y,z) and then I can ...
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Obtain function that models strange oscillating data points

I've collected some interesting data from a fairly complex Python program I've written and I'm curious to figure out the mathematics behind it; or, at least, the empirical mathematics. Analyzing the ...
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Confidence intervals for bilinear interpolation

I have 4 data points which I am using to interpolate a query point using bilinear interpolation. Each of the 4 data points is obtained from the average of several observations (typically 10-16 for ...
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47 views

Replacing missing wind speed data from a nearby site

I am doing a project that is looking at testing various imputation methods for estimating missing wind speed at a site in Trinidad. The dataset consist of hourly wind speeds for 15 years. I have tried ...
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516 views

'Amelia' command returns error message: 'matrix is singular or not positive definite'

I've followed the instructions laid out in this thread, and created 'group' and 'time' variables. Below is a small subsample of my data. The set is longitudinal and in long format. ...
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Neural net that preserves spatial information in output

I'm attempting to use a neural network as a kind of interpolator for a high-dimensional function. We're doing this to circumvent the need for a physical model that calculates this function exactly, ...
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I have the standard deviation, mean and the maximum value for a distribution between t=0 and t=T. How do I approximate the best fitting curve?

I have the time series data. The mean and maximum value, standard deviation at every minute (60s) is given. However, I want to intrapolate it as I want the data of each second. Is there any way to do ...
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345 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 ...
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Is there a name for estimating several data points representing subgroups from a single aggregated data point?

Say a country with sparse data reports the number of people who drank alcohol in the past month as a single data point, representing both sexes and ages 10-65. The goal is to be able to estimate ...
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Extrapolating Hierarchical Time-Series Data

I have time-series data of national-level population estimates from 1990 to 2015. I also have subnational-level population estimates (thus, the distribution of national data), but only for years 2000 ...
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Formulating spline interpolation as a matrix problem

I have $N\times m$ data sets, with the same independent variables (time), i.e., $(t_i, y_{nmi})$. I want to interpolate (linear is fine, but understanding the generalizing for any set of basis ...
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Is it incorrect to interpolate between known probabilities for binned data?

I have 7 bins of binary data according to a variable x as follows: x1: N=1000, success = 324, failure=676 x2: N=1000, success = 444, failure= 556 .... .... x7: N=...., success = ..., failure = ......
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Correcting wild deviations in polynomial interpolation/regression

When using polynomials to do spline interpolation or least-squares regression on a set of points which are not evenly spaced, there is a tendency for the polynomial to deviate wildly in those regions ...
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How to write the functional form of multivariate polynomial cubic spline?

I got some articles/books about the cubic splines. However, I didn't see anyone mentioning the bivariate case of cubic spline much in detail. My question is how to write the cubic spline in a ...
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Zero-counts in Kneser-Ney smoothing

Hope to get help from someone experienced with implementation of language models. I am trying to implement n-gram model based on Kneser-Ney smoothing, however met the next issue: Here is simplified ...
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Variance-weighted interpolation

I am trying to fit a function $f$ to the data pictured below: For $\hat{f}(0)$ I can take the sample mean of the 6 observations at $0$, for $\hat{f}(2)$, I average the 2 at 2. For $\hat{f}(1)$, I ...
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Interpolating new data points before curve fit

In a hypothetical situation with sparse experimental data, the researchers use interpolation (linear or cubic splines) between the points to generate more data before applying modeling (eg GLMs) and ...
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Is it valid to run t-test on interpolated vectors - if so, how to adjust alpha?

The task: I need to calculate a one-sample t-test to see if the mean of a vector of values differs significantly from zero. Data: The dataset consist of about 25 such vectors, each with a length of ...
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Calculate projectile trajectory from 3d points

I am trying to calculate the trajectory of a moving object (specifically, a thrown object) through a series of video frames. My tracking algorithm can reliably detect ~90% of the object occurrences ...
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Enhance gap between analytic and interpolated data in visualization

I have two data sets, disposed in a 3Dplot. one set represents the interpolated data, the other the analytic. Each set lies on a separate grid. I have plotted the data with python matplotlib on a ...
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215 views

What is the difference between linear interpolation and piece-wise linear interpolation?

I'm familiar with linear interpolation. I tried to search some details about piece-wise linear interpolation but failed to understand this method. Can someone explain the difference between these two ...
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188 views

How to pass equation formula to R function? [closed]

I need to interpolate simple linear equation to the set of points. Equation has the following form: $$ log10(y)=A+B/(C-X) $$ where A,B,C - coefficients of equation. So far I was able to interpolate ...
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Interpolation between two distributions

I have a list of empirical measurements describing the rents of apartments grouped by the apartment's size. I.e there are five categories, apartments with 2.5, 3.5, 4.5, 5.5, 6.5 rooms. For each of ...
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Time varying covariates and Interpolation issue

Based on my reading on time-varying survival analysis, I am encountering two different and conflicting sets of advice with regards to time-varying covariates and interpolation. The first advice is ...
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799 views

What options are there to 'normalize' values from a heavy-tailed distribution?

We have some data collected acquired from a complex setup, that is expected to come from a "fairly normal" underlying distribution. However when I investigate the data it appears that it's fairly ...