Bayesian Networks for Evaluation of Evidence from Forensic ...

Biosecurity and Bioterrorism: Biodefense Strategy, Practice, and Science Volume 11, Supplement 1, 2013 ª Mary Ann Liebert, Inc. DOI: 10.1089/bsp.2012.0081

Bayesian Networks for Evaluation of Evidence from Forensic Entomology M. Gunnar Andersson, Anders Sundstro¨m, and Anders Lindstro¨m

In the aftermath of a CBRN incident, there is an urgent need to reconstruct events in order to bring the perpetrators to court and to take preventive actions for the future. The challenge is to discriminate, based on available information, between alternative scenarios. Forensic interpretation is used to evaluate to what extent results from the forensic investigation favor the prosecutors’ or the defendants’ arguments, using the framework of Bayesian hypothesis testing. Recently, several new scientific disciplines have been used in a forensic context. In the AniBioThreat project, the framework was applied to veterinary forensic pathology, tracing of pathogenic microorganisms, and forensic entomology. Forensic entomology is an important tool for estimating the postmortem interval in, for example, homicide investigations as a complement to more traditional methods. In this article we demonstrate the applicability of the Bayesian framework for evaluating entomological evidence in a forensic investigation through the analysis of a hypothetical scenario involving suspect movement of carcasses from a clandestine laboratory. Probabilities of different findings under the alternative hypotheses were estimated using a combination of statistical analysis of data, expert knowledge, and simulation, and entomological findings are used to update the beliefs about the prosecutors’ and defendants’ hypotheses and to calculate the value of evidence. The Bayesian framework proved useful for evaluating complex hypotheses using findings from several insect species, accounting for uncertainty about development rate, temperature, and precolonization. The applicability of the forensic statistic approach to evaluating forensic results from a CBRN incident is discussed.

I

n contrast to attacks with explosives or chemical weapons, the events following a biological attack are likely to happen slowly and gradually, and once the attack is detected or suspected, it may be very difficult to distinguish it from a natural outbreak and to reconstruct the event.1 Recently, microbial forensics has emerged as a new scientific discipline that combines microbiology and forensic science with the goal of increasing the capability to investigate biocrimes. Microbial forensics is largely focused on the attribution of attack strains to a source through the use of genetic markers. However, there is often a gray zone in

which the microbial forensic evidence is not in itself sufficient for a definitive conclusion as to source, and the identification and characterization of the pathogen is rarely sufficient to identify the perpetrator. Thus, the decision will require integration with traditional forensic evidence as well as circumstantial evidence, witness testimony, and intelligence information.1 Forensic entomology is commonly used to establish a time line in a violent crime, like homicide, if insects are present.2,3 Because of their affinity for carcasses, the most common insects in forensic entomology analyses are various

M. Gunnar Andersson, PhD is senior researcher at the Department of Chemistry, Environment and Feed Hygiene; Anders Sundstro¨m, MSc, is a Bioinformatician, Department of Bacteriology; and Anders Lindstro¨m, PhD, is a Researcher, Department of Chemistry, Environment and Feed Hygiene; all at the National Veterinary Institute (SVA), Uppsala, Sweden. S64

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species of blowfly (Diptera, Calliphoridae). Blowflies develop through 6 life stages: egg, first instar larvae, second instar larvae, third instar larvae, pupa, and adult fly. Blowfly larvae develop at a certain rate at a known temperature, and the length of each life stage is known for several species at a range of temperatures. ‘‘Accumulated day degrees’’ is the sum of temperatures that the larvae have been exposed to; effectively, it is the sum of the daily mean temperatures during development.3,4 Forensic entomologists use the age of larval insects to determine the time that has elapsed since the subject’s death occurred. After a few days, the entomological estimate of the postmortem interval may be the most accurate. In certain cases, the presence or absence of certain species and the pattern of infestation on the body can give clues to other circumstances surrounding the death, such as rape, movement of the body, and the like.2 An important issue in the investigation of a suspected bioterrorism attack is the appropriate standards for interpreting and weighing forensic evidence.1 Currently, the state-of-the-art in forensic interpretation is to evaluate forensic evidence using likelihood ratios in the framework of Bayesian hypothesis testing. In those frameworks, forensic interpretation is used to evaluate to what extent results from the forensic investigation support the prosecutors’ or defendants’ hypotheses.5,6 The Bayesian approach has been applied to source determination based on measured concentrations of microorganisms.7 In the ideal case, the likelihood of observing a particular piece of evidence would be calculated using data from an explicit reference database. However, the logical approach to evaluation of evidence provided by forensic statistics is applicable also in the majority of forensic cases where an explicit reference dataset is not available.8 The opinion rendered by the expert witness is often based on an estimate of the likelihood of an observation under alternative propositions (hypothetical scenarios) based on experience, training, and the scientific literature. A prerequisite for this is, of course, that there is sufficient knowledge available to support an estimate of the likelihood or at least to provide a range of magnitude. However, in many cases there is a complex relation between the propositions and the observations involving several uncertain parameters. In such situations, Bayesian networks have proven to be a useful tool for visualizing complex relations between parameters and assessing the value of evidence accounting for the combined effect of several uncertainties6,9 as well as promoting transparency and logic.10 In forensic entomology the likelihood of observing an insect larva at a particular stage given a proposition on the time of death depends on the time for colonization, the temperature in the carcass, and the temperature-dependent growth rate of the species in question.3 Exact numbers or empirical distributions for these parameters are not readily available from databases. However, with the help of meteorological data and observations of the crime scene, it is usually possible to estimate a temperature interval that covers the true temperature inside the carcass. Similarly, Volume 11, Supplement 1, 2013

when data on the growth rate of a particular species at the relevant temperature is not available, the combination of information on growth rates of related species, the ecology of the species, and sporadic case data can often tell an expert that the growth rate is likely to be within a certain range.11 Our aim is to investigate the applicability of the forensic statistics framework to evidence from forensic entomology in a hypothetical biocrime incident. In the scenario, it is suspected that cattle died from anthrax (Bacillus anthracis) as a result of testing a spore preparation from a clandestine laboratory. A man bought a small farm in a remote village in central Sweden and restored the farm buildings, and last year a dozen cattle were bought for meat production. The farm has grazing land along a nearby lake. About 50 years earlier, the village had several cases of anthrax among cattle, and animals were buried on the ridge near a small river discharging into the lake. Despite concerns from some elderly villagers, the new farmer has used sand and gravel from the ridge when constructing roads on his lands. On Friday, July 10, a neighbor witnessed the farmer burying 5 beef carcasses and alerted police. A veterinarian who examined the carcasses concluded that the animals died from anthrax, and he collected some of the blowfly larvae thriving in the body orifices. The owner claimed that the animals were found dead in a meadow near the river. The obvious hypothesis is that the source of the anthrax was the buried cadavers,12 but because of some odd circumstances, it was suspected that the farmer was trying to dispose of animals that were part of a clandestine experiment and trying to mask it as a natural outbreak. Based on witness statements from neighbors, the animals could not have been present at the indicated site for more than 5 days. First, we show how this scenario may be described by a Bayesian network model and how the probabilities of different findings under the alternative hypotheses (p(EjHx) may be estimated using a combination of statistical analyses, expert knowledge, and simulation. Second, we show, through analyses of hypothetical cases, how entomological findings can be used to support the beliefs about the prosecutors’ and defendants’ hypotheses and how the value of evidence can be calculated. Finally, we discuss the wider application of the Bayesian framework as a tool for evaluating alternative hypotheses in the course of investigating a CBRN incident.

Materials and Methods

Constructing the Bayesian Network The Bayesian network was constructed in GeNie 2.0 (Decisions Systems Laboratory, University of Pittsburgh). This software is designed for discrete data; that is, a measurement can take only one of a limited number of predefined values. This is solved by dividing the scales for time, normalized development time, and temperature into predefined intervals. The network structure is described in Figure 1. The properties of each node are summarized in Table 1. S65

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Figure 1. Structure of a Bayesian network for estimating postmortem interval and possible movement of carcass using 2 fly species. White nodes are general hypotheses and assumptions. Light gray apply to development of L. sericata, and dark grey refer to development of L. silvarum. H: General hypothesis. T: Hypothesis on temperature. Ht: hypothesis on PMI. HT: Hypothesis on temperature. Hpse, Hpsi: Hypothesis on precolonization. PMI: postmortem interval. tpse, tpsi: Precolonization time. tdse, tdsi: Development time. tnse, tnsi: Normalized development time. Dse, Dsi: Oldest development stage. Sse, Ssi: Oldest sampled stage. Tabse, Tabsi: Data table for time to reach stage.

Selecting Interval Lengths and Prior Probabilities The boundaries of time intervals were calculated according to the formula 12*(2 - 4)n h and subsequently rounded to the closest hour, half day, or day. An alternative discretization involved the arbitrary subdivision of a 24-h period in 4, 3, or 2 equal parts. Prior probabilities for the time intervals depend on the hypotheses. If the hypothesis states that any length of the postmortem interval is equally probable, the prior probability of a time interval is set to be proportional to the length of the interval. If the hypothesis states that any magnitude of the postmortem interval is equally probable, the prior probabilities are set to be proportional to the length of a time interval divided by its mean.

as though L. silvarum has quite particular demands on the biotope, so we wanted to include it in the belief network.

Calculating Probabilities

The fictional scenario is constructed using information from several real incidents. The suspect perpetrator is based on the terrorist who performed the attacks in Oslo and Utøya on July 22, 2011.13 The noncrime scenario is based on anthrax outbreaks in Sweden in 200812 and 2011. Data for the development rate of Lucilia sericata are based on data from the literature.4,14 L. sericata is a very common blowfly, although in the northern part of its distribution range it will tend to be more synanthropic. The data on L. silvarum development is more scarce, and we used a point estimate for development rate.15 This species was chosen in part to show how even very little knowledge about a species can affect a belief network. Further, it seems

Probability values for each state in the network were calculated by simulation in @Risk for Excel 5.7.1 (Palisade Corp.), using 1,000 simulations. The probability that numbers from 2 intervals fall within a third interval or exceed an uncertain defined threshold was resolved by resampling using at least 1,000 iterations. Calculation of temperature normalized development time in node tnse was calculated in 2 ways. When temperature hypothesis involved constant average temperature, simulations were performed in a spreadsheet model using @Risk for Excel 5.7.1. When the hypothesis involved temperature variation according to observed temperature data, normalized development time was estimated by simulating development along alternative temperature profiles using a Perl 5.16.1(Active state) script. In the latter case, calculation of normalized development time was based on estimating the proportion of a developmental stage being accomplished in a 30-minute interval according to data in Table 2. In both cases, simulation involved sampling of colonization time from the development-time interval and identification of the interval of normalized time corresponding to the time of examination (t = 0). The value of evidence V for the main hypothesis Hp against the alternative hypothesis Hd is calculated manually from values of prior and posterior probabilities of Hp and Hd in the node hypothesis using the definition of the Bayes factor.8

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Sources of Data

EVALUATION OF EVIDENCE FROM FORENSIC ENTOMOLOGY Table 1. Nodes in the Bayesian Network Model Parameter H

Description General hypothesis

Type Binary

Ht

Hypothesis on PMI

Discrete

HT

Hypothesis on temperature

Discrete

Hpse

Precolonization hypothesis L. sericata Hypothesis on Precolonization hypothesis L. silvarum Postmortem interval

Fixed

Hpsi

Interval

Short time Long time Dt/t; 0,5d < t < 5d Dt/t; 1d < t Normal (24,1) Normal (22,1) Normal (20,1) Normal (18,1) Normal (16,1) Normal(14,1) e-k(t-tmin); k = 0.17, tmin 6h (flies randomly distributed over time) e-k(t-tmin); k = 0.17, tmin 6h e-k(t-tmin); k = 0.017; tmin 24h PMI- tpse

Interval

PMI- tpsi

Interval

Manual (from table2)

Interval

Manual (from table2)

Tabse

Discrete

Tabsi

Discrete

Discrete

Andersson Grassberger Andersson Grassberger Nuorteva Manual (from table 3)

Discrete

Manual (from table 3)

Discrete Discrete

Manual (from table 3) Manual (from table 3)

PMI

Discrete

States/function Procecutors hypothesis, Hp Defendants hypothesis, Hd < 5d > 3d Avr24 Avr22 Avr20 Avr18 Avr16 Avr14 Short time

Interval

T

Average temperature in carcass rounded to nearest integer

Discrete

tpse

Precolonization time L. sericata Precolonization time L. silvarum Development time L. sericata Development time L. silvarum Normalized development time L. sericata Normalized development time L. silvarum

Interval

tpsi tdse tdsi tnse tnsi

Dse

Oldest developmental stage, L. sericata Oldest developmental stage, L. silvarum Oldest L. sericata sampled Oldest L. silvarum sampled

Dsi Sse Ssi

V ¼ B ¼ ((Pr(H P jE))=(Pr(H d jE)))= ((Pr(H P ))=(Pr(H d )))

Results

Model Structure The central node in the Bayesian network is the postmortem interval (PMI), which is the parameter usually estimated Volume 11, Supplement 1, 2013

Interval

by forensic entomologists. The prior probabilities for PMI will depend on the prior knowledge of the case, and after entering the evidence, posterior probabilities for each time interval will define a Bayesian confidence interval for the PMI. The age of the insect will depend on the postmortem interval as well as the precolonization time. The development stage of the insect upon detection depends on its age and on the temperature in the carcass. A common strategy is to assume a linear model16 to calculate the accumulated temperature. An analysis of data from Grassberger and Reiter14 revealed that a S67

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linear model with a temperature threshold of *10-11C gives a reasonably good prediction of L. sericata development up to the end of the third instar. For postfeeding and pupal stages, there is an approximately linear dependence up to *22C but with Tmin of 13C and 15C, respectively, whereas at higher temperatures the development rate is relatively constant.14 To account for the nonlinear temperature dependence, the development curves including information on length in millimeters for 15, 17, 19, 21, 22, 25, 28, 30, and 34C were aligned, and the duration of each stage at intermediate temperatures was estimated by linear interpolation. For each combination of development time and temperature profile, simulation was used to estimate the time to reach the same stage at 22C. Development rate at temperatures between 10C and 15C was calculated assuming a linear model and a threshold of 10C. The node L. sericata (silvarum) oldest developmental stage defines the probability that the insect has reached a particular stage of development. Several authors report data on development of L. sericata, but the rate of development varies between and within studies. To account for this, the node L. sericata development contains alternative tables based on references 4 and 14. The alternative tables are assigned prior probabilities in the node development kinetics. In a comparison of the development data for L. sericata and the development time indicated for L. silvarum,15 we estimated that L. silvarum develops at a similar rate as L sericata or possibly faster. The node L. silvarum development thus contains alternative tables based on references 4, 14, and 15 (Table 3). The node oldest L. sericata (silvarum) sampled represents the oldest sampled stage. The probability of not finding the oldest specimen present depends on many factors, including the experience of the person performing sampling, and probabilities will reflect the expert opinion on the particular case. Accounting for non-zero probability of missing the oldest specimen is important for not overestimating confidence in the upper limit of the PMI and also for correct co-evaluation of data from different species.

Analyzing the Scenario Considering the witness statement that carcasses were not seen 5 days ago, a PMI of > 5 days would support the idea that carcasses were moved. Additionally, due to its affinity

for damp conditions,11 L. silvarum is likely to colonize dead cattle if they died in the meadow, whereas if they died at the farm, where L. silvarum is not present, precolonization time for L. silvarum would be very long. Thus, if larvae of L. sericata are apparently older than larva of L. silvarum, this fact would support the hypothesis that the carcasses were moved after death. The following cases illustrate how the Bayesian network can be used to assess the value of evidence accounting for the joint effect of all known uncertainties. Case 1 The forensic entomologist finds second instar larva of L. silvarum (max 6 mm) and first instar larva of L. sericata (3-4 mm). In this case evidence supports the hypothesis that the animals died on site (Figure 2). The ratio of Hp/Hd changed from the prior ratio of 0.5/0.5 to a posterior ratio of 7.0/93.0. This corresponds to a value of evidence (V) of 0.075 or, in other words, a value of evidence of 13.3 in favor of Hd. The postmortem interval is estimated to be in the range 1½ to 5 days, with the most probable value between 2d 16h and 3d 12h. The evidence from L. sericata alone would predict an expected value for PMI, but the range is from 1 to 7 days since then it cannot be excluded that the carcasses have been moved from a warmer or colder environment. The wide range for PMI is partly due to the uncertainty of whether data on L. sericata development from references 14 or 4 are more likely to be valid for the local insect population. Case 2 The forensic entomologist finds second instar larva of L. sericata (max 7-8 mm) and first instar larva of L. silvarum (max 2 mm). Based on the findings, the evidence points to carcasses being moved (Figure 3). The ratio of Hp/Hd changed from the prior ratio of 0.5/0.5 to a posterior ratio of 99.93/0.07. This corresponds to a value of evidence (V) of 1,427. Predicted PMI range from 1d 16h up to 12d reflects the uncertainty about temperature if the place of death is not confirmed. Obviously, it would have been possible to make a more precise assumption of temperature under the hypothesis that carcasses were moved (Hp) if it had been assumed that the only other possible place of death was the stable. This illustrates that the value of evidence is always conditional on the background information.6

Table 2. Duration of Stages at Different Temperatures based on Grassberger and Reiter Stage

10Ca

11Ca

15C

17C

19C

21C

22C

25C

28C

30C

34C

Egg Instar_1 Instar_2 Instar_3 Postfeed Pupa

N N N N N N

155.0 280.0 350.0 575.0 1700.0 N

31.0 56.0 70.0 115.0 340.0 N

28.0 39.0 54.0 79.0 200.0 442.0

24.0 27.0 42.0 60.0 118.0 239.0

19.0 23.0 29.0 47.0 103.0 158.0

17.0 19.0 26.0 46.0 94.0 137.0

14.0 16.0 19.0 36.0 87.0 125.0

11.0 11.0 16.0 30.0 87.0 120.0

10.0 10.0 15.0 27.0 87.0 119.0

8.5 9.5 12.0 27.0 82.0 120.0

a

Estimated by extrapolation.

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Figure 2. Screenshot based on case 1. Evidence speaks in favor of the defendant’s hypothesis, that the animals died at the site found no more than 5 days ago. Volume 11, Supplement 1, 2013

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Figure 2. (continued) S70



Figure 3. Screenshot based on case 2. Based on the combined evidence, the PMI is most likely in the interval 1d 16h up to 12d. The colonization by L. silvarum is most likely over 2d (20h to 5d). Evidence speaks in favor of the prosecutor’s hypothesis, that carcasses have been moved. Volume 11, Supplement 1, 2013

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Figure 3. (continued) S72


EVALUATION OF EVIDENCE FROM FORENSIC ENTOMOLOGY Table 3. Development and Sampling of L. sericata and L. silvarum Time to reach end of stage at 22C Andersona Stage Not detected egg instar1 1-2mm instar1 2-3mm instar1 3-4mm instar1 4mm instar2 4-5mm instar2 5-6mm instar2 6-7mm instar2 7-8mm instar3 8-9mm instar3 9-10mm instar3 10-11mm instar3 11-12mm instar3 12-13mm instar3 13-14mm instar3 14-15mm instar3 15mm postfeed pupa Adult/hatched pupa

Probability of sampling

Nuortevab

Stage number

Grassberger

min

Exp

max

min

Exp

max

n

n-1

n-2

17 21.8 26.5 31.3 36 42.5 49 55.5 62 67.75 73.5 79.25 85 90.8 96.5 102.3 108 202 339

21.0 26.8 32.7 38.5 48.7 57.4 66.2 75.0 77.7 84.9 92.1 99.3 106.5 113.7 120.9 128.1 136.5 254.9 477.4

21.9 28.0 34.1 40.2 48.7 57.4 66.2 75.0 81.9 89.5 97.1 104.7 112.3 119.9 127.5 135.1 144.4 288.9 556.8

22.8 29.2 35.5 41.9 48.7 57.4 66.2 75.0 86.2 94.1 102.1 110.1 118.1 126.1 134.1 142.1 152.4 356.9 636.2

11.2 14.3 17.4 20.6 23.7 28.0 32.2 36.5 40.8 44.6 48.3 52.1 55.9 59.7 63.5 67.3 71.0 132.9 223.0

14.0 17.9 21.8 25.7 29.6 34.9 40.3 45.6 51.0 55.7 60.4 65.2 69.9 74.6 79.3 84.1 88.8 166.1 278.7

16.8 21.5 26.1 30.8 35.5 41.9 48.3 54.8 61.2 66.8 72.5 78.2 83.9 89.5 95.2 100.9 106.5 199.3 334.4

0.1 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.5 0.06

0.9 0.01 0.1 0.1 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.45 0.06

0.09 0.01 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.44

n-3

n-4

0.09 0

0.05

0.44

a

Estimates of the time for L. sericata to reach a particular length are estimated from alignment with Grassberger data and interpolation. b Estimated development time for L. silvarum is based on the time to reach adult stage at 16.5C according to Nuorteva, assuming same relative interval length as L. sericata (Grassberger) and 20% uncertainty.

The sensitivity of the value of evidence to model assumptions can be assessed by systematically varying parameters. The model showed sensitivity to model parameters such as length of time interval or choice of prior probability distribution for PMI (Table 4). Assumptions on development rate for L. silvarum (Nuorteva or Grassberger/ Anderson dataset) had a clear effect on V. The logarithm of the value of evidence log(V) can be used as a way of indicating the magnitude of evidential strength,5 where the sign indicates in which direction evidence is pointing. In the cases analyzed, absolute value of log(V) was typically between 1 and 2 (Table 4). In reporting of evidence, V may be transformed into a qualitative statement using verbal scales.5,17 According to the scale proposed by Evett (cited in reference 5), a value between 1 and 2 can be expressed as moderate evidence to support one hypothesis over another. For comparison, a log(V) of 5 or > 6 can be expressed as very strong evidence and extremely strong evidence, respectively.5 In Figures 2 and 3, the probability tables in nodes tnse and tnsi (normalized development time) were calculated assuming different constant temperatures. However, tables in nodes tnse and tnsi may readily be generated by simulation (Figure 4). As illustrated in Figure 4, probability distributions for PMI have a long left tail due to the possibility of late colonization and failure to sample the oldest stage. A period of lower average temperature will result in a wider Volume 11, Supplement 1, 2013

probability distribution for the PMI. Values of evidence for hypotheses on PMI are given in Table 4.

Discussion In this work we demonstrate how the Bayesian framework makes it possible to combine different sources of information and include information on uncertainty. In addition to confidence interval for the PMI, considering all uncertainties makes it possible to estimate the value of evidence of the entomological findings in relation to alternative propositions, typically prosecutors’ and defendants’ hypotheses. Presenting evidence as a confidence interval is deemed inappropriate in court proceedings since it disregards evidence falling outside an arbitrarily chosen confidence level (eg, 95%).5 The same reasoning applies to (entomological) evidence used in criminal investigations. For example, if entomological evidence points to a PMI of 4 to 8 days at 95% confidence, posterior odds ratio for the hypothesis PMI > 8 days would be 2.25/97.5 corresponding to log(v) = - 1.59. In other words, the evidence would provide moderate support for a PMI less than 8 days.5 Depending on the shape of the probability distribution for PMI, evidence may provide strong support for a PMI of less than 11 days. It should not make investigators exclude the S73

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Figure 4. Example of PMI estimation using simulation along temperature profiles. Time 0 is the time the carcass is examined. Development of L. sericata was simulated along 5 different temperature profiles representing the most likely temperature (Exp) and alternative profiles (-2,-1, + 1, + 2) representing the range of possible temperatures in the carcass. The PMI was estimated assuming equal probability to the development tables from Grassberger and Anderson. The dashed lines represent the posterior probability density distribution for PMI after sampling an instar1, instar2, or instar3 larva.

possibility that a person or animal died earlier if other evidence points in another direction. Adopting a Bayesian framework of evidence evaluation in forensic entomology may help to prevent misuse and misinterpretation of entomological evidence in court and during investigations. It may serve as a tool for structuring and presenting information in complex investigations such as CBRN incidents. Irrespective of whether PMI is reported as a traditional confidence interval or as value of evidence for a hypothesis, the validity of the result will depend on the assumptions. Confidence interval for PMI based on temperature data for the presumptive crime scene can be very misleading if the corpse has been moved, or if the temperature at the scene has been modified, and thus evidence supporting or against moving of the carcass or modification of local temperature will affect the uncertainty about PMI. In other words, the estimated posterior distribution for PMI will be conditional on other evidence.6 In this ex-

ample, the other evidence would be the relative time of colonization for the everywhere present L. sericata and a species, L. silvarum, characteristic for damp meadows. The verdict in the case ‘‘R v T’’18 has sometimes been interpreted as Bayes theorem, and likelihood ratios should not be used in evaluating forensic evidence in UK courts, except for DNA evidence. The verdict has initiated an intense debate.10,19 However, the main issue in ‘‘R v T’’ was that the data applied did not meet the standard that justifies a probabilistic evaluation of evidence.5,18 In our opinion forensic entomologists often have substantial scientific data to back up their estimates, in comparison to experts in many other forensic disciplines,6 both when it comes to point estimates of developmental rate and estimates of uncertainty or variation. Whether the data are of sufficient quality to justify the presentation value of evidence in court as a likelihood ratio or on a corresponding verbal scale8 will have to be assessed on a case-by-case basis in accordance with the

Table 4. Sensitivity of the Value of Evidence (V) to Dataset, PMI Prior and Time Scale Discretization L. sericata: Grassberger/Anderson 50/50 L. silvarum: Nuorteva P = k*Dt/t PMI prior Interval length Case1 V log(V) Case2 V Log(V) S74

Both species: Grassberger/Anderson 50/50

P = k*Dt

P = k*Dt/t

P = k*Dt

Normal

Short

Normal

Short

Normal

Short

Normal

Short

7.0/93.0 - 1.12

8.3/91.7 - 1.04

1.9/98.1 - 1.71

4.0/96.0 - 1.38

3.43/96.6 - 1.45

1.2/99.8 - 1.92

0.91/99.1 - 2.04

0.27/97.3 - 2.56

99.93/0.07 3.15

99.9/0.10 3.00

99.9/0.1 3.00

99.75/0.25 2.60

98.7/1.3 1.88

99.2/0.79 2.1

99.8/0.19 2.72

99.6/0.36 2.44



legal tradition in the country. In any case, the presented approach will be useful for assessing how sensitive the conclusions are to assumptions and uncertainties in the data. Significant amounts of data exist on the development of insects of forensic interest.3 Data on insect development are typically not complete, and data may be missing at part of the relevant temperature interval or be based on a different geographical population that may have a different temperature optimum. Consequently, it is usually not feasible to estimate probability distributions for development rate as function of temperature by training a model with data. Since data format is not standardized, various approaches are needed to generate estimates that may include linear or nonlinear regression, automatic or visual alignment, and inter- and extrapolation. In this example, growth data for the temperature interval 15C to 34C was available only from reference 14, whereas data for a limited temperature interval was available from reference 4. Aligning data on duration of stages from dataset 14 and dataset 214 indicated that the deviation between the datasets was approximately proportional to development rate in the alignable region. The assumption in the current model is that this is true over the relevant temperature range (Figure 5). Based on this assumption, the information from reference 15 was used to estimate the growth rate of L. silvarum (Figure 5). Such an estimate is of course uncertain, and in this example, this was accounted for by the

model assumption that the growth rate can be up to 20% higher or lower (Table 3). Due to the very large uncertainty about growth rate of L. silvarum, a PMI estimate based on this species alone would come with a very wide confidence interval (results not shown). However, in combination with data from L. sericata, it is still important for the value of evidence. As illustrated in case 1, the approximately simultaneous colonization by L. silvarum and L. sericata supports the view that the animal indeed died near the water and, thus, the assumption that the temperature in the carcass has been around 18C (Figure 2, node T; Figure 3, node T). Development time is normalized in node tnse using Table 2, corresponding to the line Data 1 in Figure 5, whereas node Dse describes the variation between reference 14 and reference 4 at 22C. In the example, average temperatures were mostly in the range covered by dataset 2, and thus the simplistic model was deemed good enough. However, in cases involving temperatures closer to the critical temperature, it would be necessary to account for uncertainty about the threshold temperature and the shape of the normalization curve, for example, by providing alternative definitions tables in node tnse and tnsi. In this work we demonstrate how Bayesian frameworks can be used to estimate values of entomological evidence in an investigation using a combination of available predictive models and free BBN software. Some authors have proposed predictive models for forensic entomology based

Figure 5. Left: Growth rate (1/d) as a function of temperature. Data 1 is the table (eg, Grassberger) used for normalization of development time for L. sericata in node tnse. Data 2 is the most likely rate from the alternative dataset for L. sericata (eg, Anderson). Data 3 corresponds to the point estimate of growth rate of L. silvarum at 16.5C used to generate the table in node tnsi. The dashed lines indicate how the function for growth rate is shifted depending on the table used in nodes Dse or Dsi. Volume 11, Supplement 1, 2013

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on simulation of complex system models.20,21 In principle such predictive models could be integrated in Bayesian Belief Network approach. A predictive model will not be better than the data it is based on, and the uncertainties addressed in this work, like temperature at the site and the within- and between-species variability in temperature dependence and developmental rate, would still be of concern. Transparency of reasoning is a critical issue when expert statements are used in legal cases,10 and for this reason simpler models may be favored. In Morvan et al,20simulation is used to address influence of microbial growth on temperature in the carcass. However, differences between local temperature in the carcass and measured environment temperature could equally well be addressed by adjusting the probability distribution in node T. The different approaches to estimate the variability in growth rate illustrates why the network is referred to as a Bayesian Belief Network. Posterior probabilities for prosecutors’ and defendants’ hypotheses and the confidence interval for PMI will be based on a combination of data and expert knowledge. A forensic problem can generally be addressed at different levels of detail, resulting in different model structures.6 The appropriate level of detail depends on the available knowledge. If there is a strong reason to believe that the expected precolonization time has varied significantly over the period of interest, for example, due to fluctuations in temperature, a network structure accounting for variable colonization rates may give a greater precision in the PMI estimate and possibly a higher value of evidence. However, the higher value of evidence would be conditional on the validity of the assumption, and, in the absence of a good model, it may be wiser to use a conservative approach where variability is accounted for by increasing the variance in the prior distribution for precolonization time using the structure of Figure 1. In the examples, the value of evidence for the hypotheses are relatively low, reflecting the many sources of uncertainty. However, the value is dependent on the hypothesis to be tested. Due to the asymmetric shape of the posterior probability distributions of PMI (Figure 4), it is generally easier to obtain a high value of evidence when the hypothesis involves a lower bound for PMI. A natural extension of the evaluation of evidence in this case is to include data from genotyping as nodes in the Bayesian network. Anthrax can persist in the ground for a long time. However, due to the poor documentation of cattle graves and subsequent exploitation of the site, the failure to isolate anthrax would not be sufficient to exclude buried carcasses as the source. However, the outbreaks in Sweden in the early 21st century were associated with imported bone meal, which has been associated with the A lineage of Bacillus anthracis.12 Thus, the probability of observing a particular anthrax strain would be different under the prosecutors’ and defendants’ hypotheses, and knowing the genotype (eg, lineage) of the anthrax in the

dead cows would modify the likelihood ratio of the 2 hypotheses. The ability to combine circumstantial evidence from very different types of investigations, such as forensic entomology, witness statements, and type matching, makes the Bayesian networks a promising tool for investigating CBRN incidents.

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Acknowledgments This research was supported by/executed in the framework of the EU project AniBioThreat (Grant Agreement: Home/ 2009/ISEC/AG/191) with financial support from the Prevention of and Fight against Crime Programme of the European Union, European Commission—Directorate General Home Affairs. This publication reflects the views only of the authors, and the European Commission cannot be held responsible for any use that may be made of the information contained therein.

References 1. Koblentz GD, Tucker JB. Tracing an attack: the promise and pitfalls of microbial forensics. Survival 2010;52(1):159186. 2. Smith KGV. A Manual of Forensic Entomology. London: British Museum (Natural History); 1986. 3. Amendt J, Campobasso CP, Gaudry E, Reiter C, LeBlanc HN, Hall MJR. Best practice in forensic entomology— standards and guidelines. Int J Legal Med 2007;121:90-104. 4. Anderson GS. Minimum and maximum development rates of some forensically important Calliphoridae (Diptera). J Forensic Sci 2000;45(4):824-832. 5. Aitken C, Roberts P, Jackson G. Fundamentals of Probability and Statistical Evidence in Criminal Proceedings. Guidance for Judges, Lawyers, Forensic Scientists and Expert Witnesses. London: Royal Statistical Society; 2010. 6. Taroni F, Aitken C, Garbolino P, Biedermann A. Bayesian Networks and Probabilistic Inference in Forensic Science. Chichester: John Wiley & Sons; 2006. 7. Keats A, Lien FS, Yee E. Source determination in built-up environments through Bayesian inference with validation using the MUST array and joint urban 2003 tracer experiments. In: Proceedings of the 14th Annual Conference of the Computational Fluid Dynamics Society of Canada; July 16-18, 2006; Kingston, Canada. http://eer.cmc.ec.gc.ca/s_activites/ s_crti/s_crti-02-0093rd/s_publications/SourceReconstruction_ Keats_Lien_Yee_CFD2006.pdf. Accessed July 30, 2013. 8. Nordgaard A, Ansell R, Drotz W, Jaeger L. Scale of conclusions for the value of evidence. Law, Probability & Risk 2012;11(1):1-24. 9. Jarman KH, Kreuzer-Martin HW, Wunschel DS, et al. Bayesian-integrated microbial forensics. Appl Environ Microbiol 2008 Jun;74(11):3573-3582. 10. Sjerps MJ, Berger CHE. How clear is transparent? Reporting expert reasoning in legal cases. Law, Probability & Risk 2012;11:317-329.

EVALUATION OF EVIDENCE FROM FORENSIC ENTOMOLOGY 11. Fremdt H, Szpila K, Huijbregts J, Lindstro¨m A, Zehner R, Amendt J. Lucilia silvarum Meigen, 1826 (Diptera: Calliphoridae)—a new species of interest for forensic entomology in Europe. Forensic Sci Int 2012;222:335-339. 12. Lewerin SS, Elvander M, Westermark T, et al. Anthrax outbreak in a Swedish beef cattle herd—1st case in 27 years: case report. Acta Vet Scand 2010;52:7. 13. Bech Gjørv A, Auglend RL, Bokhari L, et al. Rapport fra 22.juli-kommisjonen. Norges Offentlige utredninger 2012:14.: Departementenes servicesenter Informasjonsforvalitning. Oslo; 2012. 14. Grassberger M, Reiter C. Effect of temperature on Lucilia sericata (Diptera: Calliphoridae) development with special reference to the isomegalen- and isomorphen-diagram. Forensic Sci Int 2001 Aug 15;120(1-2):32-36. 15. Nuorteva P. Sarcosaprophagous insects as forensic indicators. In: Tedeschi CG, Eckert WG, Tedeschi LG, eds. Forensic Medicine. Philadelphia: Saunders; 1977:1072-1095. 16. Damos P, Savopoulu-Soultani M. Temperature driven models for insect development and vital thermal requirements. Psyche 2012. 17. Nordgaard A, Hoglund T. Assessment of approximate likelihood ratios from continuous distributions: a case study of digital camera identification. J Forensic Sci 2011 Mar;56(2):390-402.

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18. Royal Courts of Justice, London. EWCA Crim 2439. 2010. http://www.bailii.org/ew/cases/EWCA/Crim/2010/2439.pdf. Accessed July 30, 2013. 19. Hamer D. Discussion paper: the R v T controversy: forensic evidence, law and logic. Law, Probability & Risk 2012;11:331-345. 20. Morvan G, Jolly D, Dupont D, Kubiak P, eds. A decision support system for forensic entomology. Proceedings of the 6th EUROSIM Congress; 2007. 21. Veremme A, Lefevrea E, Morvanc G, Dupont D, Jollya D. Evidential calibration process of multi-agentbased system: an application to forensic entomology. Expert Systems with Applications 2012;39(3):2361-2374. Manuscript received December 21, 2012; accepted for publication June 3, 2013. Address correspondence to: M. Gunnar Andersson, PhD Department of Chemistry, Environment and Feed Hygiene National Veterinary Institute (SVA) SE- 751 89 Uppsala, Sweden E-mail: [email protected]

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