Choosing Prior Hyperparameters: With Applications to Time-Varying Parameter Models

Abstract

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On the Time‐Varying Effects of Economic Policy Uncertainty on the US Economy

“…As a further robustness check and in order to highlight the relevance of estimating the hyperparameters by using the approach of Amir‐Ahmadi et al . (), we compare the IRFs from our baseline model with the ones obtained by using the fixed values in Primiceri (). Figure A.4 displays the impulse responses based on the benchmark values.…”

“…Therefore, we estimate the hyperparameters and jointly with all other model parameters using a fully Bayesian approach as proposed by Amir‐Ahmadi et al . (). This approach estimates the hyperparameters in a data‐based fashion and takes the surrounding uncertainty into account.…”

“…The approach of Amir‐Ahmadi et al . () exploits the finding that only the prior of X , X ∈ { Q , S , W }, depends on , and that, conditional on X , all other model densities are independent from . Thus, the conditional posterior iswhere denotes the prior of X and the prior of , and can be obtained by a Metropolis‐within‐Gibbs step, as all other model densities cancel out in the acceptance probability .…”

“…Moreover, previous applications do not take into account that estimation uncertainty about these hyperparameters may influence inference. We therefore estimate these hyperparameters using a fully Bayesian approach proposed by Amir‐Ahmadi, Matthes and Wang (). We find that estimating the hyperparameters is important since using the benchmark values of Primiceri () would suppress some amount of time variation.…”

Modeling Augmented Humanity

“…In supervised metamodeling, hyperparameters are fully determined by prior experience and learning (e.g., Amir-Ahmadi et al, 2018), whereas in semi-supervised systems, the initial hyperparameters are partially given, but provisional. Additional processing is required to tune and optimize them.…”