Deriving the probability of a linear opinion pooling method being superior to a set of alternatives

Aggregating predictions from experts: A review of statistical methods, experiments, and applications

“…Articles taking a Bayesian approach accounted for 25% of analysis‐set articles and emphasized how priors can complement sparse data (Abramson et al, 1996; Bolger & Houlding, 2017; Brito et al, 2012; Brito & Griffiths, 2016; Clemen & Winkler, 2007; Huang et al, 2016; Mantyka‐Pringle et al, 2014; Neves & Frangopol, 2008; Ren‐jun & Xian‐zhong, 2002; Tartakovsky, 2007; Wang & Zhang, 2018; Zio & Apostolakis, 1997). Many papers focused on assessing risk (Brito et al, 2012; Brito & Griffiths, 2016; Tartakovsky, 2007; Zio & Apostolakis, 1997).…”

“…For example, a predictive density would be built by asking each expert to provide values corresponding to the 5%, 50% (median), and 95% percentiles. Combination methods either directly combined these percentiles by assigning weights to each expert density (Bolger & Houlding, 2017; Brito & Griffiths, 2016; Cai et al, 2016; Hanea et al, 2018; Kabak & Ülengin, 2008; Morales‐Nápoles et al, 2017; Sarin, 2013; Zio & Apostolakis, 1997), or built a continuous predictive distribution that fit these discrete points (Abramson et al, 1996; Brito et al, 2012; Failing et al, 2004; Kurowicka et al, 2010; Neves & Frangopol, 2008; Wang et al, 2008).…”

“…Among all analysis‐set articles, 43% conducted a comparative experiment (Alho, 1992; Alvarado‐Valencia et al, 2017; Baecke et al, 2017; Baldwin, 2015; Bolger & Houlding, 2017; Cai et al, 2016; Craig et al, 2001; Franses, 2011; Graefe, 2015, 2018; Graefe, Armstrong, Jones Jr, & Cuzán, 2014a, 2014b; Hanea et al, 2018; Hora et al, 2013; Huang et al, 2016; Hurley & Lior, 2002; Jana et al, 2019; Mak et al, 1996; Morales‐Nápoles et al, 2017; Petrovic et al, 2006; Ren‐jun & Xian‐zhong, 2002; Satopää et al, 2014; Seifert & Hadida, 2013). We defined a comparative experiment as an evaluation of two or more models using a formal metric, like those found in Table 3.…”

“…Cooke's model also assigned experts a weight of 0 for poor predictive performance, and if an expert's performance was under some user‐set threshold they were excluded from the opinion pool. Cooke's model garnered much attention and has influenced numerous applications of combining expert opinion for forecasting (Bolger & Houlding, 2017; Brito et al, 2012; Clemen, 2008; Clemen & Winkler, 2007; Cooke, 2014, 2015; Cooke et al, 2014; Hanea et al, 2018; Hathout et al, 2016; Hora & Kardeş, 2015; Morales‐Nápoles et al, 2017; Sarin, 2013; Zio, 1996).…”

An ensemble of models for integrating dependent sources of information for the prognosis of the remaining useful life of Proton Exchange Membrane Fuel Cells

“…Various mathematical methods and approaches for combining probability distributions are discussed in [35]. Among them, in this work, we consider the Linear Opinion Pool (LOP), which is a common method for weighted linear combination of the experts probabilities [36,37,38] and it is easily understood and calculated:…”