CA2188985A1 - Statistical analysis process - Google Patents
Statistical analysis processInfo
- Publication number
- CA2188985A1 CA2188985A1 CA 2188985 CA2188985A CA2188985A1 CA 2188985 A1 CA2188985 A1 CA 2188985A1 CA 2188985 CA2188985 CA 2188985 CA 2188985 A CA2188985 A CA 2188985A CA 2188985 A1 CA2188985 A1 CA 2188985A1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
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- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
- G16H40/00—ICT specially adapted for the management or administration of healthcare resources or facilities; ICT specially adapted for the management or operation of medical equipment or devices
- G16H40/20—ICT specially adapted for the management or administration of healthcare resources or facilities; ICT specially adapted for the management or operation of medical equipment or devices for the management or administration of healthcare resources or facilities, e.g. managing hospital staff or surgery rooms
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Abstract
Temporal data representing recurring events of different types is analyzed using a graphical method of presentation. Sets of temporal data representing the different events, especially their durations, are collected andplotted in sequence on the coordinate system with the duration of each type of event being plotted cumulatively on a respective axis. Each plot represents an individual profile. Plural profiles can be plotted as group profiles using appropriate criteria for selecting individual profiles for inclusion in the group. A comparison of individual profiles with group profiles readily indicates correlations and differences allowing reasonable prediction in the case of individual profiles.
The technique is particularly applicable to recidivism data although it is not limited to such data and may also be applied to various other types of data, for example bed usage in hospitals.
The technique is particularly applicable to recidivism data although it is not limited to such data and may also be applied to various other types of data, for example bed usage in hospitals.
Description
21 889~5 STATISTICAL ANALYSIS PROCESS
The present invention relates to the analysis of temporal data representing recurring events, in particular to such analysis for use in predicting the recurrence of such events.
The present method was developed initially for use in analyzing data for the prediction of recidivism. That application will be used as a specific example in the following. It is to be understood however, that the method is applicable to other data as well. Specific examples are bed utilization in hospitals, time spent by a professional with clients and illnesses in which periods of remission and relapse occur.
In early attempts to analyze recidivism data, the data was initially described by giving a simple percentage of inmates who reoffended out of a group of inmates released. There are problems with this method of defining recidivism. The group of inmates was usually a group of individuals who were released within a specific year, but the time to reoffense was not taken into consideration when the reoffense occurred. For example, many inmates reoffend within the first six months of release, but tend to slow down after one or more years from release.
The next approach taken by criminological researchers was to use the imperial engineering technique called Survival Curve Analysis. In its simplest terms, this is a technique for defining the percentage of entities which survive as a function of time. For illustration, this technique can be explained in terms of light bulb life. Assume that a sample of light bulbs is taken from an assembly line. The light bulbs are all started at the same time in a lab and the number surviving is recorded every time a light bulb fails.
When the last light bulb burns out, the data collection is over. In applying this technique to recidivism, the idea of a light bulb burning out is equivalentto a reoffense after release. The concept seems applicable, except for the fact to start the process requires a group of inmates who were released at approximately the same time. A more significant problem with this method occurs when previous offense cycles and post offense cycles are not taken into account. In order to start Survival Curve Analysis, an inmate needs to be 5 released and tracked until he or she reoffends. The inmate may be have been released twenty times before this specific release or ten times after.
In predicting the future behavior of anything it is important to know past behavior. An example is stock markets. Box-Jenkins ARMI
statistical models are often used to analyze past stock market information for 10 the prediction of future stock levels. Similarly, previous offense history information is critical to understanding future reoffending patterns. It is important to note the extreme difficulty in predicting future stock market values and it is equally difficult, if not more so, to predict future reoffense patterns of inmates.
The present invention provides an alternative technique for analyzing data and presenting it in a way that can be used to predict future behavior. As noted above, while the technique was initially developed for use with recidivism it is also applicable to the analysis of other temporal datarepresenting recurring events. It is useful to the medical community in 20 analyzing hospital bed usage, remission and relapse data and patient visits to medical professionals. Other industries may find the predictive possibilities ofbenefit, for example the insurance industry in predicting future claim patterns in medical, life or even automobile insurance.
The present technique is also useful in intervention analysis. An 25 "intervention" is a treatment or other event that occurs along the profile being analyzed. For example, an intervention in a criminal career may be psychiatric or psychological treatment. In medicine, it may be the use of a drug treatment. An intervention may be a single incident or it may be a ~ 1 88985 sequence of incidents, for example a course of therapy of any sort. The objective is to determine if the overall profile after intervention diverges makedly from that which would otherwise be predicted.
According to the present invention there is provided a method of 5 presenting for analysis temporal data representing first and second recurring and non simultaneous events of different types, said method comprising:
collecting a first set of data comprising first event duration times, each representing the duration of a respective first event;
collecting a second set of data comprising second event duration 10 times, each representing the duration of a respective second event;
providing a coordinate system with first and second dimensions;
plotting the first and second event duration times sequentially in said coordinate system, with the first event duration times being plotted cumulatively in the first dimension and the second event duration times being 15 plotted cumulatively in the second dimension.
The preferred two dimensional coordinate system is a standard Cartesian coordinate system. Applied to recidivism data, the X axis denotes time spent in society, i.e. out of jail, and the Y axis denotes time spent in jail.
The origin denotes date of birth. Age at first offense is denoted by a point on 20 the X axis some distance in the positive directional on the X axis. If the duration of incarceration at the first offense is zero, then there is only a mark made on the axis. If the duration of incarceration is greater than zero, then that duration is plotted parallel to the Y axis in the positive direction. Afterthe inmate is released, the plot continues parallel to the X axis a distance 25 representing the time to the next offense. The process continues in this manner for each conviction date and release date.
Profiles generated in this way can be expanded to include profiles of groups of inmates. The criteria used to create the groups are 21 88~85 defined by criminologists using demographics, for example race and gender, and offense history information, for example age at first offense. The reasons for the grouping criteria are not important for present purposes, but criteria are required to build these group profiles. When group profiles have 5 been created, an individual profile may be compared with a group profile based on the same demographic characteristics. Another possibility is to compare the individual profile with different group profiles to find the group profile to which the individual most closely approximates. A visual comparison can be of the group plot with the individual's plot, providing a 10 method to make an initial prediction. This prediction does not involve mathematics manipulation, statistics or fuzzy set knowledge. All that is required is to view the individual plot in comparison with a known group.
This visual comparison yields a prediction whether the inmate will reoffend, an estimate of time to the next offense, and an estimate of how many more 15 times the inmate may continue to reoffend.
It has been suggested by experts in the area of multi-dimensional statistical theory that humans can detect subtleties in a graph much better than can be detected using mathematical techniques. Nonetheless, statistical and mathematical techniques may also be used for pattern recognition and 20 prediction.
The two dimensional coordinate system can be expanded where it is desires to analyze more than two types of events. Thus, for example, the second type of event may be subdivided into different sub types. In terms of criminal behavior, a three dimensional coordinate system may be 25 plotted with time spent out of incarceration along the X axis, time spent in incarceration for non violent crimes along the Y axis and time spent in incarceration for violent crimes along the Z axis. With additional subdivisions,additional dimensions may be included in the plot, resulting an n dimensional 2 ~ 88985 space. The data from this n dimensional space can be projected onto a three or two dimensional space for viewing and analysis.
When dealing with three or more dimensions, the second through nth types of events may overlap, in which case surfaces or 5 hypersurfaces are created, spaced along and joined by the first event axis, as will be explained further in connection with the following examples.
In the accompanying drawings which illustrate exemplary embodiments of the present invention:
Figure 1 illustrates a typical two dimensional crime and career 1 0 plot;
Figure 2 illustrates the plot of Figure 1 with an "equal time" line superimposed on the plot;
Figure 3 illustrates an individual profile superimposed on a plot carrying a group profile;
Figures 4 and 5 illustrate two and three dimensional plots of the same data; and Figure 6 is a simple example of a group intervention profile.
Referring to the accompanying drawings, Figure 1 illustrates a criminal career profile plot of one individual. The plot is generated using a 20 standard two dimension Cartesian coordinate system. The X axis denotes time spent in society, that is out of incarceration and the Y axis denotes time spent in incarceration. The origin denotes date of birth.
In this plot, the age at first offense, 18 is denoted by a mark on the X axis, a distance representing eighteen years in the positive direction 25 along that axis. The time of incarceration for that offense was zero, so thatonly a mark appears. The second offense is marked at age 21. The time of incarceration was one year and the plot travels parallel to the Y axis in the positive direction an amount equal to that one year spent in incarceration.
After release the graph travels parallel to the X axis an amount equal to the time to the next offense, 2 years. The process continues in this manner for each conviction date and for release date. The complete data are given in Table 1. Table 2 lists the plotted data.
5 Table 1: Individual's Points Example ID Number: 123456Z Birth Date: 01 Jan 50 Conviction Date Release Date Years Out Years In 01 Jan 68 01 Jan 68 18 0 01 Jan 71 01 Jan 72 21 31 Dec 72 01 Jan 75 23 2 01 Jan 78 01 Jan 79 28 01 Jan 82 01 Jan 84 32 2 Final date of 01 Jan 94 is data collection date and is still released Table 2: Plotted Data X-Axis Y-Axis Data Description Time 0 0 Birthdate 18 0 Conviction 1 0 time 18 0 Release 1 Rel 3 yrs 21 0 Conviction 2 1 yr time 21 1 Release 2 Rel 1 yr 23 1 Conviction 3 2 yrs time 23 3 Release 3 Rel 5 yrs 28 3 Conviction 4 1 yr time 28 4 Release 4 Rel 4 yrs 32 4 Conviction 5 2 yrs time 32 6 Release 5 Rel 6 yrs 38 6 Present Date Still Released Figure 2 illustrates the plot of Figure 1, with a superimposed equal time or "50-50" line. This line begins at the first offense and slopes upwards at a one to one slope. With equal scales on the two axes, the fifty/fifty line is at a 45~ angle to the X axis. If the individual profile is above the 50-50 line, then the inmate spent more time in incarceration than out. If the profile is below the 50-50 line then the inmate spends more time in society than in incarceration.
Figure 3 illustrates the expansion of the profile system to groups of inmates. The criteria used to create the groups are defined using 10 appropriate demographics such as race, gender, etc. and offense history information such as age at first offense. As shown in Figure 3, a group profile may be superimposed on an individual profile to determine similarities and differences.
A visual comparison allows the user to make a prediction of future behavior. This prediction will include factors such as whether the inmate will reoffend, an estimate of time to the next offense and an estimate of how many more times the inmate may continue to reoffend in the inmate's criminal career.
The foregoing example applies the present analysis strategy to criminal incarceration systems. The basic idea is to know when someone is incarcerated and when someone is not incarcerated. This same strategy can be applied to other forms of temporal data by substituting other events for incarceration and out of incarceration. One example is that of bed utilization in hospitals. The two events would now be "in hospital" or using a bed and "out of hospital", not using a bed. Other examples will no doubt occur to those knowledgeable in the relevant fields.
The foregoing example uses a two dimensional coordinate system. This can be expanded to a multi-dimensional environment. Again, 21 8898~
using the example of criminological data, Figure 4 illustrates a two dimensional plot of "time out" vs "time in" similar to Figures 1, 2 and 3. The X axis represents time out, which may be equated to success time. For the sake of the current example, it will be considered a constant. The Y axis, 5 which represents time in or "failure time" may represent time spent in incarceration for offenses varying from drunk driving to murdering a law enforcement officer.
To distinguish criminal behavior of different types (different "events") additional dimensions may be added to the coordinate system. In 10 the example given in Figure 5, the incarceration time is separated into time spent in respect of non-violent crimes, for example burglary, break and enter, fraud etc., and time spent in incarceration in respect of violent crimes, for example assaults, sexual assaults, robbery with violence, manslaughter and murder. Figure 5 plots the data plotted on the two dimensional plot of Figure 15 4 with time out of incarceration plotted on the X axis, time in incarcerationfor violent crimes on the Y axis and time in incarceration for non violent crimes on the Z axis.
The plot as presented may represent an inmate who came into the correctional system the first time for a break and enter offense with a two 20 months sentence, followed by six months out of incarceration, six months in incarceration for an assault, one year out, then one month in for fraud, out again for six months, then in for sexual assault for five years and out again for three years up to the end point of the plot. The plot will have many meanings since the degree of violence can be examined in the plot as well as 25 the time spent in jail for any crime.
The criminal career space represented in the coordinate system can be broken into many more dimensions. At present, offenses from the Canadian Criminal Code may be reduced to twenty five usable criminal career 2 1 88q85 categories, all potentially dimensioned in the crime space. The twenty five crime categories plus one dimension for out of incarceration will produce a twenty six dimensional crime space. The multi-dimensional plot can be plotted onto a three or two dimensional space to be viewed.
In the multi-dimensional plotting arrangement, the question of concurrent and consecutive sentences arises. If for example, an inmate is given at the same time five years for a sexual assault offense and a two months consecutive sentence for fraud, violent offense time is plotted five years in the violent direction and non violent time is plotted two months in the non violent direction. This creates a two dimensional surface in three dimensional space. This appears for higher dimensional expressions as well, producing multi-dimensional hyper surfaces in multi-dimensional space connected by the X axis.
Figure 6 illustrates another use of the system, for determining the effectiveness of interventions. In this case, criminals within a group received treatment, an "intervention" at an incarceration time of about three years. The subsequent profile shows a marked decline in slope, indicating an effect of the treatment.
It will thus be seen that the analysis system of the present invention provides a powerful tool for the analysis of recurring events, providing valuable predictive abilities.
While certain embodiments of the present invention have been described in the foregoing, it is to be understood that other embodiments in the scope of the invention and are intended to be included within the scope of the appended claims.
The present invention relates to the analysis of temporal data representing recurring events, in particular to such analysis for use in predicting the recurrence of such events.
The present method was developed initially for use in analyzing data for the prediction of recidivism. That application will be used as a specific example in the following. It is to be understood however, that the method is applicable to other data as well. Specific examples are bed utilization in hospitals, time spent by a professional with clients and illnesses in which periods of remission and relapse occur.
In early attempts to analyze recidivism data, the data was initially described by giving a simple percentage of inmates who reoffended out of a group of inmates released. There are problems with this method of defining recidivism. The group of inmates was usually a group of individuals who were released within a specific year, but the time to reoffense was not taken into consideration when the reoffense occurred. For example, many inmates reoffend within the first six months of release, but tend to slow down after one or more years from release.
The next approach taken by criminological researchers was to use the imperial engineering technique called Survival Curve Analysis. In its simplest terms, this is a technique for defining the percentage of entities which survive as a function of time. For illustration, this technique can be explained in terms of light bulb life. Assume that a sample of light bulbs is taken from an assembly line. The light bulbs are all started at the same time in a lab and the number surviving is recorded every time a light bulb fails.
When the last light bulb burns out, the data collection is over. In applying this technique to recidivism, the idea of a light bulb burning out is equivalentto a reoffense after release. The concept seems applicable, except for the fact to start the process requires a group of inmates who were released at approximately the same time. A more significant problem with this method occurs when previous offense cycles and post offense cycles are not taken into account. In order to start Survival Curve Analysis, an inmate needs to be 5 released and tracked until he or she reoffends. The inmate may be have been released twenty times before this specific release or ten times after.
In predicting the future behavior of anything it is important to know past behavior. An example is stock markets. Box-Jenkins ARMI
statistical models are often used to analyze past stock market information for 10 the prediction of future stock levels. Similarly, previous offense history information is critical to understanding future reoffending patterns. It is important to note the extreme difficulty in predicting future stock market values and it is equally difficult, if not more so, to predict future reoffense patterns of inmates.
The present invention provides an alternative technique for analyzing data and presenting it in a way that can be used to predict future behavior. As noted above, while the technique was initially developed for use with recidivism it is also applicable to the analysis of other temporal datarepresenting recurring events. It is useful to the medical community in 20 analyzing hospital bed usage, remission and relapse data and patient visits to medical professionals. Other industries may find the predictive possibilities ofbenefit, for example the insurance industry in predicting future claim patterns in medical, life or even automobile insurance.
The present technique is also useful in intervention analysis. An 25 "intervention" is a treatment or other event that occurs along the profile being analyzed. For example, an intervention in a criminal career may be psychiatric or psychological treatment. In medicine, it may be the use of a drug treatment. An intervention may be a single incident or it may be a ~ 1 88985 sequence of incidents, for example a course of therapy of any sort. The objective is to determine if the overall profile after intervention diverges makedly from that which would otherwise be predicted.
According to the present invention there is provided a method of 5 presenting for analysis temporal data representing first and second recurring and non simultaneous events of different types, said method comprising:
collecting a first set of data comprising first event duration times, each representing the duration of a respective first event;
collecting a second set of data comprising second event duration 10 times, each representing the duration of a respective second event;
providing a coordinate system with first and second dimensions;
plotting the first and second event duration times sequentially in said coordinate system, with the first event duration times being plotted cumulatively in the first dimension and the second event duration times being 15 plotted cumulatively in the second dimension.
The preferred two dimensional coordinate system is a standard Cartesian coordinate system. Applied to recidivism data, the X axis denotes time spent in society, i.e. out of jail, and the Y axis denotes time spent in jail.
The origin denotes date of birth. Age at first offense is denoted by a point on 20 the X axis some distance in the positive directional on the X axis. If the duration of incarceration at the first offense is zero, then there is only a mark made on the axis. If the duration of incarceration is greater than zero, then that duration is plotted parallel to the Y axis in the positive direction. Afterthe inmate is released, the plot continues parallel to the X axis a distance 25 representing the time to the next offense. The process continues in this manner for each conviction date and release date.
Profiles generated in this way can be expanded to include profiles of groups of inmates. The criteria used to create the groups are 21 88~85 defined by criminologists using demographics, for example race and gender, and offense history information, for example age at first offense. The reasons for the grouping criteria are not important for present purposes, but criteria are required to build these group profiles. When group profiles have 5 been created, an individual profile may be compared with a group profile based on the same demographic characteristics. Another possibility is to compare the individual profile with different group profiles to find the group profile to which the individual most closely approximates. A visual comparison can be of the group plot with the individual's plot, providing a 10 method to make an initial prediction. This prediction does not involve mathematics manipulation, statistics or fuzzy set knowledge. All that is required is to view the individual plot in comparison with a known group.
This visual comparison yields a prediction whether the inmate will reoffend, an estimate of time to the next offense, and an estimate of how many more 15 times the inmate may continue to reoffend.
It has been suggested by experts in the area of multi-dimensional statistical theory that humans can detect subtleties in a graph much better than can be detected using mathematical techniques. Nonetheless, statistical and mathematical techniques may also be used for pattern recognition and 20 prediction.
The two dimensional coordinate system can be expanded where it is desires to analyze more than two types of events. Thus, for example, the second type of event may be subdivided into different sub types. In terms of criminal behavior, a three dimensional coordinate system may be 25 plotted with time spent out of incarceration along the X axis, time spent in incarceration for non violent crimes along the Y axis and time spent in incarceration for violent crimes along the Z axis. With additional subdivisions,additional dimensions may be included in the plot, resulting an n dimensional 2 ~ 88985 space. The data from this n dimensional space can be projected onto a three or two dimensional space for viewing and analysis.
When dealing with three or more dimensions, the second through nth types of events may overlap, in which case surfaces or 5 hypersurfaces are created, spaced along and joined by the first event axis, as will be explained further in connection with the following examples.
In the accompanying drawings which illustrate exemplary embodiments of the present invention:
Figure 1 illustrates a typical two dimensional crime and career 1 0 plot;
Figure 2 illustrates the plot of Figure 1 with an "equal time" line superimposed on the plot;
Figure 3 illustrates an individual profile superimposed on a plot carrying a group profile;
Figures 4 and 5 illustrate two and three dimensional plots of the same data; and Figure 6 is a simple example of a group intervention profile.
Referring to the accompanying drawings, Figure 1 illustrates a criminal career profile plot of one individual. The plot is generated using a 20 standard two dimension Cartesian coordinate system. The X axis denotes time spent in society, that is out of incarceration and the Y axis denotes time spent in incarceration. The origin denotes date of birth.
In this plot, the age at first offense, 18 is denoted by a mark on the X axis, a distance representing eighteen years in the positive direction 25 along that axis. The time of incarceration for that offense was zero, so thatonly a mark appears. The second offense is marked at age 21. The time of incarceration was one year and the plot travels parallel to the Y axis in the positive direction an amount equal to that one year spent in incarceration.
After release the graph travels parallel to the X axis an amount equal to the time to the next offense, 2 years. The process continues in this manner for each conviction date and for release date. The complete data are given in Table 1. Table 2 lists the plotted data.
5 Table 1: Individual's Points Example ID Number: 123456Z Birth Date: 01 Jan 50 Conviction Date Release Date Years Out Years In 01 Jan 68 01 Jan 68 18 0 01 Jan 71 01 Jan 72 21 31 Dec 72 01 Jan 75 23 2 01 Jan 78 01 Jan 79 28 01 Jan 82 01 Jan 84 32 2 Final date of 01 Jan 94 is data collection date and is still released Table 2: Plotted Data X-Axis Y-Axis Data Description Time 0 0 Birthdate 18 0 Conviction 1 0 time 18 0 Release 1 Rel 3 yrs 21 0 Conviction 2 1 yr time 21 1 Release 2 Rel 1 yr 23 1 Conviction 3 2 yrs time 23 3 Release 3 Rel 5 yrs 28 3 Conviction 4 1 yr time 28 4 Release 4 Rel 4 yrs 32 4 Conviction 5 2 yrs time 32 6 Release 5 Rel 6 yrs 38 6 Present Date Still Released Figure 2 illustrates the plot of Figure 1, with a superimposed equal time or "50-50" line. This line begins at the first offense and slopes upwards at a one to one slope. With equal scales on the two axes, the fifty/fifty line is at a 45~ angle to the X axis. If the individual profile is above the 50-50 line, then the inmate spent more time in incarceration than out. If the profile is below the 50-50 line then the inmate spends more time in society than in incarceration.
Figure 3 illustrates the expansion of the profile system to groups of inmates. The criteria used to create the groups are defined using 10 appropriate demographics such as race, gender, etc. and offense history information such as age at first offense. As shown in Figure 3, a group profile may be superimposed on an individual profile to determine similarities and differences.
A visual comparison allows the user to make a prediction of future behavior. This prediction will include factors such as whether the inmate will reoffend, an estimate of time to the next offense and an estimate of how many more times the inmate may continue to reoffend in the inmate's criminal career.
The foregoing example applies the present analysis strategy to criminal incarceration systems. The basic idea is to know when someone is incarcerated and when someone is not incarcerated. This same strategy can be applied to other forms of temporal data by substituting other events for incarceration and out of incarceration. One example is that of bed utilization in hospitals. The two events would now be "in hospital" or using a bed and "out of hospital", not using a bed. Other examples will no doubt occur to those knowledgeable in the relevant fields.
The foregoing example uses a two dimensional coordinate system. This can be expanded to a multi-dimensional environment. Again, 21 8898~
using the example of criminological data, Figure 4 illustrates a two dimensional plot of "time out" vs "time in" similar to Figures 1, 2 and 3. The X axis represents time out, which may be equated to success time. For the sake of the current example, it will be considered a constant. The Y axis, 5 which represents time in or "failure time" may represent time spent in incarceration for offenses varying from drunk driving to murdering a law enforcement officer.
To distinguish criminal behavior of different types (different "events") additional dimensions may be added to the coordinate system. In 10 the example given in Figure 5, the incarceration time is separated into time spent in respect of non-violent crimes, for example burglary, break and enter, fraud etc., and time spent in incarceration in respect of violent crimes, for example assaults, sexual assaults, robbery with violence, manslaughter and murder. Figure 5 plots the data plotted on the two dimensional plot of Figure 15 4 with time out of incarceration plotted on the X axis, time in incarcerationfor violent crimes on the Y axis and time in incarceration for non violent crimes on the Z axis.
The plot as presented may represent an inmate who came into the correctional system the first time for a break and enter offense with a two 20 months sentence, followed by six months out of incarceration, six months in incarceration for an assault, one year out, then one month in for fraud, out again for six months, then in for sexual assault for five years and out again for three years up to the end point of the plot. The plot will have many meanings since the degree of violence can be examined in the plot as well as 25 the time spent in jail for any crime.
The criminal career space represented in the coordinate system can be broken into many more dimensions. At present, offenses from the Canadian Criminal Code may be reduced to twenty five usable criminal career 2 1 88q85 categories, all potentially dimensioned in the crime space. The twenty five crime categories plus one dimension for out of incarceration will produce a twenty six dimensional crime space. The multi-dimensional plot can be plotted onto a three or two dimensional space to be viewed.
In the multi-dimensional plotting arrangement, the question of concurrent and consecutive sentences arises. If for example, an inmate is given at the same time five years for a sexual assault offense and a two months consecutive sentence for fraud, violent offense time is plotted five years in the violent direction and non violent time is plotted two months in the non violent direction. This creates a two dimensional surface in three dimensional space. This appears for higher dimensional expressions as well, producing multi-dimensional hyper surfaces in multi-dimensional space connected by the X axis.
Figure 6 illustrates another use of the system, for determining the effectiveness of interventions. In this case, criminals within a group received treatment, an "intervention" at an incarceration time of about three years. The subsequent profile shows a marked decline in slope, indicating an effect of the treatment.
It will thus be seen that the analysis system of the present invention provides a powerful tool for the analysis of recurring events, providing valuable predictive abilities.
While certain embodiments of the present invention have been described in the foregoing, it is to be understood that other embodiments in the scope of the invention and are intended to be included within the scope of the appended claims.
Claims (6)
1. A method of presenting for analysis temporal data representing first and second recurring and non simultaneous events of different types, said method comprising:
collecting a first set of data comprising first event duration times, each representing the duration of a respective first event;
collecting a second set of data comprising second event duration times, each representing the duration of a respective second event;
providing a coordinate system with first and second dimensions;
plotting the first and second event duration times sequentially in said coordinate system, with the first event duration times being plotted cumulatively in the first dimension and the second event duration times being plotted cumulatively in the second dimension.
collecting a first set of data comprising first event duration times, each representing the duration of a respective first event;
collecting a second set of data comprising second event duration times, each representing the duration of a respective second event;
providing a coordinate system with first and second dimensions;
plotting the first and second event duration times sequentially in said coordinate system, with the first event duration times being plotted cumulatively in the first dimension and the second event duration times being plotted cumulatively in the second dimension.
2. A method according to Claim 1 wherein the coordinate system is a Cartesian coordinate system and the event duration times are plotted as straight lines.
3. A method according to Claim 1 for recording temporal data additionally representing third through nth events of different types, which occur non simultaneously with the first event, said method comprising:
providing the coordinate system with n dimensions;
plotting the duration times of the events sequentially in the coordinate system with the duration times of each event being plotted on a respective one of the dimensions.
providing the coordinate system with n dimensions;
plotting the duration times of the events sequentially in the coordinate system with the duration times of each event being plotted on a respective one of the dimensions.
4. A method according to Claim 1 or 2 wherein the data comprises data representing criminal behavior, each first event being freedom from incarceration and each second event being incarceration.
5. A method according to Claim 3 wherein the data comprises data representing criminal behavior, the first events being freedom from incarceration and the second through nth events being incarceration, each based on a respective category of criminal behavior.
6. A method according to Claim 3 or 5 wherein n is greater than 3 and further comprising projecting plotted data onto a two or three dimensional plot.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA 2188985 CA2188985A1 (en) | 1996-10-28 | 1996-10-28 | Statistical analysis process |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA 2188985 CA2188985A1 (en) | 1996-10-28 | 1996-10-28 | Statistical analysis process |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA2188985A1 true CA2188985A1 (en) | 1998-04-28 |
Family
ID=4159157
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA 2188985 Abandoned CA2188985A1 (en) | 1996-10-28 | 1996-10-28 | Statistical analysis process |
Country Status (1)
| Country | Link |
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| CA (1) | CA2188985A1 (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP3430518B1 (en) * | 2016-03-15 | 2022-08-03 | Microsoft Technology Licensing, LLC | Analysis of recurring processes |
-
1996
- 1996-10-28 CA CA 2188985 patent/CA2188985A1/en not_active Abandoned
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP3430518B1 (en) * | 2016-03-15 | 2022-08-03 | Microsoft Technology Licensing, LLC | Analysis of recurring processes |
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