Hierarchical Bayesian of ARMA Models Using Simulated Annealing Algorithm

When the Autoregressive Moving Average (ARMA) model is fitted with real data, the actual value of the model order and the model parameter are often unknown. The goal of this paper is to find an estimator for the model order and the model parameter based on the data. In this paper, the model order identification and model parameter estimation is given in a hierarchical Bayesian framework. In this framework, the model order and model parameter are assumed to have prior distribution, which summarizes all the information available about the process. All the information about the characteristics of the model order and the model parameter are expressed in the posterior distribution. Probability determination of the model order and the model parameter requires the integration of the posterior distribution resulting. It is an operation which is very difficult to be solved analytically. Here the Simuated Annealing Reversible Jump Markov Chain Monte Carlo (MCMC) algorithm was developed to compute the required integration over the posterior distribution simulation. Methods developed are evaluated in simulation studies in a number of set of synthetic data and real data

Planet Hunters TESS. V. A Planetary System Around a Binary Star, Including a Mini-Neptune in the Habitable Zone

We report on the discovery and validation of a transiting long-period mini-Neptune orbiting a bright (V = 9.0 mag) G dwarf (TOI 4633; R = 1.05 R ⊙, M = 1.10 M ⊙). The planet was identified in data from the Transiting Exoplanet Survey Satellite by citizen scientists taking part in the Planet Hunters TESS project. Modelling of the transit events yields an orbital period of 271.9445 ± 0.0040 days and radius of 3.2 ± 0.20 R ⊕. The Earth-like orbital period and an incident flux of 1.56−0.16+0.20 F ⊕ places it in the optimistic habitable zone around the star. Doppler spectroscopy of the system allowed us to place an upper mass limit on the transiting planet and revealed a non-transiting planet candidate in the system with a period of 34.15 ± 0.15 days. Furthermore, the combination of archival data dating back to 1905 with new high angular resolution imaging revealed a stellar companion orbiting the primary star with an orbital period of around 230 yr and an eccentricity of about 0.9. The long period of the transiting planet, combined with the high eccentricity and close approach of the companion star makes this a valuable system for testing the formation and stability of planets in binary systems