# Tagged Questions

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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### Is there a standard geometric way to apply cross over/mutation in a genetic algorithm

I am currently building a genetic algorithm to tune n parameters where n will probably be in the range of ...
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### 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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### 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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### 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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### 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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### How we can find trend of time series and turning points?

I want something like this in a time series: Currently I'm using some linear interpolation to find trend and turning points. What other methods can I use to find these turning points in a time ...
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### 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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### Nonstationarity of interpolated time series

I have a time series, which is monthly GDP of an economy. I had created it using Denton Cholette method of interpolation by using semi-annual data. The problem is that this series is nonstationary. ...
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### Polynomial curve fitting for temperature prediction

First of all, I would like to say that I know very little about statistics. I need to make a C# application to predict three days weather for school project and need some model and have been exploring ...
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### Interpolation of data points in R [duplicate]

How do i get this type of graphs like extrapolate or interpolate data points from x axis values and corresponding y axis values in R?Like as in below mentioned plot. Like when i mention point in Y ...
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### 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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### 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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### 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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### Interpolating data with errors (limited model knowledge)

I have data which I know follows a function $y = f(x)$ such that it is quadratic i.e. $y =\alpha x^2$ for some $\alpha$ when $x\rightarrow 0$ and $y = \beta x$ for large $x$. The data itself has ...
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### 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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### How to perform cross validation after bi-linear interpolation in R?

I am working with a dataset contains PM10 concentrations of 83 measurement stations of a certain hour. I want to perform ordinary kriging (OK), Inverse distance weighted interpolation (IDW) and Bi-...
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### 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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### How to use interpolation to calibrate object distance measurement based on pixels?

The current method used is triangle similarity to find the distance. A test image was used with known distance and known width. Then the area of the object in the image can be calculated. The "...
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### 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 $f$ ...
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### fractional desing and interpolation

Factorial design is an experimental design which help in determining the effects of the factors on the response. I would wonder whether there is a relation between factorial design (used for some ...
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### Difference between imputation and interpolation?

When dealing with data sets that have missing values, imputation replaces missing values with substituted values while interpolation replaces missing values with calculated values within some range. ...
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### Pearson correlation with missing values

I am trying to correlate dendrochronological data with climate data. The first one is acquired directly from trees, the second one from various stations from around the world. According to the formula ...
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### Instances where certain Interpolation Methods are suitable

When comparing interpolation methods such as Chebyshef Nodes, Splines, Kriging - are there instances (instances with fewer measurements, smaller space between measurements) where certain techniques ...
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### Using known and complete data to predict data part of which is know and the rest is unknown

It is a general problem. I have a training set(size > 1000). Each data point has 1000 features. What I want to do is to use these training data to complete a data point which has 600 known features ...
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### Basis for fitting a complete monotone

I have set of measured data: x=[x1,x2,....,xn] y=[y1,y2,....,yn] It is a multi component data. However I need to fit for only one component which is known to ...
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### Interpolation methods: splines, kriging, IDW (Inverse Distance Weighting)

In general, do any one of these methods tend to out perform the others? I have been reading a paper in which it mentions that kriging tends to out perform splines but splines would never outperform ...
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### Interpolating missing time-series data

I have time-series for creatinine levels in patients, which has missing samples, due to patients' irregular visits to doctors. The figure below represents the time-series for a patient. Task: I ...
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### Strictly increasing interpolation / spline

I have points in the x-y-plane that are strictly increasing most of the time. The problem is that there are cases with one or two outliers (Knots where an out-of-the-box spline would be decreasing). ...
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### can random forest project/interpolate based on new values of X?

Sometimes I want a model to predict what would happen when presented with values of predictor variables that it has not seen before. For example, say, I have predictor variables (X) that go from 1 ...
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### Is there a recursive version of Kriging or Inverse Distance spatial interpolation?

Classic use-case of Kriging: you have a 2d space, you have $n$ observations, each of them representing an exploratory dig. It has a $x$ and $y$ coordinate, and a $V$ representing the value discovered ...
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### How to interpolate for the normal distribution (or any other distribution)? [duplicate]

I have that X is normally distributed with mean 4 and variance 9 and I need to calculate the probability: Pr(X>9). So far, I have Pr(X>9)=Pr(Z>5/3)=1-Pr(Z<5/3). Now, the value for Pr(Z<5/3) ...
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### Weighted Minkowski RBF kernel

The radial basis function (RBF) kernel is given by $$K_{\text{RBF}}(\mathbf{x}, \mathbf{y})=\exp[-\gamma\|\mathbf{x}-\mathbf{y}\|^2_2]$$ where $\|\mathbf{x}-\mathbf{y}\|^2_2$ is the squared ...
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### Help understanding a kriging variation for bare earth extraction

Problem: The authors of a paper (http://www.isprs.org/proceedings/XXXIV/part3/papers/paper106.pdf) develop a bare earth extraction algorithm for LiDAR that is based on kriging. What I don't ...
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### “R” computing derivative of multivariate spline

I am trying to compute the derivative of a multivariate spline, in fact bi-variate I use a b-spline univariate to create a basis, for the first x1 and second variable x2, then I use the tensor product ...
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### Inversely proportional version of a nearest-neighbour results vector - how?

Short version: Given an input vector D of n values, what are the different methods that one can use to return a vector W such that each value in W is in inverse proportion to the magnitudes of the ...
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### Interpolating population data

I'm currently doing an internship where I have to calculate incidence ratios for townships for a period of 11 years. I don't have access to the population data for all years and I would like to do ...
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### What is the correct way to interpolate error?

If I have a 2-D data, say $y = f(x)$, with error in the dependent variable, $\delta y$ in this case, and I want to interpolate this data set to a coarser independent variable grid, $x$, what is the ...
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### gaussian process - missing data

One approach to deal with missing data is be to define a joint gaussian distribution / Gaussian process, and then define the (conditional) distribution of the unknown values on the known values. (e.g. ...
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### Cubic splines for interpolation through four points in R

I am attempting to write R code for cubic splines to connect points on a graph. Specifically, I am attempting to reproduce Figure 3.3 of Wood (2006) ...
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### How can we use genetic algorithm for curve fitting?

I want to use genetic algorithm in order to fit a curve to some data, or in other words, to estimate some equation that describes the relationship. Suppose that I select the equation to be a ...
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### Interpolation model to estimate missing analytics

We have about 7 months of partially (30%) missing web analytics, that is apparently missing at random across all segmentations. We need to estimate the missing data to correctly compare current and ...
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### 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 ...
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### Interpreting margins of dummy variables [duplicate]

I have estimated an ordinal probit model in Stata. The dependent variable is walkability. The main independent variables are on a Likert scale (1=agree, 2=partially agree, 3=disagree). The other ...
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### Which interpolation technique should I use?

I have an annual data set, but I have a few missing values in the series. I do not know which interpolation technique should I use to fill the missing values. ...
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### 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 ...
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### What issues may I face when interpolating my dependent variable in an OLS regression?

I'm doing my undergrad dissertation on what host-country factors impact FDI inflows - FDI inflows to the UK is my dependent variable. All of the independent variables I have managed to find at a ...
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### creating polynomials using sets of data to represent a correlation

I need some guidance in creating a polynomial function that represents sets of data and its correlation, if that makes any sense. I know there Lagrange interpolation, least squares etc. I don't know ...
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### Partition of function into pieces for interpolation needs

I've got some experimental data obtained from my mate's research. There are two sets of (x,y) points for each curve. He asked me to interpolate function values between these points, so for each curve ...