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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59 views

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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80 views

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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265 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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207 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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190 views

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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115 views

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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977 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 ...
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336 views

Multivariable piece-wise linear approximation in R?

I am trying to run linear approximation on a function of 2 or 4 variables. The approx function in R is a very nice, optimized time saver, but it only works for 1 dimension functions I think. Anyone ...
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80 views

What is 5th order kriging?

For our foray into geostatistics we got data that consists of measurements taken from the soil. The dataset has like concentrations of various different minerals. We were divided into a number of ...
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213 views

Kriging variance results

I'm quite a newb at statistics and interpolation, and I cannot understand how to interpret the error estimation computed by Kriging. For example, I performed kriging on temperature values (Celsius ...
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501 views

How do I interpret prediction interval and point prediction?

Consider a simple linear model: I have obtained a prediction interval of $(37, 66)$ and a point prediction of $52$. (the problem behind is not a concern I reckon, for the sake of the question). Now ...
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58 views

What are the considerations for spline-interpolating a whole dataset?

In Clinton, et al. 2010, the authors use splines to interpolate 100 equally spaced data points per year from only about a dozen actual measurements. The 12 (or possibly less for the NDVI data) ...
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23 views

Validating decomposition of Synthetic Tensor generated from Unevenly Sampled Tensor

I have a 3-way tensor generated from 7 experiments, with each experiment being matricized and becoming a frontal slice of the tensor (thus mode-3 is of length 7). The data is generated from ...
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42 views

Prediction/time series/data problem

I have a poverty dataset with rows containing different places and different years and I have to predict the poverty percentage for those places next year. Overall I have over a thousand rows. But I ...
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291 views

Interpolating and aggregating Median Income from binned Census data

I'm working with the most recent ACS Census data for New York City. I'm trying to calculate median income for Neighborhood Tabulation Areas (NTAs), which consist of several Census tracts. The Census ...
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46 views

Fitting an interpolating spline to show mean of interaction on cloud plot

I am surprised to not be able to find a straight forward answer to my scenario. I have created a series of mixed effects models using lme4. I am trying to plot the data in ...
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1k views

Disaggregate monthly forecasts into daily data

I would like to disaggregate monthly forecasts of sales into daily data. I have historical data about daily sales over the past two years (which mainly depends on deterministic effects like day-of-the-...
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1answer
143 views

Linear regression of B-splines with terms inside an integral?

I have encountered a problem that the literature suggests linear regression is able to solve, but I am at a loss. I have a function $F$ that I want to estimate. This function obeys $N$ equations of ...
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28 views

Smooth a function penalising lower values

I have a function $t \rightarrow f(t)$ and its values on a discrete set of time points $t_1, \dots, t_k$. I want to obtain a smooth approximation of my function $\hat f(t)$. I would have done it ...
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36 views

System of Gaussian equations

Let $N(x\ |\ \mu,\sigma^2)$ be the pdf of a normal random variable with mean $\mu$ and variance $\sigma^2$. Question: Given $n$ data points $(x_i,y_i)_{i=1,\dots,n}$, compute $\{w_i\}_i$,$\{\sigma_i^2\...
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1answer
72 views

Estimation of time for a specific value of a variable

I have a data set: ...
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1answer
559 views

Python implementation to find Natural Neighbors of a set of points on a 2D plane [closed]

I have been looking for a fast and efficient implementation of finding natural neighbors of a given point (from a set of points in a 2D plane) particularly preferred if written in python. So far, what ...
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215 views

Are there recommended methods for interpolating sparse time series?

I'm using sparse in a specific (but perhaps incorrect) way. Shown below is a time series of prices ...
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2answers
503 views

How can I interpolate a time series subject to stochastic perturbation?

I have a data set of gas prices. They are not evenly spaced in time, and have quite a few days missing. Here is a sample of the data ...
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65 views

Spline Interpolation with increased deviation in R

I'm trying to effectively increase the temporal resolution of a daily time series data to 6-hourly time series (modeled weather data). I've been using na.spline ...
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220 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, ...
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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 ...
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75 views

Cubic BSpline interpolation

I'm trying to interpolate a curve using cubic bsplines, but I cannot get it to exactly match the original curve. Could someone please give me some pointers. The original solution is from page #7 in ...
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1answer
165 views

GP regression with high-dimensional time-series data

I have what I think is a neat little problem which involves regression. My observations are somewhat sparse, and they are very high-dimensional (though this can be probably be reduced by a factor of ...
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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: ...
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1answer
115 views

create 2d array from 1d arrays of non-equidistant points?

I have been trying to create 2d array/image from three 1d arrays. The arrays are latitude, longitude and temperature. For each value of lat and lon I have temperature. But the lat-lons are not ...
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190 views

R: Fit sinusoidal curve to timeseries, and interpolate at desired times

I have ocean tide data with just high and low tides. I need to fit an appropriate curve (sinusoidal presumably, maybe just polynomial) to this, and then extract values interpolated at specific times. ...
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1answer
900 views

Convert ordinal data to continuous data

Some people I know conducted a survey. One of their goals is to estimate the hourly salary of a group of people. There are two questions in the survey that, supposedly, could answer this question: ...
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Interpolation methods for prediction of water pollution

I have the following problem - I have ran MIKE11 software to compute the c(x,t) = concentration of pollutant in point x on a river (1D case) considering a pollution scenario where quantity q of ...
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1answer
5k views

Missing data imputation in time series in R

I have got hourly temperature data from 2012 to 2016 as follows: ...
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3answers
5k views

What are the theoretical reasons for why extrapolation “less reliable” than interpolation?

Extrapolation is in general "unreliable". (See "What is wrong with extrapolation?") But it is also commonly said that extrapolation is "less reliable" than interpolation. But why should we ...
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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 ...
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18 views

Mixing types of Interpolation while Displaying Data

We have a piece of in-house software for pulling data out of our system and displaying it. It can do this at the resolution of the data, aggregate it up to a lower resolution or down to a higher ...
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1answer
105 views

Correlation between vectors with non-matching y values without using interpolation

Is there a way to calculate the correlation between two time series that have been adaptively downsampled and thus (may) have different y values? This is easiest to explain with an example, so ...
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204 views

Linear interpolation with variable grid

Suppose we are given a set of points $(x_i,y_i)$ for $i=1,\cdots,n$ with $x_1<x_2\cdots<x_n$. The usual form of linear interpolation partitions $[x_1,x_n]$ into a grid of $k$ equally spaced ...
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269 views

Interpolate a CDF to get an interpolated hazard rate, or interpolate the hazard rate directly?

My problem is that I need to do an interpolation. Eventually, I will work on the hazard rate, but I do not know if it is better to interpolate the CDF or the hazard rate. Let me explain better. I've ...
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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 ...
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239 views

Interpolating GPS coordinates in R based on coordinates of another object

I am looking at a ship and a vessel being towed behind it. I have coordinates (in decimal lat and long) for the ship at 1 second intervals. However, I only have intermittent coordinates for the towed ...
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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, ...
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1answer
472 views

Interpolation vs nonlinear Regression [duplicate]

I was playing with the concept of Interpolation in Python and ended up with this plot: ...
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1answer
2k views

What is the exact difference between Prediction and Extrapolation?

Apologies if the question is too trivial but what exactly sets these two apart? Let's say that I have a set of data for a hundred points (the independent variable may not be uniformly spaced) as: <...
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1answer
5k views

Difference between non-linear curve fitting and interpolation

I understand the difference between linear curve fitting and interpolation. In interpolation, the targeted function should pass through all given data points whereas in linear curve fitting we find ...
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27 views

Interpolate from curve data

I have these curves, From this curve I can determine the life of a prop shaft due to gyroscopic forces at different yaw angles and certain speeds. I performed curve fitting on data points to get ...
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1answer
53 views

Should an interpolation coincide the original function on the given data points?

Suppose having a model $f(x)=y$ where $f$ is unkown. Moreover, suppose you have some data points for this model i.e. $(x_1,y_1), (x_2,y_2), \dots , (x_n,y_n)$. If one can find an approximate of $f $ ...