# Tag Info

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### Splines vs Gaussian Process Regression

I agree with @j__'s answer. However, I would like to highlight the fact that splines are just a special case of Gaussian Process regression/kriging. If you take a certain type of kernel in Gaussian ...
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### How Does Kriging Interpolation work?

This answer consists of an introductory section I wrote recently for a paper describing a (modest) spatio-temporal extension of "Universal Kriging" (UK), which itself is a modest generalization of "...
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### Ordinary kriging example step by step?

Apart from this answer, there are also some nice additional answers to a similar question on gis.stackexchange.com First I'll describe ordinary kriging with three points mathematically. Assume we have ...

### Estimating probability of attack in Ukraine, given count data

This is not an answer, but rather a side comment: Keep in mind that the new attacks are not independent of the previous ones. Historical data is not necessarily relevant for the future. It is probably ...
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### Is a function describable by a Gaussian process smooth?

Not all choices of kernel function yield a smooth function. The exponential kernel $K(x_i, x_j) = \exp\left(-\gamma d(x_i, x_j)\right)$ for $\gamma > 0$ and $d$ a valid distance is the covariance ...

### Are Kriging's residuals (i.e. $Z-\hat{Z}$) spatially independent?

$$\newcommand{\E}{\mathbb{E}} \DeclareMathOperator{\cov}{Cov} \newcommand{\zhat}{\widehat{Z}}$$ I'll try and answer the title of your question, about spatial independence of the residuals. For ...

### Splines vs Gaussian Process Regression

It is a very interesting question: The equivalent between Gaussian processes and smoothing splines has been shown in Kimeldorf and Wahba 1970. The generalization of this correspondence in the case of ...

### Estimating probability of attack in Ukraine, given count data

Does anyone know what kind of model I would use for something like this? ... I was just wondering if anyone know some common approaches. Two approaches you may want to look into: "Self exciting ...
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### Gaussian process regression: leave-one-out prediction

In the general noisy or signal $+$ noise'' framework $y_i = f(\mathbf{x}_i) + \epsilon_i$, several observations can be done at the same location $\mathbf{x}_i$, so the notations $Y(\mathbf{x}_i)$ ...
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### what is the difference between Bayesian optimization and kriging?

I believe you mean Gaussian processes rather than Bayesian optimisation. Bayesian optimisation is the use of Gaussian processes for global optimisation. Essentially you use the mean and variance of ...