Prior knowledge elicitation: The past, present, and future

Abstract

Specification of the prior distribution for a Bayesian model is a central part of the Bayesian workflow for data analysis, but it is often difficult even for statistical experts. Prior elicitation transforms domain knowledge of various kinds into well-defined prior distributions, and offers a solution to the prior specification problem, in principle. In practice, however, we are still fairly far from having usable prior elicitation tools that could significantly influence the way we build probabilistic models in academia and industry. We lack elicitation methods that integrate well into the Bayesian workflow and perform elicitation efficiently in terms of costs of time and effort. We even lack a comprehensive theoretical framework for understanding different facets of the prior elicitation problem.Why are we not widely using prior elicitation? We analyze the state of the art by identifying a range of key aspects of prior knowledge elicitation, from properties of the modelling task and the nature of the priors to the form of interaction with the expert. The existing prior elicitation literature is reviewed and categorized in these terms. This allows recognizing under-studied directions in prior elicitation research, finally leading to a proposal of several new avenues to improve prior elicitation methodology.

A Subjective Bayesian Framework for Synthesizing Deep Uncertainties in Climate Risk Management

“…A related concern is that we developed our three distributions for p belief (Ψ) in an ad hoc fashion that may not represent well-calibrated beliefs. Although this is appropriate for our didactic illustration, recent advances in Bayesian elicitation of expert opinion (see Mikkola et al, 2021, and references therein) can be applied to improve decision making in real world case studies. More fundamentally, our method assumes that there exists an expert capable of integrating over the many processes that drive SLR, from global greenhouse gas emissions to the global carbon cycle to climate sensitivity and ice sheet response (Morgan, 2014).…”

Digital twinning of self-sensing structures using the statistical finite element method

“…The random loading r x ð Þ is applied in addition to the deterministic point forces of 52 kN per wheel. The choice of the two parameters σ r and ℓ r requires input from domain experts, that is, bridge engineers, and may be formalized with prior elicitation techniques from statistics, see the recent review Mikkola et al (2021). Alternatively, σ r and ℓ r can be interpreted as hyperparameters and inferred from the observed data (Kennedy and O'Hagan, 2001;Nagel and Sudret, 2016).…”

On the safe use of prior densities for Bayesian model selection

“…The literature has plenty of works devoted to the specification and classification of different priors. The interested readers can find gentle reviews in, for example, Consonni et al (2018), Wasserman (1996), andMikkola et al (2021). Here, we provide a brief summary of concepts related to the choice of the priors g θjM ð Þ over the parameters, and how this choice can affect the analysis in the two levels of inference that we have described above.…”

“…Prior elicitation ideas can be used to transform such knowledge into a prior density. See (Mikkola et al, 2021) for a review on different approaches for prior elicitation. • Priors as regularizers.…”

“…Uninformative priors. Generally, a prior is defined as uninformative, if it has been chosen in order to have a minimal impact on the posterior density (Mikkola et al, 2021). In this sense, for the inference problem of parameter estimation (Level-1), a uniform prior over all the support Θ is the maximal expression of uninformative prior.…”