Log-Linear Pool to Combine Prior Distributions: A Suggestion for a Calibration-Based Approach

Rufo, M. J.; Jd, Martín; Pérez, Carlos J.

doi:10.1214/12-ba714

Cited by 26 publications

(18 citation statements)

References 33 publications

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“…Linear and logarithmic opinion pools are two well-known models which can be used to form weighted votes [36], [37]. All previously reported locally weighted voting approaches use the linear opinion pool to integrate reliability weights in the fusion process.…”

Section: Introductionmentioning

confidence: 99%

A Logarithmic Opinion Pool Based STAPLE Algorithm for the Fusion of Segmentations With Associated Reliability Weights

Akhondi-Asl

Hoyte

Lockhart

et al. 2014

IEEE Trans. Med. Imaging

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Pelvic floor dysfunction is very common in women after childbirth and precise segmentation of magnetic resonance images (MRI) of the pelvic floor may facilitate diagnosis and treatment of patients. However, because of the complexity of the structures of pelvic floor, manual segmentation of the pelvic floor is challenging and suffers from high inter and intra-rater variability of expert raters. Multiple template fusion algorithms are promising techniques for segmentation of MRI in these types of applications, but these algorithms have been limited by imperfections in the alignment of each template to the target, and by template segmentation errors. In this class of segmentation techniques, a collection of templates is aligned to a target, and a new segmentation of the target is inferred. A number of algorithms sought to improve segmentation performance by combining image intensities and template labels as two independent sources of information, carrying out decision fusion through local intensity weighted voting schemes. This class of approach is a form of linear opinion pooling, and achieves unsatisfactory performance for this application. We hypothesized that better decision fusion could be achieved by assessing the contribution of each template in comparison to a reference standard segmentation of the target image and developed a novel segmentation algorithm to enable automatic segmentation of MRI of the female pelvic floor. The algorithm achieves high performance by estimating and compensating for both imperfect registration of the templates to the target image and template segmentation inaccuracies. The algorithm is a generalization of the STAPLE algorithm in which a reference segmentation is estimated and used to infer an optimal weighting for fusion of templates. A local image similarity measure is used to infer a local reliability weight, which contributes to the fusion through a novel logarithmic opinion pooling. We evaluated our new algorithm in comparison to nine state-of-the-art segmentation methods by comparison to a reference standard derived from repeated manual segmentations of each subject image and demonstrate our algorithm achieves the highest performance. This automated segmentation algorithm is expected to enable widespread evaluation of the female pelvic floor for diagnosis and prognosis in the future.

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Section: Introductionmentioning

confidence: 99%

A Logarithmic Opinion Pool Based STAPLE Algorithm for the Fusion of Segmentations With Associated Reliability Weights

Akhondi-Asl

Hoyte

Lockhart

et al. 2014

IEEE Trans. Med. Imaging

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“…In [39] the authors show that learning in social networks with complex neighborhood structures can be achieved if agents choose a neighbor randomly at every round and restrict their belief update to the selected neighbor each time (essentially replicating the case of a directed circle where every neighborhood is a singlton). Geometric averaging and logarithmic opinion pools have a long history in Bayesian analysis and behavioral decision models [40], [41] and they can be also justified under specific behavioral assumptions [42]. The are also quite popular as a non-Bayesian update rule in distributed detection and estimation litrature [43], [44], [10], [14], [45].…”

Section: Discussionmentioning

confidence: 99%

Distributed estimation and learning over heterogeneous networks

Rahimian

Jadbabaie

2016

2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-We consider several estimation and learning problems that networked agents face when making decisions given their uncertainty about an unknown variable. Our methods are designed to efficiently deal with heterogeneity in both size and quality of the observed data, as well as heterogeneity over time (intermittence). The goal of the studied aggregation schemes is to efficiently combine the observed data that is spread over time and across several network nodes, accounting for all the network heterogeneities. Moreover, we require no form of coordination beyond the local neighborhood of every network agent or sensor node. The three problems that we consider are (i) maximum likelihood estimation of the unknown given initial data sets, (ii) learning the true model parameter from streams of data that the agents receive intermittently over time, and (iii) minimum variance estimation of a complete sufficient statistic from several data points that the networked agents collect over time. In each case, we rely on an aggregation scheme to combine the observations of all agents; moreover, when the agents receive streams of data over time, we modify the update rules to accommodate the most recent observations. In every case, we demonstrate the efficiency of our algorithms by proving convergence to the globally efficient estimators given the observations of all agents. We supplement these results by investigating the rate of convergence and providing finite-time performance guarantees.

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“…Alternatively, they could represent an estimate of expected accuracy, determined using seed questions (discussed in Conclusion), prior assessments of the expert's background 82,110,111 or agreement of the expert's elicited data with subsequently observed data on the quantity of interest, 111 although observed data would not generally be available in a health-care context. More technically advanced methods that use only the elicited data to form weights are presented by Ranjan and Gneiting, 112 Rufo et al 113 and Hora and Kardeş. 114 Essentially, these adjust the simple linear or log-pools to give a better expected balance of overall bias and over/underconfidence.…”

Section: Mathematical Aggregationmentioning

confidence: 99%

Developing a reference protocol for structured expert elicitation in health-care decision-making: a mixed-methods study

Bojke

Soares

Claxton

et al. 2021

Health Technol Assess

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Background Many decisions in health care aim to maximise health, requiring judgements about interventions that may have higher health effects but potentially incur additional costs (cost-effectiveness framework). The evidence used to establish cost-effectiveness is typically uncertain and it is important that this uncertainty is characterised. In situations in which evidence is uncertain, the experience of experts is essential. The process by which the beliefs of experts can be formally collected in a quantitative manner is structured expert elicitation. There is heterogeneity in the existing methodology used in health-care decision-making. A number of guidelines are available for structured expert elicitation; however, it is not clear if any of these are appropriate for health-care decision-making. Objectives The overall aim was to establish a protocol for structured expert elicitation to inform health-care decision-making. The objectives are to (1) provide clarity on methods for collecting and using experts’ judgements, (2) consider when alternative methodology may be required in particular contexts, (3) establish preferred approaches for elicitation on a range of parameters, (4) determine which elicitation methods allow experts to express uncertainty and (5) determine the usefulness of the reference protocol developed. Methods A mixed-methods approach was used: systemic review, targeted searches, experimental work and narrative synthesis. A review of the existing guidelines for structured expert elicitation was conducted. This identified the approaches used in existing guidelines (the ‘choices’) and determined if dominant approaches exist. Targeted review searches were conducted for selection of experts, level of elicitation, fitting and aggregation, assessing accuracy of judgements and heuristics and biases. To sift through the available choices, a set of principles that underpin the use of structured expert elicitation in health-care decision-making was defined using evidence generated from the targeted searches, quantities to elicit experimental evidence and consideration of constraints in health-care decision-making. These principles, including fitness for purpose and reflecting individual expert uncertainty, were applied to the set of choices to establish a reference protocol. An applied evaluation of the developed reference protocol was also undertaken. Results For many elements of structured expert elicitation, there was a lack of consistency across the existing guidelines. In almost all choices, there was a lack of empirical evidence supporting recommendations, and in some circumstances the principles are unable to provide sufficient justification for discounting particular choices. It is possible to define reference methods for health technology assessment. These include a focus on gathering experts with substantive skills, eliciting observable quantities and individual elicitation of beliefs. Additional considerations are required for decision-makers outside health technology assessment, for example at a local level, or for early technologies. Access to experts may be limited and in some circumstances group discussion may be needed to generate a distribution. Limitations The major limitation of the work conducted here lies not in the methods employed in the current work but in the evidence available from the wider literature relating to how appropriate particular methodological choices are. Conclusions The reference protocol is flexible in many choices. This may be a useful characteristic, as it is possible to apply this reference protocol across different settings. Further applied studies, which use the choices specified in this reference protocol, are required. Funding This project was funded by the NIHR Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 25, No. 37. See the NIHR Journals Library website for further project information. This work was also funded by the Medical Research Council (reference MR/N028511/1).

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Log-Linear Pool to Combine Prior Distributions: A Suggestion for a Calibration-Based Approach

Cited by 26 publications

References 33 publications

A Logarithmic Opinion Pool Based STAPLE Algorithm for the Fusion of Segmentations With Associated Reliability Weights

A Logarithmic Opinion Pool Based STAPLE Algorithm for the Fusion of Segmentations With Associated Reliability Weights

Distributed estimation and learning over heterogeneous networks

Developing a reference protocol for structured expert elicitation in health-care decision-making: a mixed-methods study

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