Bayesian Hierarchical Growth Model for Experimental Data on the Effectiveness of an Incentive-Based Weight Reduction Method

The objective of this current research is to model the experimental data on the effectiveness of an incentive-based weight reduction method by using Bayesian hierarchical growth models. Three Bayesian hierarchical growth models are proposed, namely parametric Bayesian hierarchical growth model with correlated intercept and slope random effects model, parametric Bayesian hierarchical growth model with no correlated intercept and slope random effects model and semi-parametric Bayesian hierarchical growth model with Dirichlet process mixture prior model. The data is obtained from forty eight (48) students who had participated in an experiment on weight reduction method. The students were divided equally into two groups: single and pair groups. The experiment was carried out over the period of three months with a weight reading session for every two weeks. At the end of the study, we had six repeated measures of each student’s weight in kg and some measures of covariates and factors. Our results showed that the best model for the above data based on the Bayesian fit indexes and the models’ flexibility is the semi-parametric Bayesian hierarchical growth model with Dirichlet process mixture prior model. The results of the semi-parametric model showed that the ‘growth’ or reduction rates of the weight reduction experiment relate to the students’ gender, height in cm, experimental group (single or pair) and time in term of weeks.

INO: Interplanetary network of optical lattice clocks

The new technique of measuring frequency by optical lattice clocks now approaches to the relative precision of [Formula: see text]. We propose to place such precise clocks in space and to use Doppler tracking method for detecting low-frequency gravitational wave below 1[Formula: see text]Hz. Our idea is to locate three spacecrafts at one A.U. distance (say at L1, L4 and L5 of the Sun–Earth orbit), and apply the Doppler tracking method by communicating “the time” each other. Applying the current available technologies, we obtain the sensitivity for gravitational wave with third- or fourth-order improvement ([Formula: see text] or [Formula: see text] level in [Formula: see text]–[Formula: see text][Formula: see text]Hz) than that of Cassini spacecraft in 2001. This sensitivity enables us to observe black hole (BH) mergers of their mass greater than [Formula: see text] in the cosmological scale. Based on the hierarchical growth model of BHs in galaxies, we estimate the event rate of detection will be 20–50 a year. We nickname “INO” (Interplanetary Network of Optical Lattice Clocks) for this system, named after Tadataka Ino (1745–1818), a Japanese astronomer, cartographer, and geodesist.