Hypothesis Management Framework: a flexible design pattern for belief networks in decision support systems Sicco Pier van Gosliga, Imelda van de Voorde TNO Defence, Security and Safety The Hague, The Netherlands Abstract (e.g. HUGIN, Netica and GeNie)1 for modeling and analysing belief networks require expertise and skill in belief networks. Whereas in the field of criminal in- This article discusses a design pattern for vestigations, the typical user of such decision support building belief networks for application do- software is usually not a Bayesian specialist but either mains in which causal models are hard to an analyst or an expert on the area being analyzed, construct. In this approach we pursue a a so-called domain expert. To get belief networks ac- modular belief network structure that is cepted as a standard tool in criminal investigations, easily extended by the users themselves, we should improve the usability to such a degree that while remaining reliable for decision sup- a domain expert is able to produce useful models with- port. The Hypothesis Management Frame- out the assistance of a Bayesian specialist. Obviously, work proposed here is a pragmatic attempt to analysts should find it beneficial for performing their enable analysts and domain experts to con- analyses as well. struct and maintain a belief network that can be used to support decision making, with- Besides offering criminal investigators a method to use out requiring advanced knowledge engineer- belief networks, also some effort should be focused on ing skills. preventing bias arising in analyses. Where much at- tention goes into getting unbiased and accurate prior probabilities, in this paper we are more concerned with any bias within the topology; the choice of variables 1 INTRODUCTION included in the model. When an analyst looks for sup- port for a certain hypothesis, it is easy to get into a so-called tunnel view in which contradicting evidence Since their introduction by Kim and Pearl [10] belief and alternate hypotheses are neglected. When a plau- networks have become a popular framework for deci- sible alternative perspective is missing in the model, sion support and automated reasoning. Also at TNO, a potential bias is present yet invisible. It seems im- the Netherlands Organisation for Applied Scientific possible to always exclude such a bias, but applying Research, Bayesian reasoning is used in an increasing certain strategies in the design of a belief network may number of projects and application domains. One of lead to more balanced and less biased models. Among these application domains is decision support for crim- others, the following strategies might be considered. inal investigations. The typical application in this field Firstly, different domain experts can add an alterna- is to perform a quick scan on available evidence to se- tive point of view to the same model. Secondly, each lect the most likely hypothesis, and to prioritize un- domain expert can work independently on a different available evidence to aid further investigations. The hypothesis or counter-hypothesis. And finally, domain need for sound probabilistic reasoning is quite large experts can design reusable templates that are not tai- in this area, and belief networks are becoming an ac- lored for a specific case, but for generic classes of cases. cepted tool for modeling reasoning. Whatever combination of strategies may work best to Well-known examples of belief networks such as the avoid a bias, the case for a flexible and modular way Alarm [2] and Hailfinder [1] networks are quite com- 1 The software packages HUGIN Expert, Netica and plex and their development requires the co-operation GeNie are respectively found at: http://www.hugin. between both Bayesian specialists and domain ex- com, http://www.norsys.com/netica.html and http:// perts. Also, currently available software packages genie.sis.pitt.edu/ to design belief networks to aid better decision making To maximize its applicability in real world applications should be apparent. the following two requirements should be met: Various systematic techniques are available to guide 1 Reliability (or consistency) The belief network the modeling of a belief network in a systematic man- should capture the knowledge of domain experts. ner. Many of these generate a belief network by trans- Given the same set of evidence, the domain ex- lation of another type of model, e.g. ontologies [19], perts should agree on the same most likely hy- rule-based systems [11], causal maps [16], or by merg- potheses and the results of the model should in- ing quantitative and qualitative statements in a canon- tuitively make sense. ical form [5]. However, all these techniques rely on a sound understanding of the application domain to es- 2 Usability The number of priors to be elicited tablish the qualitative aspect of a belief network: the should be kept to a practical minimum. We pre- topology of the graph. When a domain is modeled fer to have a limited set of well founded priors, that is dynamic in nature and of which causality is rather than a larger set of priors of which the do- not fully known, the technique used to construct a main expert is less confident. Conditional prob- belief network must above all be modular and easily ability tables with a small set of priors are eas- extendible as new insights constantly change the per- ier to maintain and validate, especially when the spective of what variables matter to the hypotheses of number of conditioning parent variables is lim- interest. ited. Furthermore, it should be unambiguous to This led to the development of the hypothesis manage- domain experts (as well as the analysts) what the ment framework (HMF) at TNO. This design pattern variables and their priors stand for. enables a domain expert to independently create and maintain a belief network, and an analyst to evalu- These requirements are indeed very common, and gen- ate evidence in a criminal investigation. The HMF erally accepted as basic requirements in the context of is a modular belief network structure that is easily system development. We think, however, that they are expandable by the users themselves, while remaining hard to comply with without the use of a generalized reliable for decision support. The HMF adds a layer framework. of abstraction to the belief network, so the belief net- work can be kept hidden from the user. Multiple users 3 AN OVERVIEW OF HMF can independently modify or extend the model based on his or her domain knowledge. The HMF ensures The HMF places each variable of interest within a pre- that all parts of the model remain a coherent whole, defined structure, as visualized in Figure 4(c). Fur- suitable for consistent reasoning. thermore it prescribes which variables may be instanti- ated with evidence, and for some variables the content of conditional probability tables. All variables must 2 THE PURPOSE OF HMF be categorized by the user in hypotheses, indicators or information sources. Each type has its own place and While devising the HMF design pattern we had one role within the topology of the belief network: particular goal in mind: to enable the design of modu- lar and extendible Bayesian models for users that are 1 Hypotheses are statements of which we would like no Bayesian specialist. Once a first version of a model to get a posterior probability distribution. In gen- has been developed, it should be easily extended and eral, hypotheses are unobserved. The user can maintained later-on. It is likely that the set of vari- specify unconditional priors for each hypothesis, ables as well as the subjective priors for conditional or use a uniform nondiscriminative distribution probability tables require regular revisions as the field instead. As an option, one can add alternative of investigation changes over time. Therefore it should hypotheses to represent known facts that explain be possible to reconsider the set of variables, without observed indicators in an other way than existing having to elicit all of the priors on each change of the hypotheses. model. The need for multiple revisions of a develop- ing model was addressed by the AI group at the Uni- 2 Indicators are statements related to hypotheses. versity of Kentucky in [14]. A design pattern should Knowledge of an indicator helps to reveal the preferably be such that it enables the use of templates, states of related hypotheses. Indicators describe generalized submodels within the belief network, that events that are dependent on the occurrence of can be maintained independently by a group of domain one or more hypotheses. Causal relations between experts. Such templates should be applicable within hypotheses and indicators are not always obvious, multiple belief networks. or present at all. Indicators are assumed to be ‘caused’ by hypotheses, not the other way around. There are various options to elicit priors for such large For each relation between an indicator and a hy- CPTs. One could apply linear interpolation over a pothesis, a domain expert should specify condi- subset of elicited priors [20], but this requires more tional probabilities for that specific relation. elicited priors and is less flexible than the solution found for HMF. Rather than connecting indicators di- 3 Information Sources are used to express the re- rectly to hypotheses, the HMF uses intermediate vari- liability of sources related to an indicator, when ables. In this article all variables are booleans. This the user does not want to enter ’hard evidence’. is not a strict requirement, but a general recommen- For instance, an information source may be a re- dation when it simplifies the elicitation of prior prob- port, a sensor or a person. An indicator can be abilities. Elicited priors will be stored in the interme- associated to multiple information sources. diate variable between the indicator and the hypoth- esis. This reduces the number of prior probabilities Although common, it is not necessary for an arc in a to elicit, and conditions to consider for each prior. In belief network to imply causality. The HMF makes use fact, the HMF splits up each indicator in multiple vari- of this freedom by taking a more abstract perspective ables (Figure 1): one or more intermediate variables on the relations between variables of interest. The (ih1 , ih2 ) and a variable that combines them (i0 ). For structure is based on the relatively simple notion of three hypotheses i would require 16 priors, instead of hypotheses and indicators. Indicators may all support 12 priors for the three intermediate variables together. or contradict any of the hypotheses, but the indicators When evidence is available for an indicator, we in- themselves are assumed independent of one another. stantiate all associated intermediate variables. Alter- Hypotheses are independent (root nodes) and typically natively, one can use information sources. An infor- have many children. Quite similar, so-called ’naive mation source for an indicator (s in Figure 1) may Bayes’ structures [6], have been effective in other areas exist as multiple variables with identical priors in the where causality is unknown or too dynamic in nature HMF belief network (sh1 , sh2 ). The priors of an in- (e.g. e-mail spam filtering [15]). formation source variable represent the reliability of If more structure is desired, this modeling style may the source in regard the associated indicator. Infor- be applied in a recursive fashion in which a hypothe- mation source variables are children of intermediate sis may have sub-hypotheses, who are modeled in an variables, and have only one parent and no children. similar way. This is not demonstrated in this article. Either all information sources of an indicator are in- stantiated for evidence, or all associated information It is good practice to use a causal model whenever source variables. Instantiating intermediate variables possible [17], and it should be stressed that HMF does of an indicator d-separates information sources from not aim to substitute such models. The HMF design hypotheses, rendering all information sources for that pattern is specifically designed for domains in which indicator obsolete. causal dependencies are debated or not fully known. As pointed out by Biedermann and Taroni [3], in foren- When there is no evidence for an indicator, the com- sic science the availability of hard numerical data is bining indicator variable (i0 ) will resemble the poste- not a necessary requirement for quantifying belief net- rior probability of the original indicator (i) by taking works and Bayesian inference could therefore be used the average probability of all intermediate variables. nonetheless. By using HMF, a Bayesian model can This information is useful to predict the likelihood of be constructed even when the qualitative aspects of a unobserved indicators or for selecting the most influ- belief network are hard to obtain. ential unobserved indicator. Equation 1 is used to con- struct the conditional probability table of the combin- ing indicator variable. Note, that the HMF does not use a logical function (e.g. OR/MAX, AND/MIN or XOR). Logical functions that assume independence of causal influence, in a discrete or noisy variant, have been long in use [8] as a solution for variables with many parents. An extensive overview of such methods are described by Diez and Drudzel in [4]. Although many alternatives may be considered, our preference goes to an averaging method to avoid scalability prob- lems. The scalability problem will be further discussed in Section 5, while the results of using the averaging Figure 1: Indicators are substituted by multiple inter- method in Equation 1 are discussed in Section 6. mediate variables and one combining variable. manner, and assign conditional probabilities to each relation. Figure 3 shows how this may be presented to maxV alueOf (parents(X)) P (X|parents(X)) = 1.0− the domain expert. There is a column for each hypoth- valueOf (parents(X)) esis. Assuming only booleans are used, the respective (1) column requires only two elicited priors: one prior for This article focuses on how HMF can aid the construc- the likelihood of observing the indicator given the hy- tion of belief networks. It does not elaborate on how pothesis is true, and another for when the hypothesis a software tool might facilitate this process. Nonethe- is false. Qualitative descriptions or frequencies can be less, we would like to discuss briefly how we envision more effective than probabilities [7]. Such notations such a tool and how the HMF might be presented to can be used instead of probabilities, as long these de- the user. We differentiate two types of roles for users: scriptions are consistently translated into conditional domain experts and analysts. A user may have both probability tables. roles in practice. By using the HMF, the GUI can ef- fectively hide the underlying belief network from the 4 HMF WALKTHROUGH BY AN user. Both types of users need a different user inter- EXAMPLE face. To explain how the HMF may be used and why we have chosen this specific topology, we will now dis- cuss three different models based on a civil case con- cerning a car accident. The first is a logical causal model by Prakken and Renooij [18]. The second is a Bayesian belief network by Huygen [9], directly based on Prakken’s logical model. Third and finally, a Bayesian belief network that follows the HMF is con- Figure 2: The GUI for an analyst. structed for the same case. 2 The legal case concerns a nightly car accident involving a driver and a passenger, after a party which both per- sons attended. The police that arrived at the scene af- ter the accident observed that the car crashed just be- yond an S-curve and the handbrake was in a pulled po- sition. The police did observe tire marks (skid marks and jaw marks), but did not observe any obstacles. The driver claims that the passenger was drunk and pulled the handbrake. The passenger claims that the Figure 3: The GUI for a domain expert. driver speeded through the S-curve. The judge had to decide whether it is plausible that the passenger An analyst processes information sources and selects caused the accident, rather than the driver. evidence for indicators to support or contradict hy- The logical model about this case by Prakken and potheses. For analysts the GUI (Figure 2) shows indi- Renooij is aimed at reconstructing the reasoning be- cators in a foldable tree-like structure. The indicators hind the court decision on this case. Figure 4(a) shows are organized in categories and sub-categories. For the causal structure for the case. Nodes within the each indicator the analyst can choose a state (e.g. true structure visualize causal concepts (propositions), and or false) based on observed evidence. If the analyst is arcs represent causal rules between them. Each arc is uncertain about an observation, the analyst is given annotated to show whether the proposition at the head the ability the express the reliability of each informa- supports (+) or contradicts (-) the proposition at the tion source for that specific indicator. This requires tail of the arc. By using abductive-logical reasoning a prior probability for both positive observations and on the structure given evidence for some concepts, one false positives, given that the indicator is a boolean. can determine whether other concepts are plausible. Domain experts evaluate the conditional probabilities Although such a model, a causal map, like the one in of an indicator given an hypothesis, and choose prior Figure 4a may resemble a belief network, it lacks the probabilities for hypotheses. The GUI should enable a quantitative information required for Bayesian infer- domain expert to construct and maintain a list of in- ence. Nadkarni and Shenoy [16] discussed how a causal dicators and hypotheses. A domain expert is respon- 2 the belief networks discussed in this article are avail- sible for relating indicators to hypotheses in a sensible able for download at: http://www.science.uva.nl/~spg (a) A logical causal model by Prakken and Renooij. (b) The belief network by Huygen. (c) A variant that uses the HMF design pattern. Figure 4: Three different models of the same case. The colour red is used to highlight the proposed extensions. map, can be used as a foundation for constructing be- in Figure 4(b)). This effectively replaces the annota- lief networks when supplemented with casual values tions along arcs in the causal map. Huygen decided that express the strength of a causal connection. not to use evidence for variables on tire marks, be- cause in the sentence of the court it was not explicitly There is evidence for the following facts: ¬obstacles, stated that the nature of the tire marks were proof for tire marks present, observed nature of tire marks after not speeding, but gave insufficient support for the sug- S-curve, handbrake in pulled position, driver’s testi- gestion that the driver had speeded. Huygens suggests mony and drunk passenger. The hypotheses speeding to change the priors, when one would like to use this in S-curve and loss of control over vehicle explain two evidence. facts but contradicts three others. Whereas the hy- pothesis passenger pulled handbrake of moving vehi- Given evidence for: pulled position, driver’s testimony, cle explains three rules and contradicts nothing. This passenger drunk and crash, it is highly likely that the makes the drivers point of view more convincing. passenger pulled the handbrake (≈ 100%). Since the evidence against the passenger explains away the car Huygen used the causal model of Prakken to construct crash, it is unlikely that the crash was caused by lost a belief network for the same case (Figure 4b). The control of the vehicle after speeding through the S- topology was slightly changed: the node for obstacles curve (0.1%). The bayesian belief network comes to has been removed and the propositions for speeding the same conclusion as the causal map of Prakken and and slowing down in S-curve have been replaced by Renooij. a single boolean that represents both. Furthermore, each node is accompanied with a conditional probabil- When we model the same case using the HMF, we get ity table or prior probability distribution (not visible a radically different topology (Figure 4(c)) that does not resemble the causal map of Prakken and the belief HMF are flexible, meaning that a model is decompos- network of Huygen. Both claims are modeled as hy- able into independent modules. So that each module potheses in the HMF model: accident caused by speed- can be maintained or extended by a different domain ing and passenger pulled handbrake of moving vehicle. expert. This section will discuss issues that concern These hypotheses correspond to similarly named pred- the extendibility of models developed with the HMF. icates in Figure 4a and probability variables in Figure These issues will be illustrated by extending the exist- 4b. Uniform probability distributions were used as pri- ing models from the previous section. ors for these hypotheses. We use indicators to support We have pursued extendibility by modular indepen- our beliefs in the hypotheses, these are: driver’s tes- dence of the elicited priors. When an indicator is timony directly after incident, handbrake in pulled po- added to the model, the only priors to elicit are those sition after incident, passenger had drunk alcohol, ob- for the intermediate nodes of that specific indicator. served yawmarks of sliding vehicle and observed skid- Priors that were elicited before do not have to be marks beyond the curve. reconsidered. The same holds for adding hypothe- By choosing different priors, the evidence for tire ses. We will illustrate this by considering an addi- marks is now usable. Some intermediate variables that tional hypothesis for the car accident case. Suppose relate facts with the two hypotheses are no longer in the driver pulled the handbrake of the moving vehi- use. These are locking of wheels and loss of control cle. If the driver was under influence of alcohol, that over vehicle. The information source of passenger had would have also influenced the driving behavior and drunk alcohol is undisclosed. Suppose the source was therefore the likelihood of speeding as well as the pos- a guest at the party, than the reliability of this testi- sibility of pulling the handbrake of the moving vehicle. mony is represented by an information source variable In all three models we would have to add and update (Figure 4(c)). existing prior knowledge. Given the available evidence, we get a high likelihood To add the alternative hypothesis to the logical model for the passenger pulling the handbrake of the mov- of Prakken and Renooij a proposition is needed for the ing vehicle (≈ 100%). The propability for speeding is new hypothesis, and another to represent the possibil- much lower (≈ 27%), and therefore far less convincing. ity that the driver was under the influence of alcohol. These additional causal relations are highlighted in red All three approaches can adequately model the case in Figure 4(a). Together, these additions extend the and derive equally sensible conclusions. Abductive- existing set of 12 rules with 6 more. logical reasoning over a causal map explains the logi- cal correctness and contradictions of propositions. The advantage of a Bayesian approach is that by quanti- fying influence, it is able to give insight in what hy- pothesis is most credible as well as the relevance of evidence. The models of Prakken, Renooij and Huy- gen are based on a causal map. Although HMF follows a different approach to the construction of belief net- works, and therefore uses a rather different topology, it does derive the same conclusions. 5 ISSUES REGARDING EXTENDIBILITY Extendibility as well as modularity are important re- quirements. The models by Prakken and Huygen are ’static’ models in the sense that they were designed to model one single case with a fixed set of evidence and hypotheses. This is feasible when consensus has been developed on all aspects of the case. However, sup- porting decision making at an earlier stage requires a high level of flexibility. The HMF was developed to facilitate decision making when the set of evidence (or indicators) and hypotheses is still evolving and a con- Figure 5: How extending the model affects the number stant topic of discussion. Models designed with the of priors to elicit. have to be combined. On each extension the combin- Table 1: Extending the models. ing variable gets an extra parent, and as a consequence priors Prakken Huygen elicited HMF its conditional probability table (CPT) doubles in size. in original model 12 44 36 after extension 18 64 58 In the HMF an averaging function has been chosen as unchanged 12 30 36 the preferred option for these CPTs. By default, the updated and added 6 34 22 relative workload 50% 77% 61% CPT of a combining variable effectively takes the aver- age posterior distribution of all intermediate variables (Equation 1). When we add similar variables and relations to the Arguably, one might find a logical OR-function [8] belief network of Huygen, we need to specify new con- more intuitive. However, we have chosen not to use an ditional probability tables for locking of wheels, hand- OR or AND function for these CPTs since a method- brake in pulled position and driver’s testimony. Fur- ical bias may arise in the model if it is extended. A thermore, we would have to replace the prior proba- practical drawback of using OR-tables in this situation bility distributions of speeding through S-curve with a arises when more than (approximately) five alternative new conditional probability table. These changes com- hypotheses are connected to an indicator. By adding prise the elicitation of 34 new priors that substitute 14 more parents to a deterministic OR-table the proba- previously elicited priors. bility for the child variable quickly converges to unity, To add to the HMF model the hypothesis driver pulled or alternatively a pre-defined upper bound. This is the handbrake of the moving vehicle, requires a new col- shown in Figure 6(a). It is likely that this will lead umn in the model in Figure 4. The possibility of the to unintentional overestimation of the occurrence of driver being under the influence of alcohol is modeled unobserved indicators. This can be illustrated by ex- as an indicator, which adds a new row to the model. tending the belief network of Huygen, where the vari- Table I shows how many elicited priors are required able locking of wheels is modeled as an OR-table with for extending the models. The extensions of the HMF an upper bound of 0.80. Suppose the case would be model comprise only 22 elicited priors, all 36 existing extended to include one or two additional drunk back- priors remain unchanged. This makes HMF consid- seat passengers who may have pulled the handbrake erably cheaper to extend than the belief network of of the moving vehicle. The extra backseat passengers Huygen. The original causal model of Prakken is even are modeled in the same way as the passenger in front, simpler to extend. That model, however, lacks quan- using the original priors P (locking|pulled) = 80% and titative support for probabilistic inference. P (locking|¬pulled) = 0% (where pulled is true when any of the persons in the vehicle pulled the handbrake). As the car accident case shows, the HMF is tolerant to Given that the driver is sober and all passengers are extensions. Figure 5 shows the general effect of adding drunk, the probability of locking the wheels increases hypotheses and indicators to a model by outlining the rapidly (one drunk passenger: 2.4%, two drunk pas- maximum number of elicited priors. While the to- sengers: 4.7%, three drunk passengers: 7.0%). Even tal number of parameters grows exponentially when when we have not instantiated any other variables more hypotheses are added, the amount of elicited (e.g. crash or driver’s testimony). After these exten- priors grows in a linear fashion. The figure assumes sions, one might like to reconsider the original priors of the worst case in which each indicator is associated to P (pull|drunk) to prevent overestimating the probabil- all hypotheses. Although the model assumes boolean ity of locked wheels. This potential problem is avoided variables and two priors for each intermediate variable when the method in Equation 1 is used. would suffice, it is assumed that all priors for inter- mediate variables are elicited as well as a prior prob- Another potential problem that is associated with OR- ability distribution for each hypothesis. Note that we tables is the asymmetric influence of an indicator: pos- have excluded all other parameters that require elici- itive observations have less impact than a negative tation such as variable names and state definitions. As observation. This is shown in Figure 6(b)). Where a reference Figure 5 includes the number of priors of observed indicators will only have marginal impact Hailfinder (3741), Alarm (752), the original belief net- on hypotheses when observed true, the impact on in- work of Huygen (44) and the HMF model from Section termediate variables of an indicator observed as false 4 (36). The extensions proposed in this Section were is deterministic and therefore usually stronger. It is excluded from the HMF model. likely that the user will be unaware of these effects. This makes the model relatively vulnerable to errors As mentioned in Section 3 indicators are modeled in the priors. Therefore, we advice to use Equation 1 by intermediate variables and one combining variable. as the default method. Other methods for construct- The more hypotheses are associated to an indicator, ing CPTs of combining variables may hinder extending the more probabilities of intermediate variables will (a) The likelihood of an indicator. (b) The impact of evidence for an indicator. Figure 6: Extending the model affects the probabilities. the model. fore only one probability for each hypothesis has to be elicited and two for each association of an indicator with a hypothesis. For Asia this gives a total of 21 6 ISSUES REGARDING probabilities. In this case the priors for the hypothe- RELIABILITY ses and intermediate nodes were derived from the joint probability table of the original Asia belief network. To evaluate the outcomes of HMF belief networks we have translated the Asia belief network, as introduced We computed the posteriors of the hypotheses for all by Lauritzen and Spiegelhalter in [12], into the HMF possible scenario’s of evidence for the indicators. In format. each of these scenarios each indicator was either ob- served or not. Note that we instantiate the interme- We will use abbreviations that correspond to the first diate nodes for evidence, rather than the combining character of each variable. The original model is shown variables. As mentioned in Section 3 an indicator is in Figure 7 (left), the HMF version of Asia is shown on represented by both intermediate variables and a com- the right. In the HMF model of Asia we distinguish hy- bining variable. The conditional probability table of potheses: {b, l, t}, indicators: {s, v, x, d} and interme- the combining variable is implemented by Equation diate nodes: {sb , sl , vt , xb , xl , xt , db , dl , dt }. The vari- 1, whereas the elicited priors are stored in the inter- able T bOrCa is missing from the HMF model, which mediate variables. Instantiating only the combining in the original belief network combines the probabili- variable would undervalue those elicited priors. ties of tuberculosis and lung cancer with a logical OR function has become obsolete. The results are shown in Table II. For each indica- tor and hypothesis, the table shows the average and In the HMF model of Asia, the prior information for maximum absolute difference in posteriors, as well as the indicators is specified separately for each associ- the Jensen-Shannon divergence [13]. The bottom row ated hypothesis. This assumes that the influence of shows the percentage of scenario’s in which the out- e.g. lung cancer on dyspnea is unaffected by bron- comes (i.e. the most likely state) for the variables chitis. The following probabilities will have to be were equal. Especially this last criterion is important elicited from a domain expert, when using HMF on for decision making, as the ’real’ priors and posteriors Asia. Unconditional priors for each hypothesis: P (b), will always be open to debate when a causal model P (l), P (t) and conditional priors for all intermedi- is hard to obtain. The table shows that while poste- ate nodes: P (sb |b), P (sl |l), P (vt |t), P (xb |b), P (xl |l), rior distributions may vary between both versions, on P (xt |t), P (db |b), P (dl |l), P (dt |t). average the difference is relatively small (< 4 percent- The Asia model uses only boolean variables and there- age points). For almost all scenario’s the outcomes Figure 7: Left: the original Asia belief network. Right: HMF version of Asia. Both with evidence for Smoking. discussed in this paper. The Asia example shows that Table 2: Divergence between HMF verion of Asia and posteriors via a HMF model can be quite similar to the original. those derived via a belief network based on causality. vertice d v x b t c s The issues that we have encountered so far in applying max dif 0,162 0,004 0,071 0,308 0,193 0,209 0,095 av. dif 0,023 0,000 0,009 0,036 0,020 0,017 0,014 belief networks for criminal investigations have been max J-S 0,021 0,000 0,006 0,074 0,029 0,035 0,008 addressed in this paper. However, it is a continuous av. J-S 0,002 0,000 0,001 0,006 0,002 0,002 0,001 match(%) 91,4 100,0 100,0 97,5 98,8 98,8 97,5 effort to further improve the HMF. 8 FUTURE RESEARCH are identical. The few exceptions are caused by the synergistic effect between an abnormal X-Ray and the One of the complementary wishes of the authors in- presence of dyspnea. This synergistic affect is absent volves a bias measurement combined with automated in the HMF version, and in those situations we get commentary that highlights useful missing evidence. the relatively large differences in the posterior distri- By calculating how discriminative the indicators and butions of bronchitis and long cancer. the evidence is to each hypothesis and counterhypoth- esis, we can evaluate whether tunnel vision may be 7 CONCLUSIONS present. It can also be used to investigate the added value of collecting evidence for unobserved indicators. One way of getting this information is by simulating The current HMF design pattern is extendible and evidence and evaluate the posteriors of all hypotheses. modular. In our opinion the HMF succeeds in its pur- Since the maximum potential impact of an indicator pose. We have confidence that HMF comes as a relief may only occur at a certain combination of evidence to those application domains that so far have been for other indicators, the simulation should consider all relatively underequipped with practical decision sup- possible combinations of evidence for all unobserved port tools, due to the lack of ’hard and solid’ domain indicators. This may be a costly operation. Alter- knowledge that can be used as a basis for probabilistic natively one may derive the maximum impact directly models. from the conditional probability tables of the variables, The arrangement of the HMF supports a working and use message passing to investigate the maximum method which deals with tunnel-view in a well con- potential impact of each indicator. sidered manner. The HMF will not explicitly reduce The naive structure of a HMF belief network may in or prevent bias occurring within the topology of a some occasions not capture the targeted effects. In model. However, it offers the possibility to use certain those cases we would like to extend the HMF model strategies during the design of a model which lead to with constraining variables that model the synergistic more balanced and thus less biased models. Using such effect between indicators (or in between hypotheses). strategies will enlarge the awareness about tunnel-view We have not been able to test such mechanisms in real- (and bias) and as such may partly prevent it. istic cases so far. Therefore these need further investi- Although the requirements of reliability and usabil- gation to test the feasibility of adding constraints, and ity are not validated by domain experts and analysts, whether the implications of such mechanisms violate several issues concerning these requirements have been the extendibility and modularity. The HMF has been applied on several study cases [10] J. H. Kim and J. Pearl. A computation model for based on real data by the authors. 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