Bayesian Data Analysis

In the citing paper

“The inverse-gamma(α, β) model for σ 2 α can also be expressed as an inverse-χ 2 distribution with scale s 2 α = β/α and degrees of freedom ν α = 2α (Gelman et al., 2003).”

In the citing paper

“With J = 1 or 2 groups, this actually results in an improper posterior density, essentially concluding σ α = ∞ and doing no shrinkage (see Gelman et al., 2003, Exercise 5.8).”

In the citing paper

“Their capacity to handle uncertainty, incorporate prior knowledge, and update beliefs based on evidence makes them effective for modeling complex systems (Gelman et al. 1995; MacKay 2003).”

In the citing paper

“We adopt Bayesian statistics for its advantages in being able to hypothesize null effects[27,73].”

In the citing paper

“To improve the efficiency of this procedure, I use a Hamiltonian Monte Carlo algorithm (Gelman et al. 2013) and employ a hierarchical setup that considers each of the four sets of parameters as draws from four common population distributions:”

In the citing paper

“Because this model is a Bayesian extension of a conventional MFRM, its parameter estimates approach those of a non-Bayesian conventional MFRM when we have a large amount of data, which is a desirable property.”

In the citing paper

“The parameter estimates of a Bayesian model are known to approach those of its non-Bayesian counterpart as the amount of data increases. This is because the influence of the prior distribution decreases (Gelman et al., 2013).”

In the citing paper

“The use of model families is also accomodated naturally within the framework of hierarchical Bayesian models [1] and is proposed to address the well known issue of model dilution [4].”

In the citing paper

“The hierarchical Bayesian approach is an intermediate method compared to the completely pooled model and individualized model, capturing the whole population’s characteristics while allowing individual differences [43].”