# Gaussian Processes for Blazar Variability Studies

## Abstract

**:**

## 1. Introduction

## 2. Non-Parametric Models and Gaussian Processes

#### 2.1. Gaussian Processes for Regression

#### 2.2. Training the Gaussian Process

**θ**is $p\left(\mathit{y}\phantom{\rule{0.166667em}{0ex}}\right|\phantom{\rule{0.166667em}{0ex}}\mathit{x},\mathit{\theta})$. The log marginal likelihood is given by

## 3. Application to the Light Curves of the Blazar PKS 1502+106

## 4. Results and Discussion

#### 4.1. Quantifying the Broadband Outburst of PKS 1502+106

#### 4.2. Where Do the γ Rays Come from?

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Gaussian process (GP) prior and posterior distributions: (

**a**) Twenty randomly selected samples from the prior distribution, with zero mean and $\sigma =1$, using a squared exponential covariance kernel; (

**b**) Regression results after training the GP with three error-free data points; (

**c**) Same as in panel (b), but note the improved result with the addition of one more data point.

**Figure 2.**Multi-wavelength light curves of PKS 1502+106. (

**Left**) F-GAMMA light curves between 2.64 and 142.33 GHz; (

**Right**) GP regression curves for the data at 4.85, 14.6, 23.05, and 86.24 GHz. For the results at all frequencies, see Ref. [18].

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Karamanavis, V. Gaussian Processes for Blazar Variability Studies. *Galaxies* **2017**, *5*, 19.
https://doi.org/10.3390/galaxies5010019

**AMA Style**

Karamanavis V. Gaussian Processes for Blazar Variability Studies. *Galaxies*. 2017; 5(1):19.
https://doi.org/10.3390/galaxies5010019

**Chicago/Turabian Style**

Karamanavis, Vassilis. 2017. "Gaussian Processes for Blazar Variability Studies" *Galaxies* 5, no. 1: 19.
https://doi.org/10.3390/galaxies5010019