This has formally defined operational risk and introduced corresponding capital requirements. Many banks are undertaking quantitative modelling of operational risk using the Loss Distribution Approach LDA based on statistical quantification of the frequency and severity of operational risk losses. There are a number of unresolved methodological challenges in the LDA implementation. Overall, the area of quantitative operational risk is very new and different methods are under hot debate. Post a new comment Error Anonymous comments are disabled in this journal. We will log you in after post We will log you in after post We will log you in after post We will log you in after post We will log you in after post Anonymously.

Post a new comment. Preview comment. Post a new comment 0 comments. We interpret these probabilities as success rates in an infinite population of patients, undergoing the same treatment. These probabilities parameters are unknown and prior distributions are established describing the assessor's uncertainties before observations. When data become available, these distributions are updated by the standard Bayes updating procedure to give the posterior distributions for the parameters.

Probability models are introduced to carry out this updating procedure. Best estimates of the probabilities are provided, using the mean of the posterior distributions. Similar analyses are performed for the complication rates. The risk analyses are carried out according to the approach outlined in the previous section.

Expert judgments are included, to incorporate all relevant information about the treatments as well as the patient. The reported results are summarised below:. Consider patients at the hospital H, and let D be the proportion of successful treatments. General risk influencing factors, i. A discussion of these factors and possible others that could cause unsuccessful results is carried out.

The above risk picture provides the basis for the patient's decision. Using the new treatment the expressed risk is lower, when we look at the probability of successful treatment.

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This new treatment also has the potential of giving the patient full recovery. However, the experience basis for this treatment is also lower. This creates some uncertainty, which has to be balanced against the lower computed risk numbers. Summary of main features of the traditional text-book Bayesian approach and the predictive Bayesian approach. The differences are demonstrated by the above example. For this example, we consider the predictive approach to produce the most informative risk picture, as it is the patient perspective that is of concern.

It may be responded that it is also possible to produce predictive distributions in the traditional text-book Bayesian approach by taking the expectations of the p i s. Yes, that is true. However, such a distribution includes the assessor's uncertainties of the p i s. Why should we incorporate this uncertainty when our ambition is to assess uncertainties about successful treatment of patient L. We have to be careful in defining what are relevant populations.

If we shift to the hospital or national level, would we conclude in the same way? Yes, the key quantity of interest is:. D: the proportion of successful treatments among those to be carried out the coming years. By introducing such a probability, we introduce a limiting quantity, a fictional element, which leads to the wrong focus, accurate estimation of p instead of D. According to the Bayesian perspective, probability is a subjective measure of uncertainty [ 20 ] Lindley Probabilities are used to express uncertainties about unknown quantities.

However, we have to acknowledge that uncertainties about observables cannot be adequately described and evaluated simply by reference to summarising probabilities. There is a need for seeing beyond these values. Computed probabilities are subjective assignments conditioned on the background information including assumptions and suppositions. The probabilities are not objective values. The analysis could produce poor predictions. The risk picture has to include aspects related to uncertainties in phenomena and processes. Surprises may occur and by just addressing probabilities such surprises may be overlooked.

We are of course not able to predict all surprises — if that had been the case, they would not have been surprises. The risk perspective should be broad enough to allow the uncertainties and possible surprises to be an important part of the overall risk picture. A search procedure needs to be established to identify the uncertainty factors. Such a procedure can be based on an initial analysis addressing historical records and expert judgments. The risk influencing factors mentioned above also indicate areas that may be of concern. Such could be reflected in the background information of the assigned probabilities, or calculation procedures could be developed which more explicitly take them into account, see e.

Furthermore, the assumptions and suppositions of the probability assignments provide an additional checklist. We would also like to draw attention to the list of special consequence features presented by [ 21 ] Renn and Klinke see also [ 22 ] Kristensen et. Examples of such features are:. This feature classification system can be used as a checklist for ensuring the right focus of the analysis, i.

But it can also be used as a checklist for identifying relevant uncertainty factors. For example, the feature "delay effects" could lead to a focus on activities or mechanisms that could initiate deteriorating processes causing future surprises. Addressing the uncertainties also mean to consider the manageability ; i. Some risks are more manageable than others, meaning that the potential for reducing the risk is larger for some risks compared to others. By proper uncertainty management, we seek to obtain desirable consequences. Expressing risk, also means to perform sensitivity analyses.

## [Doc] Modelling Operational Risk Using Bayesian Inference Free Online

The purpose of these analyses is to show how sensitive the output risk indices are with respect to changes in basic input quantities, for example assumptions and suppositions. Risk is described by addressing such issues along with the probabilities. It gives in our view a sound basis for risk analysis in general and for the health care in particular. Such a broad perspective on risk is in line with the following definition of risk:. Risk related to an activity is defined by the combination of the possible consequences of the activity and associated uncertainties [ 23 ] Aven and Kristensen Subjective probabilities are used to assess the uncertainties.

Risk analyses are tools providing insights about risks. But they are just tools — they have limitations. Their results are conditioned on a number of assumptions and suppositions. The analyses are not expressing objective results. We should not put more emphasis on the predictions and assessments of the analyses than what can be justified by the methods being used. Nonetheless, risk analyses could be useful as a decision supporting tool in situations with large uncertainties. They summarize the knowledge and lack of knowledge concerning critical operations and other activities, and give in this way a basis for making rational decisions.

To ensure high quality risk analyses we believe that the following points, among others, should be highlighted [ 24 ] Aven Adopting the predictive Bayesian approach is no guarantee for meeting all these requirements. However, it provides a framework for ensuring quality of the analyses along these lines. Risk analyses of health operations, such as PRAs, must in our view be based on the use of subjective probabilities. The probabilistic analyses need to be based on modelling and use of expert judgments, and the probabilities should express uncertainties in events and other real quantities, given the available information.

The essential points of the analyses are identification of observable quantities, prediction and uncertainty assessments of these quantities, using all the relevant information. Bayesian updating procedures are of less importance, as seen from the examples above. The Bayesian updating procedure may be used for incorporating new information, but its applicability is in many cases rather limited.

In practice we will often not perform a formal Bayesian updating to incorporate new observations — rethinking of the whole information basis and approach to modelling is required when we conduct the analysis at a particular point in time. Of course, there are situations where such procedures provide a useful basis of the analysis. As an example, consider an operation where we are concerned about a quantity U expressing the health condition of the patient. The quantity U is unknown and continuous measurements V 1 , V 2 , Then starting from a prior distribution of U , we establish a posterior distribution of U using the measurements V 1 , V 2 , We then need a distribution of V given U , reflecting the accuracy of the measurements.

Such a procedure is consistent with the predictive Bayesian approach as all quantities introduced are observables. For a successful implementation of risk analysis in health care, we need an assignment process which is simple, that works in practice for the number of probabilities and probability distributions to be determined. We should not introduce distribution classes with unknown parameters when not required. Furthermore, meaningful interpretations must be given to the distributions classes and the parameters whenever they are used.

There is no point in speaking about uncertainty of parameters unless they are observables, i. The authors have contributed equally to this work. Both authors have read and approved the final manuscript. The authors are grateful to the reviewers for useful comments and suggestions to an earlier version of the paper. The research was supported by Helse Vest. National Center for Biotechnology Information , U. Published online Aug Terje Aven 1 and Karianne Eidesen 1.

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## Modelling Operational Risk Using Bayesian Inference (Repost)

Corresponding author. Terje Aven: on. Received Jan 31; Accepted Aug This article has been cited by other articles in PMC. Abstract Background The Bayesian approach is now widely recognised as a proper framework for analysing risk in health care. Methods The essential points of the risk analyses conducted according to the predictive Bayesian approach are identification of observable quantities, prediction and uncertainty assessments of these quantities, using all the relevant information. Results It is shown that Bayesian risk analysis can be significantly simplified and made more accessible compared to the traditional text-book Bayesian approach by focusing on predictions of observable quantities and performing uncertainty assessments of these quantities using subjective probabilities.

Conclusion The predictive Bayesian approach provides a framework for ensuring quality of risk analysis. Background To analyse risk in health care, the Bayesian approach is widely acknowledged as a proper framework, see e. This approach to risk analysis has in our view three main weaknesses: 1. Focus is on fictional parameters which are difficult to understand. The analysis is too complex to be implemented in practice. To cite [ 7 ] Marx and Slonim , "Healthcare is in many ways different from other industries.

Methods The predictive Bayesian approach.

A simple PRA health care application In the predictive Bayesian approach there are no fictional parameters introduced, and no reference to true probabilities. Open in a separate window. Figure 1. Results Comparison of the predictive Bayesian approach and the traditional text-book Bayesian approach Consider a patient L suffering from a specific disease and faced with the following treatment options: Treatment A.

Traditional text-book Bayesian analysis Let p 1 denote the probability that treatment A results in success for an arbitrary patient. The reported results are summarised below: Consider patients at the hospital H, and let D be the proportion of successful treatments. Traditional text-book Bayesian approach Predictive Bayesian approach Theoretical perspective Application oriented perspective Theoretical perspective Application oriented perspective Focus on fictional parameters Average patient performance Focus on observable quantities Performance of the individual or group considered Prior and posterior distributions The experts' uncertainties about the unknown parameters Prior and posterior distributions The experts' uncertainties about the observable quantities There exists underlying true probabilities Probabilities and risks are unknown and need to be estimated Probability is a subjective measure of uncertainty, conditional on the assessor's background information Probability is assigned by the assessor Model uncertainty exists Model uncertainty needs to be covered by the analysis Model uncertainty does not exist.

The accuracy of the models needs to be addressed. Competing interests The author s declare that they have no competing interests. Authors' contributions The authors have contributed equally to this work. Acknowledgements The authors are grateful to the reviewers for useful comments and suggestions to an earlier version of the paper.

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