The hot intra-cluster medium (ICM) surrounding the heart of galaxy clusters is a complex medium comprised of various emitting components. Although previous studies of nearby galaxy clusters, such as the Perseus, the Coma, or the Virgo cluster, have d
emonstrated the need for multiple thermal components when spectroscopically fitting the ICMs X-ray emission, no systematic methodology for calculating the number of underlying components currently exists. In turn, underestimating or overestimating the number of components can cause systematic errors in the emission parameter estimations. In this paper, we present a novel approach to determining the number of components using an amalgam of machine learning techniques. Synthetic spectra containing a various number of underlying thermal components were created using well-established tools available from the textit{Chandra} X-ray Observatory. The dimensions of the training set was initially reduced using the Principal Component Analysis and then categorized based on the number of underlying components using a Random Forest Classifier. Our trained and tested algorithm was subsequently applied to textit{Chandra} X-ray observations of the Perseus cluster. Our results demonstrate that machine learning techniques can efficiently and reliably estimate the number of underlying thermal components in the spectra of galaxy clusters, regardless of the thermal model (MEKAL versus APEC). %and signal-to-noise ratio used. We also confirm that the core of the Perseus cluster contains a mix of differing underlying thermal components. We emphasize that although this methodology was trained and applied on textit{Chandra} X-ray observations, it is readily portable to other current (e.g. XMM-Newton, eROSITA) and upcoming (e.g. Athena, Lynx, XRISM) X-ray telescopes. The code is publicly available at url{https://github.com/XtraAstronomy/Pumpkin}.
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related and which ar
e due to the neural network. This means that predictions by neural networks have biases which cannot be trivially distinguished from being due to the true nature of the creation and observation of data or not. In order to attempt to address such issues we discuss Bayesian neural networks: neural networks where the uncertainty due to the network can be characterised. In particular, we present the Bayesian statistical framework which allows us to categorise uncertainty in terms of the ingrained randomness of observing certain data and the uncertainty from our lack of knowledge about how data can be created and observed. In presenting such techniques we show how errors in prediction by neural networks can be obtained in principle, and provide the two favoured methods for characterising these errors. We will also describe how both of these methods have substantial pitfalls when put into practice, highlighting the need for other statistical techniques to truly be able to do inference when using neural networks.
