Evaluate the claim "we can predict who will become a criminal"

Matrix Forecasting and Behaviour Sequence Analysis: Part of the Timeline Toolkit for Criminal Investigation

D. A. Keatley1,2 & D. D. Clarke1,3

# Society for Police and Criminal Psychology 2020

Abstract Solving serious crimes such as sexual assault, rape, and murder takes a considerable amount of investigation time. Despite efforts, many crimes may be unsolved, and go ‘cold’. These cases are typically extensive and reviewing the material can be prohibitively time consuming. The current manuscript proposes the combination of two methods, or ‘tools’, for timeline analyses: Matrix Forecasting and Behaviour Sequence Analysis (BSA). Matrix Forecasting provides a clear and comprehensive approach to outlining predictions investigators make, the rationale underlying these predictions, the accuracy, and the evidence. Matrix Forecasting also outlines areas for future investigation, for example, if new technology becomes available or new test results are returned. The BSA provides a statistical, visual pathway map that outlines the proposed or proven steps in a crime. The combination of these methods provides a new approach to mapping criminal investigations and has been effectively used in several real-world cold case reviews. To illustrate the benefits of this combined approach, a real-world example, the Jeffrey MacDonald, aka Green Beret Killer case, will be analysed using Matrix Forecasting and BSA to show the benefits of the method in terms of providing a quick-guide for future review and solvability factors.

Keywords Matrix forecasting . Behaviour sequence analysis . Cold case . Criminal investigation

A person is murdered. The investigation into this most serious of crimes is intense and dedicated. To begin, a number of criminological and forensic approaches are taken. Suspect lists are developed and interviews begin in earnest. Not for lack of person-power, time, or effort, the investigation loses momentum in terms of fresh leads and new hopes for solv- ability. Eventually, the case is labelled ‘cold’ and relegated to the area of police investigation that typically slips from most people’s collective conscience—most, except the families in- volved and Detectives still working tirelessly to solve it. It is at this stage that the likelihood of solving the case reduces rap- idly. Resources are allocated to other cases, and potential for new leads reduces as time moves forward. Every few years, with the changing of Detectives, or from external pressures,

new reviews of cold cases may be undertaken. One of the difficulties with each new review is effective time manage- ment. Many Detectives prefer to use a grounded or bottom-up approach, starting at the beginning and working forwards through the case for themselves. This provides the opportunity to re-analyse and examine every piece of evidence; however, in cases spanning multiple decades, it can prove prohibitively time consuming—in the case presented here, it would include the reading of tens of thousands of pages of documents. It can also lead to Detectives focusing on early suspect lists only to later realise that the suspect was cleared. Clearly, a better method or toolkit is needed to help solve these cases, and that is what is outlined here.

To expedite the review process, many Detectives prefer to give a summary, an ‘Executive Report’, at the beginning of their case files. This report outlines the main progression of the case and serves as a reminder for the Detective, who may have to work other cases for a prolonged period, as well as offering new Detectives or outside assistance a quick over- view of the case. While a helpful resource, these reports can suffer from various biases or heuristic reasoning (Nisbett and Ross 1980; Sniezek and Henry 1989), which may unintention- ally misguide future investigation attempts. These reports also do not always outline the full extent of the investigation in

* D. A. Keatley [email protected]

1 Researchers in Behavior Sequence Analysis (ReBSA), Nottingham, UK

2 School of Law, Murdoch University, Perth 6150, Australia 3 School of Psychology, University of Nottingham, NG72RD,

Nottingham, UK

Journal of Police and Criminal Psychology https://doi.org/10.1007/s11896-020-09367-1

terms of all the avenues explored and all the potential possi- bilities for further investigation. Indeed several authors have highlighted the risks of biases in criminal investigation cases (Chapman et al. 2019; Roach 2019). The difficulty is that many detectives may remain sceptical of the applied validity of academic research, preferring to rely on their experience or ‘gut instinct’ as a means of progressing in a case, such confir- mation bias is particularly problematic in cold cases, wherein later investigators may be more likely to agree with and sup- port prior investigators’ decisions and conclusions rather than derive new ones (Roach 2019).

Police investigations are open to cognitive biases, such as heuristics (Chapman et al. 2019, Goldsmith 2001). Many Cold Case Task Force and major police investigations use a paramilitary, rank-style structure (Chapman et al. 2019), in which final decision making comes down to a Senior Investigating Officer (in the UK). In Task Forces in USA, Detectives may be the sole investigating officer, thus making all of their own decisions, or take direction from their Chiefs. This structure of investigations means decision making plays a large role and therefore biases in decision making can affect outcomes of cases. Many officers adopt a blue ‘curtain of silence’ (Chapman et al. 2019) meaning that awareness of improprieties are often left hidden or undiscovered until re- view (Goldsmith 2001). Clearly, scientific labs and studies are not free from biases either; however, researchers are often more aware of these biases and the move towards preregistered reporting shows a conscious effort to improve the scientific practice more generally. A method that makes police more aware of these biases in their investigation pro- cess is more likely to lead to better, more well-informed deci- sion making (Chapman et al. 2019). The Matrix Forecast outlined in the current paper has a column asking investigators to list biases that may affect their decisions and thinking, which can then be independently reviewed if needed.

Traditional academic approaches to Forensic Psychology and Criminology typically take a statistical approach (using regression analyses for example) or qualitative means (e.g. thematic or interpretative phenomenological analysis). These methods are useful for understanding the effect of individual risk factors on ‘predicting’ outcome behaviours, as is the case with regression model approaches. They may also provide key insight into the themes or intra-personal views of victims and criminals, as is the case with qualitative methods. However, these methods typically lack ability to account for complex, temporal chains of behaviours that evolve over time. Regression models, for example, can take multiple predictor variables (e.g. age, gender, personality, motivation) to predict an outcome (e.g. crime); however, regression analysis reduces complex outcomes to a single behaviour, omitting whether other behaviours and events affect the outcome. More com- plex statistical models exist (such as hierarchical modelling

etc.); however, these methods quickly become unintelligible to police investigation, and still cannot easily be used to cal- culate longitudinal complex dynamics (Keatley 2018). Qualitative methods, in contrast, allow for in-depth under- standing of behaviours, but are harder or impossible to quan- tify in a meaningful way, and often end in reports that are almost as long as the base material in the investigation.

What is required is a method that allows a comprehensive executive summary of the main findings in the case, as well as which pathways have been explored, and which remain open to future investigation (perhaps in the advent of new technol- ogy or evidence being found), and finally, a method that forces investigators to confront and explicitly label their potential for biases. The focus of the current paper is to outline a novel approach currently being used on several current and cold case investigations. The approach merges two existing methods: Matrix Forecasting (Clarke 1992, 2004) and Behaviour Sequence Analysis (Keatley 2018) to provide investigators with a new approach for their cases. While there is a growing body of research on BSA, there is much less recent research on the type of matrix forecasting, Seven-Column Forecasting, presented in this paper. Each method will be outlined and then a real-world case will be presented to show how the combined approaches of forecasting and sequencing can be used in on- going police investigations. This is the first article, to the au- thors’ knowledge to tentatively combine these methods, and is presented as a novel area for research with the aim of being qualified and developed by researchers in the area, alongside police investigations as well as on cold cases available for general research practice (such as the one used as an example in this paper).

Matrix Forecasting

The ability to accurately predict or forecast future events is clearly beneficial in a wide range of disciplines and applied fields. Many researchers have developed multiple methods for improving human judgements and forecasting accuracy (Makridakis 1994); however, most humans and computer programmes remain relatively inaccurate at predicting future events (Clarke 1992; Makridakis and Hibon 2000). A large reason for the inaccuracies of human judgement is an individ- ual’s inability to correctly assess their own biases and adjust further judgements based on that (self-) awareness or group biases (Budowle et al. 2009; Cooper and Meterko 2019; Sniezek 1992; Sniezek and Henry 1989). This is typically further complicated by complexity of measuring and mapping temporal, dynamic behaviours (Keatley 2018). Typically, when a forecast is made by a practitioner or researcher, the accuracy is recorded, and the next prediction may be about another behaviour or event entirely. Research using regression models suffer this type of issue. To improve this area, a

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method was developed to help improve human judgement and forecasting accuracy: Matrix Forecasting (MF; Clarke 2004).

Quantitative forecasting methods use increasingly complex computer algorithms and artificial intelligence operations to predict future events (Geurts, Box, and Jenkins 1977; Seymour, Brockwell, and Davis 1997). However, such methods typically require larger datasets structured in a way that is not practical or possible in criminal (cold) case investi- gations. Also, many police officers are sceptical of using com- puter programmes or ‘black box’ approaches to solving crime, which they do not fully understand or feel able to defend if called upon in court. Therefore, a method that helps improve officers’ forecasting accuracy and ability to move forward and apply the same principles in similar crimes is practical and clearly beneficial. Many individuals, guided by television rep- resentations of investigations, may believe that all police have access to large databases of data, and while it is true that police can access such databases, the reality is that they are often facing a large backlog of requests and cold cases are seldom prioritised. Therefore, while these databases may prove useful for some investigations, for older cold cases, they are either not readily accessible or the lack of information in the cold case means that the database is not useful.

The method proposed here is a qualitative approach that has similar logic to that of machine learning, more specifically ‘genetic algorithms’ (Forsyth 1989). These genetic algorithms are rule-inducing programmes that borrow Darwinian evolu- tion principles to constantly improve the accuracy of predic- tions. Rules are created and evaluated, and those that do not lead to improved forecasting are abandoned, while the better ones are retained. Rules can then be developed (‘bred’ or ‘mutated’ in evolutionary terms) to offer further rules for evo- lutionary testing. Matrix Forecasting uses the same principle in refining and improving judgement forecasts. Furthermore, Matrix Forecasting does not require expensive programmes or machines and can be run in cold case task forces to assist with investigations. It may be that after completing the Matrix Forecast, new potential leads are highlighted, which detectives can then forward to machine databases, rather than attempting to scan old hand-written or typed pages and then forward these in some meaningful format.

Matrix forecasting (MF; Clarke 1992) is designed for use with a group of experts, such as Cold Case Detectives. Experts consider a structured series of events and progress step-by- step to forecast future behaviours or events in the timeline. Effectively, they forecast what happened next. The first col- umn in Matrix Forecasting is the first step in the process, in which an individual makes an ad hoc prediction of the next event. Then, the expert is asked to provide a rationale for why they made this prediction, this is important in order to under- stand the possible inferences or biases being made (perhaps the detective is drawing from similar past cases etc.). Step 3 is to provide a summary of the real next event as it becomes

known. Following this, a quantitative estimate or accuracy in Step 4 is provided for the match or mismatch between steps 1 and 3 (i.e. how accurate was the ad hoc prediction compared with reality). Step 5 requires a more qualitative summary of the nature of the discrepancy (was it entirely inaccurate or wrong-by-degrees). Following this, experts are asked to con- sider what changes would be required to their predictive strat- egy (steps 1 and 2) in order to prevent such errors (shown in step 5) from occurring again. Finally, step 7 is a cumulative list of predictive guidelines based on step 6 that should be taken forward for future forecasts. These columns can be reduced or elaborated as seen fit by the investigators.

While the MF approach has proved useful for improving judgements of future events, it has needed to be developed to make it more applied for cold cases. In terms of cold cases, Detectives are more interested in agreement between investiga- tors, routes for further investigation, and possible leads. These have been taken into account in the approach presented in this paper (see Fig. 1). While the MF provides an in-depth, infor- mative approach to the decision-making process and offers greater insight for future investigation, it leads to complex ma- trices being formed that may be harder to follow for new de- tectives. The MF approach may also lose or obfuscate some of the timeline that is important to understand in criminal investi- gations. A method is required, therefore, that outlines clearly and succinctly the temporal progression of behaviours. Such a method exists and has been widely used in Forensic and Criminological areas: Behaviour Sequence Analysis (Ivanouw 2007; Keatley 2018; Keatley, Barsky, and Clarke 2017).

Behaviour Sequence Analysis

Understanding the temporal dynamics of a crime has obvious benefits for investigations. Detectives can piece together the likely progression of events and begin to form an overview of the crime commission. This temporal outline allows detectives to consider discrepancies between crime scenes so that they may consider whether the current crime is unique and distinct, or forms part of a series (Keatley and Clarke 2019). One leading method for statistically analysing and providing flow diagrams of behavioural chains is Behaviour Sequence Analysis (BSA; Keatley 2018). Temporal Analysis has been applied across a wide range of crimes, including burglary and theft (Homel, Macintyre, and Wortley 2014); violence (Taylor, Keatley, and Clarke 2017); sexual assault and rape (Ellis, Clarke, and Keatley 2017; Fossi, Clarke, and Lawrence 2005); and serial homicide (Keatley, Golightly, Shephard, Yaksic, and Reid 2018). The output of BSA is a flow diagram (called a State Transition Diagram) that shows how one be- haviour follows another, creating lengthier sequences of steps in a crime. Although underpinned by statistics, diagrams can be interpreted without any further statistical understanding.

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The method of BSA requires three stages. First, a crime episode is parsed into separate, distinct behaviours. These behaviours are then categorised so that similar types of be- haviours across different crime scenes can be compared. For example, if we see ‘stabbed’ in crime 1, and ‘knife penetra- tion’ in crime 2, we may consider these Behaviour type ‘A’ (although we should check with Detectives, autopsy and Medical Examiners, if possible, to ensure that the two types of injuries are commensurate). This categorisation process is repeated across the entire episode, or multiple episodes, until every behaviour has been given an agreed category label.1

This typically produces chains of code, which stand for be- haviours: A➔B➔C➔D…n (where each letter refers to a be- haviour type category until the crime episode ends, n). The final stage of BSA is the analysis, wherein the transitions between behaviour pairs are analysed. Therefore, whereas the crime episode gives a chain ‘A➔B➔C➔D’, the lag-one sequence analysis focuses on transitions between pairs of be- haviours (A➔B, B➔C, C➔D etc.). More complicated forms of BSA exist allowing for longer chains to be analysed (e.g. [AB]➔C, [BC]➔D); however, there are various reasons why these higher-order BSA approaches are not favourable in re- search or application (See Keatley 2018 for a review).

A strength of the BSA approach is that it shows the chain of behaviours as they fit together across a crime, and/or multiple crimes. This allows investigators to begin to see patterns emerg- ing, and most recently, researchers have developed a method for linking crimes using BSA, known as Behaviour Fingerprinting (Keatley and Clarke, 2019), as well as using BSA to predict geographic movements, known as Behaviour Tracking (Keatley et al., 2018). Both Behaviour Fingerprinting and Tracking methods are useful alongside the Matrix Forecasting approach. Clearly, BSA works best with multiple cases or for collating multiple investigators’ views, in which common path- ways can be detected and analysed. But, cold cases are typically single-homicides, without others in a series to link to. Furthermore, BSA works best when all behaviours in a se- quence are known and can be mapped clearly, which is

obviously not the case in many cold cases, where missing or unknown information is typically a cause of the case going cold. Therefore, BSA needs to be developed to better handle single cases, with missing segments of the episode, which is where predictions of future behaviours in the sequence are crit- ical. Combining matrix forecasting with BSA is a parsimoni- ous, effective means of moving both methods forward for investigations.

Combining the Methods

Combining MF with BSA has proved useful in a number of real-world cold cases the authors are currently actively in- volved in; however, as on-going cases, these are currently not open to publication. To show the benefits of a timeline toolkit approach combining MF and BSA, an open-access case will first be outlined, and then analysed using the novel approach. The Jeffrey Macdonald ‘Green Beret Killer’ case will be used to show how MF and BSA could have been used to assist with investigation process and follow-up case re- views.2 A full portrayal of the case spans around 10,000 pages of court and investigative documents, and 3 books (totaling around 2000 pages)—clearly beyond the scope of the present article. Therefore, a brief summary of the case as it first be- came known to investigators responding to the scene is given below. For ease of comprehension, the details of the case as they became known have been re-written into a clearer se- quence (obviously, in real cases some parts are not so imme- diately apparent).

Dispatchers at Fort Bragg receive an emergency call at 0342, on February 17th, 1970. Jeffrey Macdonald re- ports a “stabbing”. First responders arrive on scene and are confronted by the bodies of Colette (wife), Kristen (Daughter), and Kimberly (Daughter), all are found dead in their bedrooms. Jeffrey was located next

1 Best practice is to seek agreement between multiple coders and experts involved in the case.

2 We appreciate that the case is now legally ‘solved’ and no longer cold; however, it took 9 years before a conviction was made, and so for the purposes of this paper it stands as a useful example.

1. Prediction 2. Rationale 3. Degree of

certainty

4. number of other

routes

5. Discrepancy

between routes

6. Number of

investigative leads

7. Actual outcome

if known (and

continue with 7

column if so)

Awoken by intruders

Suspect statement 75 (only available evidence at present) N=3

1 Wholly different suspects

Forensic test for intruders

For future follow- up

Wakes up (no intruders)

High percentage of familicide cases

25 (based solely on experience /bias) N=1

1

Note. N = number of investigators who agree on this transition being the most likely next step. Fig. 1 Matrix Forecast for start node. N = number of investigators who agree on this transition being the most likely next step

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to his wife, alive but bleeding, on the floor of their bed- room. Colette and the daughters had all been viciously attacked (blunt force trauma and multiple stab wounds3). Jeffrey was bleeding from the abdomen area, and immediately taken to hospital. When first-responders arrived, Jeffrey claimed (and still does) that he had fallen asleep in the living room, to be awoken to the sounds of his wife, Colette screaming. Stood over him, as he awoke, were 4 intruders (3 men, and a woman). He described the woman as wearing a floppy white hat and a blonde wig, and said she was holding a flickering light (like a candle) and chanting “Acid is groovy, kill the pigs”. The 3 men then attacked Jeffrey with a club and he felt something sharp in his chest/abdomen. He passed out and when he awoke he checked on the state of his family – to find them all dead. He then phoned the base CID to raise help. The CID, after investigation, held a different view – that Jeffrey himself, alone had viciously attacked and mur- dered his wife and children, and then staged the scene and his own injuries to fit his narrative.

This was the information given to investigators first arriv- ing at the scene and interviewing Jeffrey MacDonald at the hospital. Given the open-access of Fort Bragg, closing down the base was not quickly and effectively possible. Of impor- tance, a female matching the description that Jeffrey had given was seen in the area by a responding officer. The aim here is not to get into the prolonged legal aspects of the case, which have spanned multiple decades. Instead, the next step is to show how a combination of forecasting and BSA could have been used in the investigative process.

In the case of Jeffrey MacDonald, the process would begin by establishing each Detectives perceived timeline of events. This is best done in isolation, so that each Detective's timeline is not biased or influenced by others. The coding process is then very similar to standard BSA. Timelines are first parsed into discrete behaviours and events, then categorised such that all Detectives’ accounts can be cross-examined. Finally, anal- yses can be conducted on the sequences to show behavioural chains. For the current case, many Detectives may believe MacDonald and put his being knocked unconscious very soon after been awoken. Others, however, may be suspicious of the events as told by MacDonald, and consider alternative time- lines entirely, for example: Jeffrey is on sofa ➔ Jeffrey goes to his bedroom ➔ Jeffrey assaults Colette.

The state transition diagrams provide a clear and informa- tive way of showing the most likely timelines, as perceived by detectives. These timelines could be assessed for consistency (Abbott and Hrycak 1990; Rosenbaum 1989) or Behavioural Fingerprints (Keatley and Clarke 2019), which is a more so- phisticated method of analysing similarity between sequential timelines. The major benefit of combining BSA with MF,

however, is to take the state transition diagram a step further and break-down the decision-making process for each transi- tion in the chain. This clarifies reasoning and biases, and high- lights opportunities for future investigation. This process al- lows clear mapping of the investigative process for future investigators if the case goes cold. In the current case, the starting point of the sequence can be put into the matrix to clarify why different starting positions have occurred (see Fig. 2).

Clearly, there are two proposed starting points to this se- quence of events, depending on whether we believe Jeffrey’s account or not. Each has a very different ramification in terms of proposed suspect(s). While the state transition diagram pro- vides a very quick overview of the possible pathways (see Keatley 2018 for overview), the matrix provides more in- depth detail of how each node and transition were decided. Future investigations may look to this to decide whether new tests have become available (i.e. M-VAC), or whether all leads have been investigated. Use of dates in column 7 allows in- vestigators to keep a track of when testing has been conducted. Again, the columns can be developed to suit the investigators needs; but over several cases, the 7 presented here provide the most parsimonious starting point for building a Matrix Forecasting approach, and fits most closely with published examples (Clarke 1992). These columns for further testing are what may also prompt Detectives to begin a targeted vet- ting of computer databases to answer specific questions, thus expediting the process.

As is typical in the early stages of investigations, multiple Detectives will have competing and divergent views, a pro- cess that is helpful for the investigation, but can lead to con- fusion of facts and uncertainty of leads. Combining MF with BSA offers a way of bringing-together multiple views and theories and documenting them in a way that current and future investigators (if the case goes cold) can review and update accordingly, if new technology, testing, or testimony becomes known. Figure 2 outlines how matrix forecasting and BSA can be combined to show the possible chains of behav- iours, underlying rationales for pathways, and areas for future investigation.

Behaviour Tracking

Another timeline tool that is useful for investigations and can be used as part of the proposed approach is Behaviour Tracking (Keatley et al., 2019), which can be used to show pathways of movements around the home or other geo-spatial areas. These perceived geo-temporal movements can then be compared with known blood stains and forensic evidence in attempts to sup- port or refute them. One of the key areas of initial investigation in the MacDonald case was the blood stains around the prop- erty. Owing to the fact that each member of the MacDonald

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family had a different blood type (Colette: Type A; Jeffrey: Type B; Kimberly: Type AB; Kristen: Type O), the prosecution soon drew a proposed route that Jeffrey walked and the order in which he killed his family (the arrows in Fig. 3). Figure 3 pro- vides a simplified version of the prosecution’s proposed se- quence of movements. In active investigations or cold cases, the Behaviour Tracking approach could be used to show mul- tiple different possible pathways (derived from investigators’ proposed sequence of movements, and supported by evidence where possible). Behaviour Tracking can show transitions agreed by the majority of investigators (shown as line thick- ness); it can also be a useful pictorial display of different spatio- temporal movements, which can focus testing of evidence to remove or support particular routes.

The Combined Approach and Solvability

In an ideal world, all crimes would be given the maximum amount of time needed to investigate and solve; however, Police Departments are typically overworked and under-staffed, so a system for prioritizing solvability of cases is needed. A further benefit of the current combined approach is to use it as a method of solvability scaling. Within Cold Case investigation teams, a major hurdle before investigating a case is knowing which cases to prioritise. It is not always clear or easy to know which cases are more likely to be solved, without full and exten- sive reviews. Currently, a number of Law Enforcement Organisations around the world have developed their own metric

system for rating solvability of cases (typically relating to avail- ability of evidence, witnesses, and time-since-crime). The new approach outlined here could be used to show how many possi- ble leads remain in a case, in a quick and clear way. The sequence chains and matrices could be used as a simple counting method of how many new leads are now possible, by quickly scanning column 7. If column 7 has a lot of ‘unknown’ outcomes, then investigators could code how many of these could be further investigated, perhaps with new methods or new witness informa- tion. Cases could be ranked in terms of how many nodes or links they have, and how many of these are open to testing (to either remove as possible leads or support as most likely routes). More recent advances in technology might suggest more opportunities for more testing of evidence to be conducted.4

This is also a point in the case in which solvability issues can also be illustrated (see Fig. 4). For example, if we look at the events in the sequence ‘Colette stabbed’, then this leads to there being blood in the Master Bedroom. Blood stains are clearly an important part of police investigations; but, the interpretations and tests that could be done on them can be listed and marked- off once completed. Therefore, the traditional state transition diagram in BSA can be developed to quickly show future in- vestigators what evidence exists (or existed) and what tests

4 In reality, the property has been re-built and no evidence remains; however, within the 9 years before Jeffrey was sentenced, such testing could have been conducted. Similarly, in several current cold cases, there are nodes in the sequence chain that have multiple possibilities for further testing. The argu- ment here is a case with many more open links for further testing are likely more solvable than those showing only ‘dead-ends’ (i.e. no fresh routes for testing or investigation).

Start

Jeffrey awoken

Intruders break in

Intruders move to Living Room

Intruders a�ack Colle�e

Fig. 2 Combining BSA with MF. The BSA is presented in the top right, and is underpinned by the standard BSA approach of Chi-square analyses and standardised residuals. Each node of the BSA is underpinned by a

row from the MF. This can be animated more clearly on digital formats, or presented like this for printed reports

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were or were not completed. Aside from the obvious investiga- tive leads, this could be used for, it also provides investigators with a relatively simple approach to calculating solvability: more ‘unknown’ nodes in the diagram indicate more opportu- nity for further testing or investigation. If no new avenues for investigation exist, then the review may more quickly discern the case remains cold.

Further Testing

At present, the combined MF-BSA approach only passes the face validity test, and clearly more testing and trialling is needed in order to develop and validate the method further. In real-world contexts, the method has been applied mostly to homicide cases. More testing is required to show whether the method is useful across different criminal cases, and whether it needs to be devel- oped for different crimes. The first proposed step for academics interested in the area is to continue testing the method on ‘known’ cases, so that it can be developed further if needed, known cases also have the benefit of allowing rolling horizon forecasting to be conducted to test the process more quickly. Once several papers have been published, preferably on different cases and crimes, a final matrix approach can be outlined, which

can then be more strongly suggested to police departments to use. The method could be used in a rolling horizon forecast approach, wherein solved cases are re-started with the use of this method, and researchers map how much ‘quicker’ the case can be solved with this method. This may also highlight which biases are most important to misleading investigations, as well as which strategies are most useful in solving (different types of) crime.

1. BEGIN

2. Cole�e stabbed

4. A�acks Kristen

3. A�acks Kimberly

5. Throws weapons outside

7. Phones for help

6. Stabs himself

Fig. 3 Simplified Behaviour Tracking of Jeffrey MacDonald’s movements around the home, according to the prosecution. For ease of clarity, only the first few transition arrows have been included. Behaviour Tracking is better suited to digital presentations, which allow overlapping and divergences to be more easily presented. Not presented here is Jeffrey

MacDonald’s own Behaviour Tracking of movements. The important part for investigations, in several cases, is to map all of the different possible pathways and see which account for the evidence, and which are outliers

Fig. 4 BSA, testing, and solvability. The oval nodes are the BSA transitions. The rectangle nodes show testing that needs to be conducted related to each node. Grey nodes indicate testing has been completed, unshaded indicate testing still needed. This can be animated on computer systems, or printed out clearly for reports

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Conclusions

Police detectives and cold case task forces in particular are overworked and under-staffed. Demands of daily crime push many cold cases to the edges of police departments’ budgets and many go unsolved for several decades. Recent media inter- est, however, is likely to put the spotlight back on solving cold cases, and applied methods are needed to assist police officers in this. Many cold cases do not have the forensic evidence that modern cases can provide, so alternative methods of investiga- tion and summarising are required. The added benefit of the proposed combined approach is that it works best with specialist academics involved, who are well-versed in the cognitive bias, decision making, forecasting, and sequencing literature. This method, therefore, helps to build bridges between academics and practitioners and has so far proven a useful tool in real- world cases. When using the method ‘in vivo’ has becomes even more powerful as even basic computer–generated presentations can show the flow of sequences, spotlight particular areas of future investigation, and highlight what specialist knowledge might be necessary (e.g. forensic odontology, profiling).

Compliance with Ethical Standards All procedures per- formed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research commit- tee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards

Conflict of Interest The authors declare that they have no conflict of interest.

Ethical Approval There are no participants in the current study.

Informed Consent There are no participants in the current study.

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