One way of revealing the nature of the coronal heating mechanism is by comparing simple theoretical one dimensional hydrostatic loop models with observations at the temperature and/or density structure along these features. The most well-known method
for dealing with comparisons like that is the $chi^2$ approach. In this paper we consider the restrictions imposed by this approach and present an alternative way for making model comparisons using Bayesian statistics. In order to quantify our beliefs we use Bayes factors and information criteria such as AIC and BIC. Three simulated datasets are analyzed in order to validate the procedure and assess the effects of varying error bar size. Another two datasets (Ugarte-Urra et al., 2005; Priest et al., 2000) are re-analyzed using the method described above. In one of these two datasets (Ugarte-Urra et al., 2005), due to the error estimates in the observed temperature values, it is not posible to distinguish between the different heating mechanisms. For this we suggest that both Classical and Bayesian statistics should be applied in order to make safe assumptions about the nature of the coronal heating mechanisms.
Determining the preferred spatial location of the energy input to solar coronal loops would be an important step forward towards a more complete understanding of the coronal heating problem. Following on from Sarkar & Walsh (2008) this paper presents
a short 10e9 cm global loop as 125 individual strands, where each strand is modelled independently by a one-dimensional hydrodynamic simulation. The strands undergo small-scale episodic heating and are coupled together through the frequency distribution of the total energy input to the loop which follows a power law distribution with index ~ 2.29. The spatial preference of the swarm of heating events from apex to footpoint is investigated. From a theoretical perspective, the resulting emission measure weighted temperature profiles along these two extreme cases does demonstrate a possible observable difference. Subsequently, the simulated output is folded through the TRACE instrument response functions and a re-derivation of the temperature using different filter-ratio techniques is performed. Given the multi-thermal scenario created by this many strand loop model, a broad differential emission measure results; the subsequent double and triple filter ratios are very similar to those obtained from observations. However, any potential observational signature to differentiate between apex and footpoint dominant heating is possibly below instrumental thresholds. The consequences of using a broadband instrument like TRACE and Hinode-XRT in this way are discussed.
