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2 Fax to: or (UK) or (INDIA) To: Re: Springer Correction Team 6&7, 5th Street, Radhakrishnan Salai, Chennai, Tamil Nadu, India Artificial Intelligence and Law DOI: /s Validation of a bayesian belief network representation for posterior probability calculations on national crime victimization survey Authors: Michael Riesen Gursel Serpen Permission to publish I have checked the proofs of my article and q I have no corrections. The article is ready to be published without changes. q q I have a few corrections. I am enclosing the following pages: I have made many corrections. Enclosed is the complete article. Date / signature

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4 Metadata of the article that will be visualized in OnlineFirst ArticleTitle Article Sub-Title Please note: Images will appear in color online but will be printed in black and white. Validation of a bayesian belief network representation for posterior probability calculations on national crime victimization survey Article CopyRight - Year Springer Science+Business Media B.V (This will be the copyright line in the final PDF) Journal Name Artificial Intelligence and Law Corresponding Author Family Name Serpen Particle Given Name Suffix Division Organization Address Gursel Author Family Name Riesen Particle Given Name Suffix Division Organization Address Electrical Engineering and Computer Science, College of Engineering University of Toledo 43606, Toledo, OH, USA gserpen@eng.utoledo.edu Michael College of Law University of Toledo 43606, Toledo, OH, USA Schedule Abstract Received Revised Accepted This paper presents an effort to induce a Bayesian belief network (BBN) from crime data, the national crime victimization survey (NCVS). This BBN defines a joint probability distribution over a set of variables that were employed to record a set of crime incidents, with particular focus on characteristics of the victim. The goals are to generate a BBN to capture how characteristics of crime incidents are related to one another, and to make this information available to domain specialists. The novelty associated with the study reported in this paper lies in the use of a Bayesian network to represent a complex data set to non-experts in a way that facilitates automated analysis. Validation of the BBN s ability to approximate the joint probability distribution over the set of variables entailed in the NCVS data set is accomplished through a variety of sources including mathematical techniques and human experts for appropriate triangulation. Validation results indicate that the BBN induced from the NCVS data set is a good joint probability model for the set of attributes in the domain, and accordingly can serve as an effective query tool. Keywords (separated by '-') National crime victimization survey - Bayesian belief network - Machine learning - Probabilistic query - Posterior probability calculations - Joint probability distribution - Model validation Footnote Information

5 1 Artif Intell Law DOI /s Validation of a bayesian belief network representation 3 for posterior probability calculations on national crime 4 victimization survey 5 Michael Riesen Gursel Serpen 6 7 Ó Springer Science+Business Media B.V Abstract This paper presents an effort to induce a Bayesian belief network (BBN) 9 from crime data, the national crime victimization survey (NCVS). This BBN defines 10 a joint probability distribution over a set of variables that were employed to record a 11 set of crime incidents, with particular focus on characteristics of the victim. The 12 goals are to generate a BBN to capture how characteristics of crime incidents are 13 related to one another, and to make this information available to domain specialists. 14 The novelty associated with the study reported in this paper lies in the use of a 15 Bayesian network to represent a complex data set to non-experts in a way that 16 facilitates automated analysis. Validation of the BBN s ability to approximate the 17 joint probability distribution over the set of variables entailed in the NCVS data set 18 is accomplished through a variety of sources including mathematical techniques and 19 human experts for appropriate triangulation. Validation results indicate that the 20 BBN induced from the NCVS data set is a good joint probability model for the set 21 of attributes in the domain, and accordingly can serve as an effective query tool. 22 Keywords National crime victimization survey Bayesian belief network 23 Machine learning Probabilistic query Posterior probability calculations 24 Joint probability distribution Model validation 25 A1 A2 A3 A4 A5 A6 M. Riesen College of Law, University of Toledo, Toledo, OH 43606, USA G. Serpen (&) Electrical Engineering and Computer Science, College of Engineering, University of Toledo, Toledo, OH 43606, USA gserpen@eng.utoledo.edu

6 M. Riesen, G. Serpen 26 1 Introduction 27 The national crime victimization survey (NCVS) data is available for online access 28 by the public-at-large (ICPSR 2005). The same online resource also offers basic 29 statistical analysis on the data as well. In the event more sophisticated statistical 30 analysis is desirable, the NCVS data can be further processed through a standard 31 statistics package like the SPSS (SAS 2004). It is no secret that performing 32 statistical analysis is a difficult task even where a software package such as the 33 SPSS is at one s disposal. A certain degree of expertise in statistics is needed as well 34 as the ability to use a sophisticated software package. It is desirable to provide the 35 domain experts, professionals, and researchers in criminal justice who may not be 36 necessarily well-versed in statistics with the ability to perform more comprehensive 37 statistical analysis on a data set like the NCVS. Specifically, querying for posterior 38 probability calculations of any subset of variables or attributes in the NCVS data 39 and further providing access to the knowledge entailed by this data are highly 40 attractive. 41 A Bayesian belief network (BBN) offers a convenient means to model a dataset 42 through empirical means using Bayesian statistics. A specific instance of a BBN is 43 an approximation under the conditional independence assumption to the joint 44 probability distribution of all the attributes included in the analysis. Once the BBN 45 model is generated, it can be queried for posterior probability calculations for any of 46 the attributes of the NCVS dataset, which has well above 200 variables (U.S. Dept. 47 of Justice 2005). It would be possible to query any variable for its posterior 48 probability distribution or posterior expectation. The intended utility is that the BBN 49 model provides information that is not readily available through the main NCVS 50 repository or other online resources but can only be generated following application 51 of appropriate and advanced statistical techniques. A BBN manages to capture the 52 model for the joint probability distribution of all attributes (associated with the 53 NCVS) under certain domain-specific independence assumptions, thereby making 54 the model development and subsequent querying (inferencing) process computa- 55 tionally feasible with respect to time and space (memory) cost. 56 Traditionally, statistical techniques have been used to extract implicit informa- 57 tion from data, but effective statistical analysis requires a mathematical background 58 that even few domain experts typically possess. Moreover, statistical analysis is 59 time consuming, as the analyzer must formulate and test each hypothesis 60 individually; a daunting task, given the number of possibilities implicit in even a 61 moderately sized database. Likewise, the NCVS dataset has been used in research 62 for a variety of social and scientific disciplines. The United States Department of 63 Justice Bureau of Justice Statistics (BJS) has produced and published statistical 64 reports for use by the public and by academics, a sample of which can be found at 65 Outside the statistical reports produced by BJS, users 66 are limited in their analysis of NCVS by their own mathematical background. 67 It becomes apparent how desirable it would be to offer easy access to this dataset 68 for the domain experts, professionals, and researchers in criminal justice. This can 69 be accomplished through a BBN model of the NCVS that can easily be queried for 70 any subset of the attributes. In essence, the mathematics-based challenges that the

7 Posterior probability calculations on national crime victimization survey 71 user might face are potentially minimized as the query model permits the user to 72 specify the types of information desired, with the analysis conducted autonomously 73 or with minimal human guidance. Once a BBN is developed either through 74 inductive means, constructive means, or a combination of two methods, any 75 variable or attribute may be queried for posterior probability calculations for all of 76 its states or values. Particularly, the query model provides a unique and valuable 77 ability to probe any attribute of interest regardless of the user s knowledge of 78 advanced mathematical and statistical skills. This query model is further poised to 79 enhance our understanding about complex social and economic dynamics and 80 processes at interplay Problem statement 82 Despite the recent pioneering work in the research and application of Bayesian 83 networks, it is clear that the legal profession remains generally uninformed and 84 inexperienced when it comes to Bayesian reasoning. (Fenton and Neil 2000). 85 Accordingly, there is a need to further expose the knowledge that is potentially 86 hidden and embedded within the NCVS dataset beyond the basic statistical 87 presentation offered by the published and online literature including the USDOJ 88 BJS and others. Accordingly, this study aims to assess the feasibility of developing a 89 query model based on a BBN for the NCVS data for use by the domain specialists in 90 criminal justice. Steps involved in realizing this aim include development of a BBN 91 model of the NCVS data, integration of the BBN model with an inferencing 92 mechanism, and comprehensive validation of the BBN model. Emphasis of the 93 study reported herein is on the validation of the BBN model s ability to faithfully 94 capture the conditional independence relationships among the attributes in the 95 NCVS data Background The national crime victimization survey 98 The NCVS series, previously called the National Crime Survey (NCS), has been 99 collecting data on personal and household victimization since 1973 (U.S. Dept. of 100 Justice 2007). An ongoing survey of a nationally representative sample of 101 residential addresses, the NCVS is the primary source of information on the 102 characteristics of criminal victimization and on the number and types of crimes not 103 reported to law enforcement authorities. It provides the largest national forum for 104 victims to describe the impact of crime and characteristics of violent offenders. 105 Twice each year, data are obtained from a nationally representative sample of 106 roughly 49,000 households comprising about 100,000 persons on the frequency, 107 characteristics, and consequences of criminal victimization in the United States. The 108 survey is administered by the U.S. Census Bureau (under the U.S. Department of 109 Commerce) on behalf of the BJS (under the U.S. Department of Justice). 110 Occasionally there have been extract or supplement files created from the NCVS

8 M. Riesen, G. Serpen 111 and NCS data series. This extract contains two data files, a weighted person-based 112 file, and a weighted incident-based file, which contain the core counties within 113 the top 40 NCVS Metropolitan Statistical Areas (MSAs). Core counties within these 114 MSAs are defined as those self-representing primary sampling units that are 115 common to the MSA definitions determined by the Office of Management and 116 Budget for the 1970-based, 1980-based, and 1990-based sample designs. Each MSA 117 is comprised of only the core counties and not all counties within the MSA. The 118 person-based file contains select household and person variables for all people in 119 NCVS-interviewed households in the core counties of the 40 largest MSAs from 120 January 1979 through December The incident-based file contains select 121 household, person, and incident variables for persons who reported a violent crime 122 within any of the core counties of the 40 largest MSAs from January 1979 through December Household, person, and incident information for persons reporting 124 certain non-violent crime are excluded from this file. 1 The 40 largest MSAs were 125 determined based on the number of household interviews in an MSA. 126 Significant highlights of the NCVS are as follows. The geographic coverage is United States with the time period of 1979 through Also, the date(s) of 128 collection comprises 1979 through The unit of observation entails household, 129 person, and crime incident. The sampled population consists of persons in the 130 United States aged 12 and over in core counties within the top 40 NCVS 131 Metropolitan Statistical Areas. A stratified multistage cluster sample was used with 132 the data files including three weight variables which are household, person, and 133 incident. The data was collected by face-to-face interview or computer-assisted 134 telephone interview. 135 For this study, we chose to use the NCVS MSA Incident File. The incident-based 136 file contains select household, person, and incident variables for persons who 137 reported a violent crime within any of the core counties of the 40 largest MSAs from 138 January 1979 through December The NCVS MSA Incident file contains ,203 instances and a total of 259 attributes Bayesian belief network 141 A joint probability distribution defines probability values for all value combinations 142 for a given number of random variables and can be used to perform statistical 143 inference or reasoning. In other words, any query can be computed from the full 144 joint distribution. The challenge is of course the computation complexity of such an 145 endeavor. More specifically the space complexity is on the order of d n, where n is 146 the number of random variables and d is the number of values, which suggests the 147 total number of probability values that need to be stored and remembered. Also 148 certain queries might take up to d n steps to compute, hence indicating the time 149 complexity. Perhaps more importantly from a pragmatic viewpoint is the issue of 150 how all these probability values will be determined, i.e. the acquisition bottleneck. 1FL01 1FL02 1 The incident-based file includes five property crimes: Attempted/completed purse snatching and pocket picking; Burglary; Attempted forcible entry; Attempted forcible entry; and Attempted/completed theft.

9 Posterior probability calculations on national crime victimization survey 151 Bayesian networks offer a way for a compact representation of the joint 152 probability distribution through conditional independence. A BBN may be 153 considered as a directed acyclic graph (DAG) where nodes represent random 154 variables and directed edges encode a set of conditional independence relationship, 155 for example, each variable is conditionally independent of its non-descendents 156 given its parents. Each node in the BBN has a conditional probability table (CPT) 157 associated with it. The DAG and the CPTs together uniquely define a joint 158 probability distribution in factored form. The conditional independence assumptions 159 among a subset of variables, in most cases, will effectively reduce the space and 160 time complexity associated with the full joint distribution to a manageable level. A 161 brief introduction to BBN is provided in the Appendix. 162 The process of developing or inducing a Bayesian network from data entails two 163 phases: the first one is to learn the structure of the network from the data while the 164 second one is to learn the values of the parameters, or more specifically the entries 165 in the CPT for each of the variables. Compared to the structure learning, the 166 parameter learning problem is relatively straightforward and is well established in 167 the literature (Mitchell 2006). On the other hand, structure learning is a much more 168 challenging aspect and still receives significant attention from the research 169 community. 170 A BBN enables the user to extract a posterior belief. All conditional 171 independence relationships and conditional probabilities are incorporated into the 172 network and are accessible through a highly automated process typically imple- 173 mented in software. Accordingly, a once tedious and costly (in terms of 174 computation) method of extracting posterior beliefs in a given domain is now 175 space- and time-efficient for most practical purposes. 176 The main technical objective of the proposed work is to develop a good 177 representation of the joint probability distribution for the set of attributes in the 178 NCVS data in the form of a BBN. Such an endeavor requires the following 179 methodology for success. The initial phase entails the BBN development, which is a 180 highly empirical undertaking. There are numerous structure, i.e. the specific 181 instance of the DAG, and parameter, i.e., entries in the CPTs for each node in the 182 DAG, learning algorithms that must be tested to determine which combination 183 offers an optimal BBN model of the NCVS data. 184 A set of software packages will be utilized as development and deployment tools, 185 which will entail SSPS (SAS 2004) to generate the data in comma-separated value 186 (CSV) format, WEKA (Witten and Frank 2005) to preprocess the data and generate 187 the BBN model, and JavaBayes (Cozman 2007) to facilitate the querying of the 188 BBN. The WEKA software is used to develop a BBN model of the NCVS dataset 189 (Bouckaert 2005). This model is then imported into the JavaBayes tool to facilitate 190 the querying process. In more specific terms, the WEKA software application is 191 utilized to develop a BBN using the NCVS MSA data set. Next, WEKA is used to 192 export the BBN for the NCVS to the JavaBayes package, complete with CPTs and 193 identified conditional independence relationships. Now with the network at one s 194 disposal, it is possible to extract a posterior belief by making a query on any variable 195 (attribute) of choice. All relevant CPTs are accessed through the already-created 196 dependency arcs in the network and the BBN inference algorithm works through the

10 M. Riesen, G. Serpen 197 once tedious computations, and produces the requested probability. Prior to the 198 availability of a BBN and a computationally feasible inference mechanism (i.e. as in 199 JavaBayes), a query for a posterior belief of a given attribute would require a long 200 sequence of of probability calculations all dependant on the evidence that is 201 provided. 202 The BBN creation process consists of multiple phases. Once the dataset is 203 identified, i.e. in this case the NCVS MSA, the discrete variables of each attribute 204 must be converted to nominal values, as required by WEKA 2. Upon said 205 conversion, the dataset is imported into the WEKA software platform. 3 During 206 the next phase, any particular pre-processing algorithms that are appropriate must be 207 implemented in order to prepare the data for the learning process. Once the dataset 208 is preprocessed and ready for application of learning algorithms, the next step is to 209 select the appropriate structure learner to be implemented on the dataset. 210 Empirical experimentation with the parameters of each learner enables the user to 211 optimize the learning algorithm for any particular dataset. After the WEKA 212 software constructs the BBN network in the form of a classifier for a user- 213 designated class attribute, the BBN is tested on a sub-sample of the data and the 214 class prediction accuracy is reported. In the end, a complete BBN embedded with 215 the CPTs for each attribute (node) and a representation of the links (arcs) is 216 produced. WEKA is able to store the newly-created BBN in an XML (Version 3.0) 217 format file (Bray et al. 2006), which is compatible with the supported input file 218 formats for the software application next in the tool chain, i.e. JavaBayes. It is 219 important to note that the WEKA environment introduces a bias for the specific 220 instance of the BBN network that could be developed from a given dataset: that bias 221 is in the form of requiring designation of a specific class variable and subsequent 222 development effort geared towards optimizing the various performance metrics with 223 respect to this class variable. It is conceivable that this particular bias might not be 224 necessarily desirable for all cases, and hence a different BBN development tool (that 225 employs inductive machine learning techniques and domain expertise in a 226 collaborative context to construct the network) might be appealing. 227 The WEKA software environment, being mainly a classifier development tool, 228 does not facilitate querying the BBN for any attribute other than the class attribute 229 which is specified by the user. On the other hand, the JavaBayes software tool, 230 through its graphical user interface (GUI), is able to import an already-built BBN 231 model and facilitate querying of any attribute, and not just the class attribute, for its 232 posterior probability value among many other options. Accordingly, the XML- 233 formatted BBN produced in WEKA is imported into JavaBayes. Once imported, 234 JavaBayes allows the user to identify the evidence and query a posterior belief of 235 any attribute. 236 The version of the NCVS MSA dataset employed for the proposed research study 237 uses 200? variables with over 200,000 instances. Accordingly, it is necessary to 2FL01 2FL02 3FL01 3FL02 2 For proper processing by WEKA, each discrete value was converted into a nominal value by introducing an x as a prefix to the represented value. 3 The use of the GUI interface: Explorer is appropriate for the user not familiar with command line interface. The GUI interface becomes quite costly in terms of memory usage on the computing platform.

11 Posterior probability calculations on national crime victimization survey 238 utilize a computing platform that has the needed memory and processing power to 239 effectively handle such computations as typically associated with inducing a BBN. 240 The computing platform used for this study is a Sun Fire TM V480 server and runs 241 the Solaris TM 10, the Sun TM version of the UNIX operating system. The server has 242 four 1.05/1.2 GHz UltraSPARC TM III Cu processors, a main memory of 8 GB 243 DRAM configured for these four processors, and high-capacity and high-speed main 244 storage Development of bayesian belief network model for NCVS 246 This section presents the development of a BBN model of the NCVS data. The BBN 247 model is conceived to approximate the full joint probability distribution of the 248 attributes in the NCVS data and is intended as a generic query tool. The main 249 objective is to develop a highly accurate representation of the joint probability 250 distribution for the set of attributes in the NCVS data in the form of a BBN 251 (Chickering et al. 1995; Cooper and Herskovits 1992). Such an endeavor requires a 252 particular methodology for success. The initial phase entails the BBN development, 253 which will necessitate managing the inductive learning process and maintaining a 254 wide scope and depth while noting the highly empirical nature of this undertaking. 255 There are numerous structure and parameter learning algorithms that must be tested 256 to determine which combination offers an optimal BBN model of the NCVS data. 257 Some of the specific issues to be dealt with include the instance of the DAG, and 258 computation of entries in the CPTs for each node in the DAG. Once the NCVS data 259 is preprocessed, a (classifier) model of the BBN for the victimization attribute 4 is 260 developed through comprehensive empirical work. Next, the leading performer 261 BBN classifier is selected for importation to the JavaBayes tool to facilitate 262 inferencing. The BBN model of the NCVS data is then validated through a set of 263 queries formed with the help of domain experts, published literature, and the dataset 264 itself. 265 The NCVS MSA dataset (U.S. Dept. of Justice 2007) originally consisted of discrete-valued attributes (variables) and 216,000 distinct instances of reporting. 267 Due to redundancy and the scope of this study, 34 attributes were excluded. It is 268 common in the pre-processing stage to be concerned with missing values within the 269 dataset that would inevitably adversely affect the development of the BBN. The 270 original NCVS data has a discrete value of 9 representing a value of out of 271 universe for any values that are potentially problematic: 272 Out of Universe (or INAP) is used in the codebook documentation to 273 designate those items on the questionnaire that were not appropriate for certain 274 respondents (based on information gathered throughout the interview) and 4FL01 4FL02 4FL03 4FL04 4 The class attribute Victimization is variable V4529, which represents a list of 16 personal (violent) crimes and property crimes as defined by the NCVS. The V4529 was selected as the class attribute due to the general interest focused on the end-crime committed and the inherent crime classification nature of the variable itself.

12 M. Riesen, G. Serpen 275 therefore should not have been asked. For example, hospital tenure questions 276 are not asked of victims who were not injured. (U.S. Dept. of Justice 2007) 277 The INAP value therefore alleviates any pre-processing concerns for missing or 278 unusable values, but conversely floods the network with discrete values consisting 279 of a 9 value. Furthermore, for the software development tool chain that we intend 280 to employ, there is a need that all discrete values for every attribute be a nominal 281 value. The data set used in this study is available in multiple formats, but for the 282 purposes of our tool chain, it had to undergo certain conversions to address these 283 specific issues. 284 The NCVS MSA Data ( ) is compiled into two data files. The files are 285 labeled as date set one (DS1), Person File, and data set two (DS2), Incident File. 286 Both files are available from the Inter-university Consortium for Political and Social 287 Research (ICPSR) in the following formats: Logical Record Length with SAS, 288 SPSS, and Stata setup files, SAS transport (XPORT) file, SPSS portable file, and 289 Stata system file. We retrieved the data in SAS format. Using the SAS software, we 290 converted the SAS file into a CSV formatted file, a format that is recognized by 291 WEKA. Once the SAS file was converted, we were able to load the dataset into 292 WEKA as a CSV file. For ease of editing and practicality, we used WEKA to simply 293 save the NCVS MSA Incident file as an attribute relation format file (ARFF). At this 294 point the incident data is now in the required format and available for use in the tool 295 chain, which also requires that all discrete values be nominal. Using a simple text 296 editor, numeric values were manually changed into discrete nominal values. To be 297 sure that all values were proper and included, the values were cross referenced with 298 the codebook provided by the ICPSR. Finally, the BBN models developed through 299 WEKA were saved in the XML BIF format (Bray et al. 2006) to be loaded in 300 JavaBayes in order to facilitate the querying process. 301 The BBN induction algorithms were trained and tested on the NCVS Incident 302 dataset of 216,000 instances with 66 33% training-testing data split. Results suggest 303 that a number of BBN models performed exceptionally well as classifiers for the 304 Victimization attribute. In fact, all listed versions of the local hill climbers and 305 local K2 search algorithms (de Campos et al. 2003; Madden 2003) led to 306 classification performances with 97% or better accuracy. It is noted that the build 307 time for these algorithms are on the same order and therefore, the build time was not 308 considered as a further significant factor in performance comparisons. However, 309 since the classification accuracy rates are so close to each other, the value of 310 parameter number of parent nodes was identified as the next significant 311 discriminating factor. Accordingly, the BBN model generated through the local K2 312 structure learning algorithm with up to four parent nodes and with Bayesian scoring 313 function then became the choice for further experimentation since it facilitates up to 314 four parent nodes in addition to superior performance in terms of high classification 315 accuracy. 5 The Bayesian Interchange Format (BIF) file description of best 316 performing BBN classifier model for the Victimization attribute of the NCVS data, 5FL01 5FL02 5FL03 5 The complexity of model should be kept as low as possible. However, since BBN by definition approximates a joint PDF, we would desire the approximation quality to be good: this is achieved by a slightly more complex model through a greater value for the number of parents variable.

13 Posterior probability calculations on national crime victimization survey 317 which includes the complete connectivity as represented by directed edges and 318 CPTs for all attributes is available from the authors upon request Validation of bayesian belief network model 320 Once the BBN is induced from the data and subsequently tuned by the domain 321 experts, the next step is the testing for validation of the premise that the network 322 faithfully represents the full joint probability distribution subject to conditional 323 independence assumptions. 6 This validation can be accomplished through a two- 324 step process. The first step is to compare values computed by the BBN with those 325 supplied by the domain experts, statistical analysis, and the literature. The second 326 step is to query any variable for its posterior distribution or posterior expectation 327 based upon a subset of or all of the variables in the network. Domain experts may be 328 consulted to formulate a set of so-called interesting, meaningful or signif- 329 icant queries to pose to the BBN. 330 The best-performing BBN classifier model generated by WEKA for the NCVS 331 dataset is intended as a reasonable approximation for the full joint probability 332 distribution for the set of attributes in that dataset. Evaluation and validation of the 333 BBN model was subjected to a rigorous process through the JavaBayes and entails 334 the following phases: 335 Perform elicitation review that consists of reviewing the graph structure for the 336 model, and reviewing and comparing probabilities with each other. 337 Perform sensitivity analysis that measures the effect of one variable on another. 338 Compare the model with expert judgment. Two domain specialists were 339 recruited to help with this phase. Dr. Lois A. Ventura who is an assistant 340 professor in the Department of Criminal Justice, and Ms. Gabrielle Davis who 341 teaches in the College of Law Legal Clinic and directs the Domestic Violence 342 Clinic provided domain expertise needed for this task. 343 Compare the model predictions with the ground truth (i.e. including but not 344 limited to the statistical data furnished by the US Department of Justice Bureau 345 of Justice Statistics) Elicitation review 347 The elicitation review involved an overall review of node definitions, observable 348 links (edges), independence assumptions, and probability distributions as defined by 349 the CPTs for each node. Initial attention focused on NCVS attributes V (Victimization) and V4399 (Reporting Incident to Police). The variable V represents a list of 16 personal (violent) crimes and property crimes as defined by 352 the NCVS. When training the Bayesian model the V4529 attribute was selected as a 6FL01 6FL02 6FL03 6 Building a single Bayes net and computing inferences for all types of queries through this one structure may not be optimal. It might be beneficial to learn a query-dependent Bayes net structure on the fly using a fast structure learning method assuming that the high computational cost can be managed effectively.

14 M. Riesen, G. Serpen Table 1 Values for NCVS Attribute V4529 Victimization National Crime Victimization Survey: MSA Data, ICPSR 4576 United States Department of Justice, Bureau of Justice Statistics Codebook Value label x60 x61 x62 x63 x64 x65 x66 x67 x68 x69 x70 x71 x72 x73 x74 x75 Description of violent/property crime Completed/attempted rape Sexual attack/assault/serious assault Attempted/completed robbery with injury from serious assault Attempted/completed robbery with injury from minor assault Attempted/completed robbery without injury Attempted/completed aggravated assault Threatened assault with weapon Simple assault completed with injury Assault without weapon without injury Verbal threat of rape/sexual assault Verbal threat of assault Attempted/completed purse snatching and pocket picking Burglary Attempted forcible entry Attempted/completed motor vehicle theft Attempted/completed theft 353 class attribute. As the selected class attribute, V4529 represents the classification of 354 other variables and attributes based upon the criminal act committed on a victim. 355 With over 200 potential class attributes to select from, the focus remained on V as a reasonable selection of crime classification values on which to train and build 357 the Bayesian model. 7 Specifically, the discrete values associated with the V Victimization attribute as used by the NCVS represent a specific classification of 359 crime and are defined in Table Although the best performing BBN model, did not include any parent nodes for 361 V4529, the CPT values reported in Table 2 are consistent with general victimization 362 values reported by the BJS (Catalano 2004). Considering the CPT for V4529 we 363 observed the general probabilities for the victimization of the general public. In 364 review, the CPT for V4529 was consistent and concordant with similar statistical 365 reports published by the BJS (Catalano 2004). Specifically and as an illustrative 366 case, the probabilities associated with property crime make up about 77% of total 367 crime as reported by the BJS. The CPT values for x72 through x75 reported in 368 Table 2 represent property crimes, and when combined, offer an estimate of 79.79% 369 for the victims of property crime. These two values, namely the 77% and 80%, are 370 reasonably close to be considered a good approximation. 7FL01 7FL02 7FL03 7FL04 7FL05 7 The selection of the V4529 attribute as a class attribute was driven the author s and experts interest in classifying the data based upon the end crime committed. It is understood that other class attributes may provide interesting models and final results; however, with over 200 attributes and the extensive processing time in training and building, a single constant class attribute provided a constant for comparison in developing the final model.

15 Posterior probability calculations on national crime victimization survey Table 2 Conditional probability table for the victimization attribute V4529 with no evidence in the BBN model of NCVS data Description of crimes for victimization attribute V4529 label p(v4529) Completed/attempted rape x Sexual attack/assault/serious assault x Attempted/completed robbery with injury from serious assault Attempted/completed robbery with injury from minor assault x x Attempted/completed robbery without injury x Attempted/completed aggravated assault x Threatened assault with weapon x Simple assault completed with injury x Assault without weapon without injury x Verbal threat of rape/sexual assault x Verbal threat of assault x Attempted/completed purse snatching and pick pocketing x Burglary x Attempted forcible entry x Attempted/completed motor vehicle theft x Attempted/completed theft x In the case of CPT for the V4399 (NCVS attribute representing whether victim 372 reports incident to police) the BBN model used in this study contained four parent 373 nodes, which were V4529, V4335, V4024, and V4030. Translating the NCVS 374 notation, this indicates that depending on the values indicated for a particular crime 375 (V4529), whether household furnishings were taken (V4335), where the incident 376 happened (V4024), and whether there was evidence of forcible entry in the form of 377 damage to window (V4030), the CPT for V4399 will be affected. The parent 378 nodes selected by this model are reasonable and in accordance with general trends. 379 It is well documented that attempted or completed rape is less frequently reported 380 than car theft and such a distinction in the type of crime (V4529) would reasonably 381 affect the probability of reporting to the police (V4399). It is also well documented 382 that the probability of reporting a crime to police is dependent on where the incident 383 occurred (V4024) and the severity of such an incident (Hart and Rennison 2003). 384 To recognize the consistency of the CPTs from one attribute to the next, we next 385 considered an attribute representing race. Table 3 presents the CPT for V3023 (race 386 of victim). The CPT for V3023 includes parent nodes V3012 (representing the 387 relationship of the victim to the reference person, where reference person is 388 defined as the individual identified as owning, buying, or renting the dwelling), and 389 V2049 (representing the race of the reference person). In Table 3, the attribute 390 V3012 is represented by the variable x1, and a discrete value of x1 for V indicates that the victim is the husband of the reference person. From this prior 392 condition, the CPT displays the probabilities of the victim s race given specific

16 M. Riesen, G. Serpen Table 3 The conditional probability table for NCVS attribute V3023 (Race) when prior evidence suggests the relationship of victim to reference person is husband to wife V3012=x1 V3023 V2049 x1 (white) x2 (black) x3 (American Indian, Aleut, Eskimo) x4 (Asian, Pacific Islander) x1 (white) x2 (black) x3 (American Indian, Aleut, Eskimo) x4 (Asian, Pacific Islander) x values of V2049 (race of reference person). We expected to find a correlation 394 between the race of the reference person and the race of the victim. In fact, the CPT 395 demonstrates the expected trend: if the reference person is white (V2049 = x1) 396 there is a 98.18% chance the victim is white (V3023 = x1) given that the 397 relationship between the two is husband and wife (V3012 = x1). 398 To better display the correlation, we considered the same CPT, but now with the 399 victim being the daughter of the reference person, where V3012 is represented by 400 the variable x4). The CPT for this case is displayed in Table 4. A review of the CPT 401 in Table 4 demonstrates the stronger correlation between a victim s race (V3023) 402 and her parents race (i.e. reference person race V2049). Again, when a specific 403 discrete value for the reference person s race is considered, there is a high 404 probability that the victim, in this case daughter (V3012 = x4), will have the same 405 race value. 406 Additionally, CPTs for V2024, V2026 and MSACC were analyzed for consistency 407 with modern trends and known relationships as presented by the experts in the field. 408 As shown in Table 5, the number of housing units in the victim s living structure Table 4 The conditional probability table for NCVS attribute V3023 (Race) given the relationship of victim to reference is daughter to parent V3012=x4 V3023 V2049 x1 (white) x2 (black) x3 (American Indian, x4 (Asian, Pacific Aleut, Eskimo) Islander) x1 (white) x2 (black) x3 (American Indian, Aleut, Eskimo) x4 (Asian, Pacific Islander) x x9 x9

17 Posterior probability calculations on national crime victimization survey Table 5 The conditional probability table for NCVS attribute V2024 (number of units in the living structure) given MSACC (core MSA county) and V2015 (own/rent status of the structure) MSACC=x1 V2024 V2015 x1 (owned or being bought) x2 (rented for cash) x3 (no cash rent) x1 (one) x2 (two) x3 (three) x4 (four) x5 (five to nine) x6 (ten or more) x7 (mobile home or trailer) x8 (only other units) x (V2024) has parent nodes V2015 (representing whether the structure is owned, 410 rented, or no cash rent) and MSACC (representing the 40 core geographical areas of 411 the NCVS). As an example, in Anaheim/Santa Anna, California (MSACC = x1) 412 with the victim owning the living structure (V2015 = x1), the conditional 413 probability that the victim lives in a single housing unit (V2024 = x1) is A correlation between renting an apartment in a large city versus owning a home in 415 the suburbs is an expected correlation. 416 Similarly, Table 6 illustrates the relationship between household income (V2026) 417 as a child node to V2015 (representing whether the structure is owned, rented, or no 418 cash rent), MSACC (representing the 40 core geographical areas of the NCVS), and 419 V2024 (representing the number of units in the living structure). As an example, 420 with MSACC = x1 (Anaheim/Santa Anna, California) and V2024 = x1 (a single 421 unit), the conditional probability for V2015 = x1 (victim owns living structure) Table 6 The conditional probability table for NCVS attribute V2026 (household income) given V2024 (number of units in the living structure) MSACC (the core MSA county) and V2015 (the own/rent status of the structure) MSACC=x1 V2024=x1 V2026 V2015 x1 (owned or being bought) x2 (rented for cash) x3 (no cash rent) x1 (\$7,500) x2 ($7,500 $14,999) x3 ($15,000 $24,999) x4 ($25,000 $29,999) x5 ($30,000 $49,999) x6 ($50,000 and over) x

18 M. Riesen, G. Serpen 422 increases as the household income (V2026) increases. Again, the CPT has captured 423 a reasonable correlation between the parent attributes and the child attributes in the 424 Bayesian model. 425 Further critique of CPTs and a global consideration of the final model affirmed 426 that the model was consistent with reported trends and empirical probabilities, and 427 moreover presented no notable counterintuitive representations Sensitivity analysis 429 Sensitivity analysis for a given variable, which is the class attribute in this case, 430 measures the impact on the class variable s belief of obtaining evidence about each 431 of a set of other variables (the evidence variables). The method we implemented 432 analyzes the evidence variables one at a time, evaluating the worth of an attribute by 433 measuring the gain ratio with respect to the class. Table 7 lists the top ten variables 434 with the highest gain ratio based upon the class attribute V4529. From the list of 435 attributes in Table 7 we immediately observe the pattern of variables concerned 436 with the use of a particular weapon. Considering that the query attribute is V4529, 437 which describes specific violent and property crimes, it is logical to find a high gain 438 ratio for variables involving the use of weapons. Experts in the domain of 439 victimization agree that, variables regarding the use of weapons should have a 440 direct effect on the probability of being a victim of a specific crime (Davis 2007, 441 Private communications). The variable V4026, which asks whether the offender 442 got inside the victim s residence, reported the highest gain ratio with respect to the 443 class attribute V4529. Again, there is a natural distinction between a burglary and a 444 purse snatching that is reflected by the gain ratio of variable V Influence of some of the variables presented in Table 7 were further analyzed by 446 presenting a series of queries of the V4529 attribute. Results are presented in 447 Table 8. For example, we queried V4529 given V4026=0 (i.e. a No answer for 448 the question Did offender get inside ) and then given V4026 = 1 (i.e. a Yes Table 7 NCVS attributes with the highest gain ratio based upon class attribute V4529 (victimization) Gain ratio NCVS variable V4026: Did offender get inside? (1: Yes, 2: No) V4052: Was a gun, other than a hand gun used by offender? (0: No, 1: Yes) V4056: Was a weapon used that does not fit into an NCVS category? V4078: Was there a threat of rape? (0: No, 1: Yes) V4127: Did victim receive medical care for injury? (1: Yes, 2: No) V4053: Was a knife used? (0: No, 1: Yes) V4051: Was a handgun used? (0: No, 1: Yes) V4085: Was the victim shot at and missed? (0: No, 1: Yes) V4086: Was there an attempted attack with a knife? V4111: Did the victim suffer no injuries?