  Microcanonical thermostatistics analysis has become an important tool to
reveal essential aspects of phase transitions in complex systems. An efficient
way to estimate the microcanonical inverse temperature $\beta(E)$ and the
microcanonical entropy $S(E)$ is achieved with the statistical temperature
weighted histogram analysis method (ST-WHAM). The strength of this method lies
on its flexibility, as it can be used to analyse data produced by algorithms
with generalised sampling weights. However, for any sampling weight, ST-WHAM
requires the calculation of derivatives of energy histograms $H(E)$, which
leads to non-trivial and tedious binning tasks for models with continuous
energy spectrum such as those for biomolecular and colloidal systems. Here, we
discuss two alternative methods that avoid the need for such energy binning to
obtain continuous estimates for $H(E)$ in order to evaluate $\beta(E)$ by using
ST-WHAM: (i) a series expansion to estimate probability densities from the
empirical cumulative distribution function (CDF), and (ii) a Bayesian approach
to model this CDF. Comparison with a simple linear regression method is also
carried out. The performance of these approaches is evaluated considering
coarse-grained protein models for folding and peptide aggregation.
