{"title": "Probabilistic detection of short events, with application to critical care monitoring", "book": "Advances in Neural Information Processing Systems", "page_first": 49, "page_last": 56, "abstract": "We describe an application of probabilistic modeling and inference technology to the problem of analyzing sensor data in the setting of an intensive care unit (ICU). In particular, we consider the arterial-line blood pressure sensor, which is subject to frequent data artifacts that cause false alarms in the ICU and make the raw data almost useless for automated decision making. The problem is complicated by the fact that the sensor data are acquired at fixed intervals whereas the events causing data artifacts may occur at any time and have durations that may be significantly shorter than the data collection interval. We show that careful modeling of the sensor, combined with a general technique for detecting sub-interval events and estimating their duration, enables effective detection of artifacts and accurate estimation of the underlying blood pressure values.", "full_text": "Probabilistic detection of short events, with\n\napplication to critical care monitoring\n\nNorm Aleks\nU.C. Berkeley\n\nnorm@cs.berkeley.edu\n\nStuart Russell\nU.C. Berkeley\n\nrussell@cs.berkeley.edu\n\nMichael G. Madden\n\nNational U. of Ireland, Galway\nmichael.madden@nuigalway.ie\n\nDiane Morabito\nU.C. San Francisco\n\nmorabitod@\n\nneurosurg.ucsf.edu\n\nKristan Staudenmayer\n\nStanford University\n\nkristans@\nstanford.edu\n\nMitchell Cohen\nU.C. San Francisco\n\nmcohen@\n\nGeoffrey Manley\nU.C. San Francisco\n\nmanleyg@\n\nsfghsurg.ucsf.edu\n\nneurosurg.ucsf.edu\n\nAbstract\n\nWe describe an application of probabilistic modeling and inference technology to\nthe problem of analyzing sensor data in the setting of an intensive care unit (ICU).\nIn particular, we consider the arterial-line blood pressure sensor, which is subject\nto frequent data artifacts that cause false alarms in the ICU and make the raw data\nalmost useless for automated decision making. The problem is complicated by\nthe fact that the sensor data are averaged over \ufb01xed intervals whereas the events\ncausing data artifacts may occur at any time and often have durations signi\ufb01cantly\nshorter than the data collection interval. We show that careful modeling of the\nsensor, combined with a general technique for detecting sub-interval events and\nestimating their duration, enables detection of artifacts and accurate estimation\nof the underlying blood pressure values. Our model\u2019s performance identifying\nartifacts is superior to two other classi\ufb01ers\u2019 and about as good as a physician\u2019s.\n\n1 Introduction\n\nThe work we report here falls under the general heading of state estimation, i.e., computing the\nposterior distribution P(Xt|e1:t) for the state variables X of a partially observable stochastic system,\ngiven a sequence of observations e1:t. The speci\ufb01c setting for our work at the Center for Biomedical\nInformatics in Critical Care (C-BICC) is an intensive care unit (ICU) at San Francisco General\nHospital (SFGH) specializing in traumatic brain injury, part of a major regional trauma center. In this\nsetting, the state variables Xt include aspects of patient state, while the evidence variables Et include\nup to 40 continuous streams of sensor data such as blood pressures (systolic/diastolic/mean, arterial\nand venous), oxygenation of blood, brain, and other tissues, intracranial pressure and temperature,\ninspired and expired oxygen and CO2, and many other measurements from the mechanical ventilator.\nA section of data from these sensors is shown in Figure 1(a). It illustrates a number of artifacts,\nincluding, in the top traces, sharp deviations in blood pressure due to external interventions in the\narterial line; in the middle traces, ubiquitous drop-outs in the venous oxygen level; and in the lower\ntraces, many jagged spikes in measured lung compliance due to coughing.\nThe artifacts cannot be modeled simply as \u201cnoise\u201d in the sensor model; many are extended over time\n(some for as long as 45 minutes) and most exhibit complex patterns of their own. Simple techniques\nfor \u201ccleaning\u201d such data, such as median \ufb01ltering, fail. Instead, we follow the general approach\nsuggested by Russell and Norvig (2003), which involves careful generative modeling of sensor state\nusing dynamic Bayesian networks (DBNs).\nThis paper focuses on the arterial-line blood pressure sensor (Figure 1(b)), a key element of the\nmonitoring system. As we describe in Section 2, this sensor is subject to multiple artifacts, including\n\n1\n\n\fFlush solution\n(heparinized saline)\n\nPressure bag\nand gauge\n\nTransducer\n\nInput to\nbedside\nmonitor\n\n3-way stopcock\nwith site for zeroing\nor blood draw\n\nRadial artery\ncatheter\n\n(a)\n\n(b)\n\nFigure 1: (a) One day\u2019s worth of minute-by-minute monitoring data for an ICU patient. (b) Arterial-\nline blood pressure measurement.\n\narti\ufb01cially low or high values due to zeroing, line \ufb02ushes, or the drawing of blood samples. These\nartifacts not only complicate the state estimation and diagnosis task; they also corrupt recorded data\nand cause a large number of false alarms in the ICU, which lead in turn to true alarms being ignored\nand alarms being turned off (Tsien & Fackler, 1997). By modeling the artifact-generating processes,\nwe hope to be able to infer the true underlying blood pressure even when artifacts occur.\nTo this point, the task described would be an applied Bayesian modeling problem of medium dif-\n\ufb01culty. What makes it slightly unusual and perhaps of more general interest is the fact that our\nsensor data are recorded as averages over each minute (our analysis is off-line, for the purpose of\nmaking recorded data useable for biomedical research), whereas the events of interest\u2014in this case,\nre-zeroings, line \ufb02ushes, and blood draws\u2014can occur at any time and have durations ranging from\nunder 5 seconds to over 100 seconds. Thus, the natural time step for modeling the sensor state tran-\nsitions might be one second, whereas the measurement interval is much larger. This brings up the\nquestion of how a \u201cslow\u201d (one-minute) model might be constructed and how it relates to a \u201cfast\u201d\n(one-second) model. This is an instance of a very important issue studied in the dynamical systems\nand chemical kinetics literatures under the heading of separation of time scales (see, e.g., Rao &\nArkin, 2003). Fortunately, in our case the problem has a simple, exact solution: Section 3 shows\nthat a one-minute model can be derived ef\ufb01ciently, of\ufb02ine, from the more natural one-second model\nand gives exactly the same evidence likelihood. The more general problem of handling multiple\ntime scales within DBNs, noted by Aliferis and Cooper (1996), remains open.\nSection 4 describes the complete model for blood pressure estimation, including artifact models, and\nSection 5 then evaluates the model on real patient data. We show a number of examples of artifacts,\ntheir detection, and inference of the underlying state values. We analyze model performance over\nmore than 300 hours of data from 7 patients, containing 228 artifacts. Our results show very high\nprecision and recall rates for event detection; we are able to eliminate over 90% of false alarms for\nblood pressure while missing fewer than 1% of the true alarms.\nOur work is not the \ufb01rst to consider the probabilistic analysis of intensive care data. Indeed, one\nof the best known early Bayes net applications was the ALARM model for patient monitoring un-\nder ventilation (Beinlich et al., 1989)\u2014although this model had no temporal element. The work\nmost closely related to ours is that of Williams, Quinn, and McIntosh (2005), who apply factorial\nswitching Kalman \ufb01lters\u2014a particular class of DBNs\u2014to artifact detection in neonatal ICU data.\nTheir (one-second) model is roughly analogous to the models described by Russell and Norvig,\nusing Boolean state variables to represent events that block normal sensor readings. Sieben and\n\n2\n\n\fFigure 2: 1-second (top) and 1-minute-average (bottom) data for systolic/mean/diastolic pressures.\nOne the left, a blood draw and line \ufb02ush in quick succession. On the right, a zeroing.\n\nGather (2007) have applied discriminative models (decision forests and, more recently, SVMs) to\ncorrection of one-second-resolution heart-rate data. Another important line of work is the MIMIC\nproject, which, like ours, aims to apply model-based methods to the interpretation of ICU data (Heldt\net al., 2006).\n\n2 Blood Pressure Monitoring\n\nBlood pressure provides informs much of medical thinking and is typically measured continuously in\nthe ICU. The most common ICU blood pressure measurement device is the arterial line, illustrated\nin Figure 1(b); a catheter placed into one of the patient\u2019s small arteries is connected to a pressure\ntransducer whose output is displayed on a bedside monitor.\nBecause blood \ufb02ow varies during the cardiac cycle, blood pressure is pulsatile. In medical records,\nincluding our data set, blood pressure measurements are summarized in two or three values: systolic\nblood pressure, which is the maximum reached during the cardiac cycle, diastolic, which is the\ncorresponding minimum, and sometimes the mean.\nWe consider the three common artifact types illustrated in Figure 2: 1) in a blood draw, sensed\npressure gradually climbs toward that of the pressure bag, then suddenly returns to the blood pressure\nwhen the stopcock is closed, seconds or minutes later; 2) in a line \ufb02ush, the transducer is exposed to\nbag pressure for a few seconds; 3) during zeroing, the transducer is exposed to atmospheric pressure\n(de\ufb01ned as zero). We refer to blood draws and line \ufb02ushes collectively as \u201cbag events.\u201d\nFigure 2(top) shows the artifacts using data collected at one-second intervals. However, the data\nwe work with are the one-minute means of the one-second data, as shown in Figure 2(bottom). A\nfairly accurate simpli\ufb01cation is that each second\u2019s reading re\ufb02ects either the true blood pressure\nor an artifactual pressure, thus our model for the effect of averaging is that each recorded one-\nminute datum is a linear function of the true pressure, the artifactual pressure(s), and the fraction\nof the minute occupied by artifact(s). Using systolic pressure s as an example, for an artifact of\nlength p (as a fraction of the averaging interval) and mean artifact pressure x, the apparent pressure\ns(cid:31)= px + (1(cid:30) p)s.\nOur DBN model in Section 4 includes summary variables and equations relating the one-minute\nreadings to the true underlying pressures, artifacts\u2019 durations, bag and atmospheric pressure, etc.;\nit can therefore estimate the duration and other characteristics of artifacts that have corrupted the\ndata. Patterns produced by artifacts in the one-minute data are highly varied, but it turns out (see\nSection 5) that the detailed modeling pays off in revealing the characteristic relationships that follow\nfrom the nature of the corrupting events.\n\n3 Modeling Sub-Interval Events\n\nThe data we work with are generated by a combination of physiological processes that vary over\ntimescales of several minutes and artifactual events lasting perhaps only a few seconds. A natural\n\n3\n\n\fFigure 3: (left) DBN model showing relationships among the fast event variables fi, interval count\nvariables GN j, and measurement variables EN j. (right) A reduced model with the same distributions\nfor G0(cid:44) GN(cid:44)\n\n(cid:44) GNt.\n\nchoice would be a \u201cfast\u201d time step for the DBN model, e.g., 1 second: on this timescale, the sensor\nstate variables indicate whether or not an artifactual event is currently in progress. The transition\nmodel for these variables indicates the probability at each second that a new event begins and the\nprobability that an event already in progress continues. Assuming for now that there is only one\nevent type, and given memoryless (geometric) distribution of durations such as we see in Section 5,\nonly two parameters are necessary: p = P( fi = 1(cid:124) fi(cid:30)1 = 1) and q = P( fi = 1(cid:124) fi(cid:30)1 = 0). Both can be\nestimated simply by measuring event frequencies and durations.\nThe main drawback of using a fast time step is computational: inference must be carried out over 60\ntime steps for every one measurement that arrives. Furthermore, much of this inference is pointless\ngiven the lack of evidence at all the intervening time steps.\nWe could instead build a model with a \u201cslow\u201d time step of one minute, so that evidence arrives at\neach time step. The problem here is to determine the structure and parameters of such a model. First,\nto explain the evidence, we\u2019ll need a count variable saying how many seconds of the minute were\noccupied by events. It is easy to see that this variable must depend on the corresponding variable\none minute earlier: for example, if the preceding minute was fully occupied by a blood draw event,\nthen the blood draw was in progress at the beginning of the current minute, so the current minute is\nlikely to be at least partially occupied by the event. (If there are multiple mutually exclusive event\ntypes, then each count variable depends on all the preceding variables.) Each count variable can\ntake on 61 values, which leads to huge conditional distributions summarizing how the preceding 60\nseconds could be divided among the various event types. Estimating these seems hopeless.\nHowever, as we will now see, CPTs for the slow model need not be estimated or guessed\u2014they can\nbe derived from the fast model. This is the typical situation with separation of time scales: slow-\ntime-scale models are computationally more tractable but can only be constructed by deriving them\nfrom a fast-time-scale model.\nConsider a fast model as shown in Figure 3(a). Let the fast time step be (cid:31) and a measurement interval\nbe N(cid:31)\ni=N( j(cid:30)1) fi\ncounts the number of fast time steps within the jth measurement interval during which an event is\noccurring. The jth observed measurement EN j is determined entirely by GN j; therefore, it suf\ufb01ces\nto consider the joint distribution over G0(cid:44) GN(cid:44)\nTo obtain a model containing only variables at the slow intervals, we simply need to sum out the\nfi variables other than the ones at interval boundaries. We can do this topologically by a series of\narc reversal and node removal operations (Shachter, 1986); a simple proof by induction (omitted)\nshows that, regardless of the number of fast steps per slow step, we obtain the reduced structure\nin Figure 3(b). By construction, this model gives the same joint distribution for G0(cid:44) GN(cid:44)\n(cid:44) GNt.\nImportantly, neither fN j nor GN j depends on GN( j(cid:30)1).1\nTo complete the reduced model, we need the conditional distributions P(GN j(cid:124) fN( j(cid:30)1)) and\nP( fN j(cid:124) fN( j(cid:30)1)GN j). That is, how many \u201cones\u201d do we expect in an interval, given the event sta-\ntus at the beginning of the interval, and what is the probability that an event is occurring at the\nbeginning of the next interval, given also the number of ones in the current interval? Given the fast\nmodel\u2019s parameters p and q, these quantities can be calculated of\ufb02ine using dynamic programming:\n\n(where N =60 in our domain). fi =1 iff an event is occurring at time i(cid:31) ; GN j (cid:29)(cid:31) N j(cid:30)1\n\n(cid:44) GNt.\n\n1Intuitively, the distribution over GN j for the Nth interval is determined by the value of f at the beginning of\nthe interval, independent of GN( j(cid:30)1), whereas fN j depends on the count GN j for the preceding interval because,\nfor example, a high count implies that an event is likely to be in progress at the end of the interval.\n\n4\n\n(cid:46)\n(cid:46)\n(cid:46)\n(cid:46)\n(cid:46)\n(cid:46)\n(cid:46)\n(cid:46)\n(cid:46)\n\fa table is constructed for the variables fi and Ci for i from 1 up to N, where Ci is the number of ones\nup to i\u2212 1 and C0 =0. The recurrences for fi and Ci are as follows:\n\nP(Ci, fi =1| f0) = pP(Ci\u22121 =Ci \u2212 1, fi\u22121 =1| f0) + qP(Ci\u22121 =Ci, fi\u22121 =0| f0)\n\nP(Ci, fi =0| f0) = (1\u2212 p)P(Ci\u22121 =Ci \u2212 1, fi\u22121 =1| f0) + (1\u2212 q)P(Ci\u22121 =Ci, fi\u22121 =0| f0)\n\n(1)\n\n(2)\n\nExtracting the required conditional probabilities from the table is straightforward. The table is of\nsize O(N2), so the total time to compute the table is negligible for any plausible value of N. Now\nwe have the following result:\n\nTheorem 1 Given the conditional distributions computed by Equations 1 and 2, the reduced model\nin Figure 3(b) yields the same distribution for the count sequence G0,GN, . . . ,GNt as the \ufb01ne-grained\nmodel in Figure 3(a).\n\nN\n\nThe conditional distributions that we obtain by dynamic programming have some interesting limit\ncases. In particular, when events are short compared to measurement intervals and occur frequently,\nwe expect the dependence on fN( j\u22121) to disappear and the distribution for GN j to be approximately\n1+p/(1\u2212q). When p=q, the fis become i.i.d. and GN j is exactly binomial\u2014the\nGaussian with mean\nrecurrences compute the binomial coef\ufb01cients via Pascal\u2019s rule.\nGeneralizing the analysis to the case of multiple disjoint event types (i.e., fi takes on more than\ntwo values) is mathematically straightforward and the details are omitted. There is, however, a\ncomplexity problem as the number of event types increases. The count variables GN j, HN j, and so\non at time N j are all dependent on each other given fN( j\u22121), and fN j depends on all of them; thus,\nusing the approach given above, the precomputed tables will scale exponentially with the number\nof event types. This is not a problem in our application, where we do not expect sensors to have\nmore than a few distinct types of \u201cerror\u201d state. Furthermore, if each event type occurs independently\nof the others (except for the mutual exclusion constraint), then the conditional distribution for the\ncount variable of each depends not on the combination of counts for the other types but on the sum\nof those counts, leading to low-order polynomial growth in the table sizes.\nThe preceding analysis covers only the case in which fi depends just on fi\u22121, leading to indepen-\ndently occurring events with a geometric length distribution. Constructing models with other length\ndistributions is a well-studied problem in statistics and most cases can be well approximated with\na modest increase in the size of the dynamic programming table. Handling non-independent event\noccurrence is often more important; for example, blood draws may occur in clusters if multiple sam-\nples are required. Such dependencies can be handled by augmenting the state with timer variables,\nagain at modest cost.\nBefore we move on to describe the complete model, it is important to note that a model with a \ufb01ner\ntime scale that the measurement frequency can provide useful extra information. By analogy with\nsub-pixel localization in computer vision, such a model can estimate the time of occurrence of an\nevent within a measurement interval.\n\n4 Combined model\n\nThe complete model for blood pressure measurements is shown in Figure 4. It has the same basic\nstructure as the reduced model in Figure 3(b) but extends it in various ways.\nThe evidence variables ENj are just the three reported blood pressure values ObservedDiaBP, Ob-\nservedSysBP, and ObservedMeanBP. These re\ufb02ect, with some Gaussian noise, idealized Appar-\nent\n\nvalues, determined in turn by\n\u2022 the true time-averaged pressures: TrueDiaBP, TrueSysBP, and TrueMeanBP;\n\u2022 the total duration of artifacts within the preceding minute (i.e., the GN j variables): BagTime\n\nand ZeroTime;\n\n\u2022 the average induced pressure to which the transducer is exposed during each event type:\n\nBagPressure and ZeroPressure (these have their own slowly varying dynamics).\n\n5\n\n\fFigure 4: The blood pressure artifact detection DBN. Gray edges connect nodes within a time slice;\nblack edges are between time slices. \u201cNodes\u201d without surrounding ovals are deterministic functions\nincluded for clarity.\n\nThe Apparent\n\nvariables are deterministic functions of their parents. For example, we have\n\nApparentDiaBP =\n\n1\nN\n\n(cid:31) BagTime(cid:183) BagPressure + ZeroTime(cid:183) ZeroPressure +\n(N (cid:30) BagTime(cid:30) ZeroTime)(cid:183) TrueDiaBP(cid:30)\n\nThe physiological state variables in this model are TrueSystolicFraction (the average portion of each\nheartbeat spent ejecting blood), TruePulseBP (the peak-to-trough size of the pressure wave gener-\nated by each heartbeat), and TrueMeanBP. For simplicity, basic physiologic factors are modeled\nwith random walks weighted toward physiologically sensible values.2\nThe key event variable in the model, corresponding to fN j in Figure 3(b), is EndingValveState.\nThis has three values for the three possible stopcock positions at the one-minute boundary: open\nto patient, open to bag, or open to air. The CPTs for this variable and for its children (at the next\ntime step) BagTime and ZeroTime are the ones computed by the method of Section 3. The CPT for\nEndingValveState has 3(cid:215) 3(cid:215) 61(cid:215) 61=33(cid:44) 489 entries.\n\n5 Experimental Results\nTo estimate the CPT parameters (P( ft+1 =1(cid:124) ft =0) and P( ft+1 =1(cid:124) ft =1)) for the one-second\nmodel, and to evaluate the one-minute model\u2019s performance, we \ufb01rst needed ground truth for event\noccurrence and length. By special arrangement we were able to obtain 300 hours of 1Hz data, in\nwhich the artifacts we describe here are obvious to the human eye; one of us (a physician) then\ntagged each of those data points for artifact presence and type, giving the ground truth. (There were\na total of 228 events of various lengths in the 300 hours\u2019 data.) With half the annotated data we\nveri\ufb01ed that event durations were indeed approximately geometrically distributed, and estimated the\none-second CPT parameters; from those, as described in Section 3, we calculated corresponding\none-minute-interval CPTs.\nUsing averaging equivalent to that used by the regular system, we transformed the other half of\nthe high-resolution data into 1-minute average blood pressures with associated artifact-time ground\ntruth. We then used standard particle \ufb01ltering (Gordon et al., 1993) with 8000 particles to derive\nposteriors for true blood pressure and the presence and length of each type of artifact at each minute.\nFor comparison, we also evaluated three other artifact detectors:\n\na support vector machine (SVM) using blood pressures at times t, t (cid:30) 1, t (cid:30) 2, and t (cid:30) 3 as\nits features;\na deterministic model-based detector, based on the linear-combination model of Section 2,\nwhich calculates three estimates of artifact pressure and length, pairwise among the cur-\nrent measured systolic, diastolic, and mean pressures, to explain the current measurements\n\n2More accurate modeling of the physiology actually improves the accuracy of artifact detection, but this\n\npoint is explored in a separate paper.\n\n6\n\n(cid:46)\n(cid:149)\n(cid:149)\n\fFigure 5: ROC curves for the DBN\u2019s performance detecting bag events (left) and zeroing events\n(right), as compared with an SVM, a deterministic model-based detector, and a physician.\n\nFigure 6: Two days\u2019 blood pressure data for one patient, with the hypertension threshold overlaid.\nRaw data are on the left; on the right are \ufb01ltering results showing elimination (here) of false decla-\nrations of hypertension.\n\ngiven the assumption that the true blood pressure is that recorded at the most recent minute\nduring which no artifact was detected; it predicts artifact presence if the sum of the esti-\nmates\u2019 squared distances from their mean is below some threshold. (Because this model\u2019s\nprediction for any particular minute depends on its prediction at the previous minute, its\nsensitivity and speci\ufb01city do not vary monotonically with changes in the threshold; the\nROC curve shown is of only the undominated points.)\n\na physician working only with the one-minute-average data.\n\nFigure 5(left) shows results for the detection of bag events. The DBN achieves a true positive rate\nof 80% with almost no false positives, or a TPR of 90% with 10% false positives. It does less well\nwith zeroing events, as shown in Figure 5(b), achieving a TPR of nearly 70% with minimal false\npositives, but beyond that having unacceptable false positive levels. The physician had an even lower\nfalse positive rate for each artifact type, but with a true positive rate of only about 50%; the SVM\nand deterministic model-based detector both had better-than-chance performance but were clinically\nuseless due to high false positive rates.\nThe model\u2019s accuracy in tracking true blood pressure is harder to evaluate because we have no\nminute-by-minute gold standard. (Arterial blood pressure measurements as we\u2019ve described them,\ndespite their artifacts, are the gold standard in the ICU. Placing a second arterial line, besides being\nsubject to the same artifacts, also exposes patients to unnecessary infection risk.) However, on a\nmore qualitative level, four physicians in our group have examined many hours of measured and\ninferred blood pressure traces, a typical example of which is shown in Figure 7, and have nearly\nalways agreed with the inference results. Where the system\u2019s inferences are questionable, examining\nother sensors often helps to reveal whether a pressure change was real or artifactual.\n\n7\n\n(cid:149)\n\fFigure 7: Sensed blood pressure (dark lines) and inferred true blood pressure (lighter bands, repre-\nsenting mean (cid:177) 1SD) across an observed blood draw with following zeroing. The lowest two lines\nshow the inferred fraction of each minute occupied by bag or zero artifact.\n\n6 Conclusions and Further Work\n\nWe have applied dynamic Bayesian network modeling to the problem of handling aggregated data\nwith sub-interval artifacts. In preliminary experiments, this model of a typical blood pressure sensor\nappears quite successful at tracking true blood pressure and identifying and classifying artifacts.\nOur approach has reduced the need for learning (as distinct from modeling and inference) to the\nsmall but crucial role of determining the distribution of event durations. It is interesting that the more\nstraightforward learning approach, the SVM described above, had performance markedly inferior to\nthe generative model\u2019s.\nModi\ufb01ed to run at 1Hz, this model could run on-line at the bedside, helping to reduce false alarms.\nWe are currently extending the model to include more sensors and physiological state variables and\nanticipate further improvements in detection accuracy as a result of combining multiple sensors.\n\nReferences\nAliferis, C., & Cooper, G. (1996). A structurally and temporally extended Bayesian belief network\nmodel: De\ufb01nitions, properties, and modeling techniques. Proc. Uncertainty in Arti\ufb01cial Intelli-\ngence (pp. 28\u201339).\n\nBeinlich, I., Suermondt, H., Chavez, R., & Cooper, G. (1989). The ALARM monitoring system.\n\nProc. Second European Conference on Arti\ufb01cial Intelligence in Medicine (pp. 247\u2013256).\n\nGordon, N. J., Salmond, D., & Smith, A. (1993). Novel approach to nonlinear/non-Gaussian\n\nBayesian state estimation. Radar and Signal Processing, IEE Proceedings\u2013F, 140, 107\u2013113.\n\nHeldt, T., Long, W., Verghese, G., Szolovits, P., & Mark, R. (2006). Integrating data, models, and\nreasoning in critical care. Proceedings of the 28th IEEE EMBS International Conference (pp.\n350\u2013353).\n\nRao, C. V., & Arkin, A. P. (2003). Stochastic chemical kinetics and the quasi-steady-state assump-\n\ntion: Application to the Gillespie algorithm. Journal of Chemical Physics, 18.\n\nRussell, S. J., & Norvig, P. (2003). Arti\ufb01cial intelligence: A modern approach. Upper Saddle River,\n\nNew Jersey: Prentice-Hall. 2nd edition.\n\nShachter, R. D. (1986). Evaluating in\ufb02uence diagrams. Operations Research, 34, 871\u2013882.\nSieben, W., & Gather, U. (2007). Classifying alarms in intensive care\u2014analogy to hypothesis test-\n\ning. Lecture notes in computer science, 130\u2013138.\n\nTsien, C. L., & Fackler, J. C. (1997). Poor prognosis for existing monitors in the intensive care unit.\n\nCritical Care Medicine, 25, 614\u2013619.\n\nWilliams, C. K. I., Quinn, J., & McIntosh, N. (2005). Factorial switching Kalman \ufb01lters for condi-\n\ntion monitoring in neonatal intensive care. NIPS. Vancouver, Canada.\n\n8\n\n\f", "award": [], "sourceid": 884, "authors": [{"given_name": "Norm", "family_name": "Aleks", "institution": null}, {"given_name": "Stuart", "family_name": "Russell", "institution": null}, {"given_name": "Michael", "family_name": "Madden", "institution": null}, {"given_name": "Diane", "family_name": "Morabito", "institution": null}, {"given_name": "Kristan", "family_name": "Staudenmayer", "institution": null}, {"given_name": "Mitchell", "family_name": "Cohen", "institution": null}, {"given_name": "Geoffrey", "family_name": "Manley", "institution": null}]}