User:Aarondmytro/sandbox

INTRODUCTION:

I. Definition of Kernel Density Estimation:

Kernel density estimation is a widely used method for estimating a distribution based on a sample of points drawn from that distribution. (Fortmann-Roe, Starfield & Getz, 2012)

(Emanuel Parzen & Murray Rosenblatt)
 * These are the two men who helped conceptualize Kernel Density Estimation:

(Picture 1)

(Picture 2)

1. Kernel Density Estimation is based off of pin charts of crime: (Picture 3)


 * (This is an example of crime hotspots using a pin chart. Each pin in this map represents a crime that has been committed at the exact location/ address perpetrated.)

Various clustering technologies (including both those from the statistical and artificial intelligence literature) can be usefully employed to explore the data, and cluster analysis and factor analysis. (Oatley, Ewart, 2003)

2. The advantages of kernel density over a pin chart.

Kernel density builds on pin charts by adding another dimension, namely time. It takes into account the amount of crime perpetrated within the confines of a given area over time in that space. “Spacial & temporal analysis of crime … helps analysts who already have mapping capability … examine Hot Spot Areas on the map.” (ICJIA 1987)


 * This is an example of what Kernel Density looks like.

(Picture 4)



1. What it represents:

The darker the color covering the space, the higher the amount of crime present in that general vicinity. The outlying areas where the map is white is supposed to be free of reported crimes. The yellow and gold area represent low amounts of crime present in these given areas. The light green areas possess slightly larger amounts of crime than the yellow. The darker the green gets, the higher amount of crime there is. The blue areas are high crime areas. The dark blue have very high numbers of criminal or deviant activities being perpetrated in a localized vicinity. White is low, Yellow low, Green is moderate, and the Blue are high crime areas. These blue areas are an example of crime hotspots.

2. What it means to the social sciences:

Social sciences can benefit greatly from the use of Kernel Density Estimation information technologies if handled in the correct fashion. If employed correctly, police agencies can use the information present in these kernel density maps to better serve their population by placing more police force in the areas which tend to be more saturated with criminal activities. Police officers and subsequent administrations need to realize that these kernel density estimation charts clearly diagram that “crime was not generally spread throughout the city or even throughout disadvantaged areas of the city. Rather it was concentrated in crime “hot spots”. ( Weisburd, Maher, Sherman, 1992)


 * This is what the equation instrumental in finding Kernel Density looks like:

(Picture 5)



'''II. What is Moran's I Test:'''

Moran’s I statistic works by comparing the value at any one location with the value at all other locations (Levine, 2002; Bailey and Gatrell, 1995; Anselin, 1992; Ebdon, 1985).

Moran’s I requires an intensity value for the crime point, which is often represented as the centroid of the geographic boundary area. This point is then assigned an intensity value. For crime applications, this most often is the count of crimes within that geographic area. The Moran’s I result varies between –1.0 and +1.0. Where points that are close together have similar values, the Moran’s I result is high. The significance of the result can be tested against a theoretical distribution (one that is normally distributed) by dividing by its theoretical standard deviation. (Eck Et. All 2005)

A. This is who conceptualized and subsequently created Moran's I Test.
 * (Patrick Alfred Pierce Moran)

(Picture 6)

1. The measurements used when:

If analysts have access only to crime point data that are aggregate counts (representing the number of crime events within a certain 	geographic area, e.g., census blocks), an appropriate method to apply to test for clustering is the spatial autocorrelation technique, 	Moran’s I. (Eck Et. All 2005)

2. What advantages it possesses:

The Statistic known as Moran's I is widely used to test for the presence of spatial dependence in observations taken on a lattice. Under the null hypothesis that the data are independent and identically distributed normal random variates, the distribution of Moran's I is known, and hypothesis tests based on this statistic have been shown to have various optimality properties. (Li Calder & Cressie 2007)

B. This is the equation for Moran's I Test.

(Picture 7)


 * $$I=\frac{N}{\sum_i\sum_j w_{ij} }\frac{\sum_i\sum_j w_{ij}(X_i-\bar X)(X_j-\bar X)}{\sum_i(X_i-X)^2}$$

C. This is an example of what the application of Moran's I Test looks like.

(Picture 8)


 * (Moran's I seems very similar to kernel density estimation however it contains a few very important differences.)

1. What it represents.

Spatial autocorrelation techniques require an intensity value, be it a weighting linked to the event or a count of crimes where the crime point relates to the coordinate of an area to which crime events have been aggregated (e.g., the centroid of the area). If the original crime event data exist as accurate point geo-referenced data, aggregating this data to a common point will lose spatial detail. With the increased availability of accurate and precise geocoded records of crime, it would seem more important to use methods that do not require an intensity value but retain and perform tests on the original crime event point data. (Eck Et. All 2005)

2. Benefits for the criminal justice system:

The phenomenon of alternating clusters or hotspots can be interpreted to result from the rational choices of crime offenders interacting with local policing activities. Acquiring local knowledge of a different region would be costly for offenders. Results highlight the importance, in designing effective preventative actions against this crime, of monitoring clusters of offenders by evaluating the space-time relationships in a widespread space-time context between areas of elevated risks. (Nakaya & Yano 2010)


 * What this means is police administrators and like professionals can look at the patterns made obvious through employing Moran's I testing and see how closely related certain crimes are which gives these professionals the opportunity to react in the beginning before coming up with more proactive designs. These designs could be focused on finding the key opportunity being taken advantage of in these crime ridden areas. Once the advantageous opportunity is recognized, it may be disbanded likewise possibly disbanding crime.

'''III. Definition of crime hotspot:'''

Areas of concentrated crime are often referred to as hot spots. Researchers and 	police use the term in many different ways. Some refer to hot spot addresses (Eck and Weisburd, 1995; Sherman, Gartin, and Buerger, 1989), others refer to hot spot blocks (Taylor, Gottfredson, and Brower, 1984; Weisburd and Green, 1994), and others examine clusters of blocks (Block and Block, 1995). Like researchers, crime analysts look for concentrations of individual events that might indicate a series of related crimes. They also look at small areas that have a great deal of crime or disorder, even though there may be no common offender. Analysts also observe neighborhoods and neighborhood clusters with high crime and disorder levels and try to link these to underlying social conditions. (Eck Chainey & Cameron, 2005)


 * What are the uses of crime hotspot knowledge:

Hotspot mapping is a popular analytical technique that is used to help identify where to target police and crime reduction resources. In essence, hotspot mapping is used as a basic form of crime prediction, relying on retrospective data to identify the areas of high concentrations of crime and where policing and other crime reduction resources should be deployed. (Chainey Tompson & Uhlig, 2008)


 * How do we use this information to our advantage in the criminal justice profession:

1. Community Policing:

Community policing is particularly attentive to high-crime neighborhoods, where residents have great difficulty exerting social controls. (Eck Chainey & Cameron, 2005)

2. Problem-oriented policing:

Problem-oriented policing pushes police officials to identify concentrations of crime or criminal activity, determine what causes these concentrations, and then implement responses to reduce these concentrations. (Eck et. All 2005)
 * What do crime hotspots mean for surrounding and surrounded communities:

1. More has been written about neighborhood concentrations of crime (hot spots) than about any other form of concentration of crime. (Visher & Weisburd, 1998).

2. Surrounding neighborhoods are often studied from theoretical bases in hopes to come to a conclusion of what causes such neighborhoods to be such viable targets for becoming crime prone territories/ areas. Theories applied include but are not necessarily limited to broken windows theory, social disorganization theory, social efficacy, as well as other crime opportunity theories. (Nakaya & Yano, 2010)


 * What are the characteristics of a crime hotspot.

Though no common definition of the term hot spot of crime1 exists, the common understanding is that a hot spot is an area that has a greater than average number of criminal or disorder events, or an area where people have a higher than average risk of victimization. (Eck Et. All 2005)

Criticisms

1. Moran's I and Kernel Density Estimation are not designed to deal with crime in particular.

2. Moran's I and Kernel Density Estimation do not give as precise of an understanding of exact positions/ locations of criminal activity centers.

3. Both may count a single address containing multiple crimes skewing the results of breadth/ impact of such criminal activities within that neighborhood or general area.

(Transition: How do we as professionals combine these bits of information to benefit the average citizen?)

BODY:

I. Combining information gathered by Kernel Density and applying it to the criminal justice world:

A. Using Kernel Density to create representations of criminal activity

1. This information can be used to create a better suited police force in known high crime areas.

2. Why is criminality fixated/concentrated in specific locations.

3. What types of criminality persistence is present in which types of areas. (i.e. industrial, residential, public areas such as parks, businesses, etc.)

B. Using Kernel Density within the realm of criminology could effectively limit criminal persistence in given locations.

1. Kernel Density representations of crime in a given area could justify placement of additional officers in specified areas (beats) focusing more on crime hotspots.

2. Kernel Densities of other living factors such as income or urbanization could be juxtaposed with crime data to possibly deal with persisting crime trends in manners outside of courts and prisons.

(Transition: Moran's I Test could be just as advantageous as Kernel Density in relation to criminological/ societal advancements.)

I. Moran's I Test applied to criminological needs: Spatial autocorrelation tests, of which Moran’s I is one commonly applied method, have been used previously to test for evidence of crime event clustering (Chakravorty, 1995).

1. Moran's I Test can be used to create a composite measure of a proximity-correlation of criminal activity within a given geographic area.
 * Moran's I Test and crime hotspots.

2. Effective use to identify specific opportunities present in areas where high amounts of crime seem to persist over time and space. (long-term criminality)

3. Representations of proximal distancing between and amongst criminal activities could produce opportunities to glimpse situational crime variables allotting for criminal activities. (new-found criminality)

(Transition: In summation.)

CONCLUSION:

I. Summary:


 * Kernel Density Estimation and Moran's I Spatial Testing can be effectively used to document crime hotspots in a given area.


 * Effective use of such information can be highly beneficial to the criminological world through application of such documentations of crime hotspots.

VISUAL AIDS:

Different types of graphs and visual representations of useful visual data constructed through effective use of Kernel Density Estimations and Moran's I Spatial Testing.

3-D KERNEL DENSITY ESTIMATION FIGURE 1:

(Picture 9)

Examples of crime maps using both Kernel Density as well as Moran's I Test.

KERNEL DENSITY FIG. 1:

(Picture 10)

MORAN'S I FIGURE 1:

(Picture 11)



Formulas focused on obtaining data based on Kernel Density & Moran's I Test.

(Picture 12)