UCI Statistics Spatial Data Analysis Final Report

2. wirte 2 pages report,explain each questions how i solve answers and solutions.

I have done the code parts, need to use my code to write 2 pages report about how i solve the questions.

Year
2019
2019
2019
2019
2019
2019
2019
2019
2019
2019
2019
2019
2019
2019
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
Month
8
8
9
9
9
9
10
10
10
11
11
12
12
12
1
1
1
1
1
1
1
1
1
1
2
2
3
3
3
4
4
5
7
12
Day
29
30
2
5
24
29
13
15
19
6
19
9
22
31
5
6
27
27
30
29
29
29
30
30
2
4
22
30
31
2
20
31
24
1
Longitude
114.1693
114.17215
114.17559
114.17546
114.00669
114.27202
114.16934
114.16973
114.16609
113.97251
114.16936
114.17619
114.21206
114.13849
114.14124
114.1633
114.15329
114.16806
114.00081
114.00241
114.12949
114.16953
114.17771
114.16909
114.11334
114.13843
114.12838
114.18699
114.17319
113.96638
114.16869
114.13606
114.09786
114.16917
Latitude
22.320018
22.277359
22.371026
22.322965
22.464653
22.381567
22.3193
22.32027
22.279975
22.390829
22.319304
22.274312
22.320563
22.340073
22.495015
22.326543
22.341277
22.305512
22.458226
22.449856
22.35677
22.318361
22.315293
22.324291
22.528219
22.34014
22.497559
22.26706
22.452208
22.396774
22.278437
22.377414
22.350409
22.327702
District
Yau Tsim Mong
Wan Chai
Sha Tin
Kowloon City
Yuen Long
Sai Kung
Yau Tsim Mong
Yau Tsim Mong
Central & Western
Tuen Mun
Yau Tsim Mong
Wan Chai
Kwun Tong
Sham Shui Po
North
Sham Shui Po
Sham Shui Po
Yau Tsim Mong
Yuen Long
Yuen Long
Sha Tin
Yau Tsim Mong
Kowloon City
Yau Tsim Mong
North
Sham Shui Po
North
Wan Chai
Tai Po
Tuen Mun
Wan Chai
Sha Tin
Kwai Tsing
Sham Shui Po
summary
08/29/2019: Assailants, armed with baseball bats and knives, attacked Jimmy Sham, an activist and protest organizer, in Mon
08/30/2019: Assailants attacked Davin Wong, the University of Hong Kong (HKU) Student Union President and pro-democrac
09/02/2019: Assailants attacked Isaac Cheng, vice president of Hong Kong’s pro-democracy Demosisto party, in Tai Wai neigh
09/05/2019: Assailants threw petrol bombs at the home of Jimmy Lai Chee-ying, the founder of pro-democracy newspaper A
09/24/2019: Assailants attacked Roy Kwong, a Democratic Party Lawmaker, near Wetland Park in Tin Shui Wai neighborhood
09/29/2019: Assailants, armed with metal rods and sticks, attacked Stanley Ho, a Labor Party member and pro-democracy ac
10/13/2019: An explosive device detonated targeting police personnel between Nathan Road and Kuai Fu Street in Yau Tsim
10/15/2019: Assailants, armed with hammers and knives, attacked Jimmy Sham, an activist and protest organizer, in Yau Tsim
10/19/2019: An assailant stabbed a pro-democracy activist handing out leaflets in Admiralty neighborhood, Hong Kong, China
11/06/2019: An assailant armed with a knife attacked Junius Ho, a pro-government lawmaker, while campaigning in Tuen Mu
11/19/2019: Assailants set fire to the printing press at the Hong Kong Epoch Times warehouse in Hong Kong, China. There we
12/09/2019: Authorities discovered and defused two explosive devices at the Wah Yan College in Wan Chai neighborhood, H
12/22/2019: Assailants threw a petrol bomb at Ngau Tau Kok Police Station in Kowloon neighborhood, Hong Kong, China. The
12/31/2019: Assailants threw petrol bombs at government offices in Lai Chi Kok, Hong Kong, China. There were no reported c
01/05/2020: Assailants threw petrol bombs at the Sheung Shui police station in Fanling, Hong Kong, China. There were no rep
01/06/2020: Two assailants threw petrol bombs at Spicegirl, a restaurant, on Lai Chi Kok Road in Sham Shui Po, Hong Kong, C
01/27/2020: An explosive device detonated in a restroom at the Caritas Medical Centre in So Uk, Hong Kong, China. There we
01/27/2020: An explosive device detonated inside a public restroom at King George V Memorial Park along Jordan Road in Ho
01/30/2020: Assailants firebombed a Best Mart 360 in a shopping mall in Tin Shui Wai, Hong Kong, China. There were no casu
01/29/2020: Assailants threw petrol bombs at the Tin Shui Wai police station in Hong Kong, China. There were no reported ca
01/29/2020: Assailants threw three petrol bombs at the Kwai Chung Police Station in Hong Kong, China. There were no repor
01/29/2020: Assailants threw two petrol bombs at a police vehicle in Mong Kok, Hong Kong, China. There were no reported c
01/30/2020: Assailants threw seven petrol bombs at the Hung Hom Police Station in Ho Man Tin, Hong Kong, China. There we
01/30/2020: Assailants threw two petrol bombs at the Mong Kok Police Station in Prince Edward, Hong Kong, China. There w
02/02/2020: One explosive device partially detonated and another was safely defused on a train at the Lo Wu station in Lo W
02/04/2020: An explosive device detonated in a restroom of the Lai Chi Kok public library in Lai Chi Kok, Hong Kong, China. No
03/22/2020: An assailant threw four Molotov cocktails at Sheung Shui Police Married Quarters in Fanling, Hong Kong, China.
03/30/2020: Assailants threw three incendiary devices at the Happy Valley Police Station in Wan Chai, Hong Kong, China. The
03/31/2020: Assailants threw five incendiary devices at the Tai Po -Police Station in Tai Po, Hong Kong, China. There were no
04/02/2020: Assailants threw petrol bombs targeting a Best Mart 360 store along Ming Kum road in Tuen Mun neighborhood
04/20/2020: Police personnel safely defused a letter bomb sent to police commissioner Chris Tang Ping-keung at the police h
05/31/2020: An incendiary device detonated outside a residence on the 24th floor of Wing Shue House at Lei Muk Shue Estat
07/24/2020: An incendiary device detonated at the entrance of Lok Sin Tong Leung Chik Wai Memorial School in Cheung Hon
12/01/2020: Assailants threw Molotov cocktails at the Police Sports and Recreation Club in Mongkok, Hong Kong, China. The
and protest organizer, in Mong Kok neighborhood, Hong Kong, China. Sham was injured in the attack. No group claimed responsibility for
n President and pro-democracy activist, near the Southorn Playground in Wan Chai neighborhood, Hong Kong, China. Wong was injured in
mosisto party, in Tai Wai neighborhood, Hong Kong, China. Cheng was injured in the attack. No group claimed responsibility for the incide
f pro-democracy newspaper Apple Daily, along Kadoorie Avenue in Ho Man Tin neighborhood, Hong Kong, China. There were no reported
in Tin Shui Wai neighborhood, Hong Kong, China. Kwong was injured in the attack. No group claimed responsibility for the incident.
member and pro-democracy activist, in Sai Kung neighborhood, Hong Kong, China. Two people, including Ho, were injured in the attack. N
and Kuai Fu Street in Yau Tsim Mong neighborhood, Hong Kong, China. There were no reported casualties in the blast. No group claimed r
d protest organizer, in Yau Tsim Mong neighborhood, Hong Kong, China. Sham was injured in the attack. No group claimed responsibility f
eighborhood, Hong Kong, China. The activist was injured in the attack. An individual claimed responsibility for the incident and stated “Hon
while campaigning in Tuen Mun neighborhood, Hong Kong, China. In addition to the assailant, Ho and two other people were injured in th
in Hong Kong, China. There were no reported casualties in the attack. No group claimed responsibility for the incident.
orhood, Hong Kong, China. There were no reported casualties. An unknown group claimed responsibility for the incident and wrote “Dare
Kong, China. There were no reported casualties in the attack, but a vehicle was damaged in the attack. No group claimed responsibility for
n Sham Shui Po, Hong Kong, China. There were no reported casualties in the attack. No group claimed responsibility for the incident.
Uk, Hong Kong, China. There were no reported casualties in the blast. No group claimed responsibility for the incident; however, an anony
al Park along Jordan Road in Hong Kong, China. There were no reported casualties in the attack. No group claimed responsibility for the in
ong, China. There were no casualties reported in the attack. No group claimed responsibility for the incident.
ina. There were no reported casualties in the attack. This was one of five related attacks targeting police within a 24-hour period. No grou
ng, China. There were no reported casualties in the attack. This was one of five related attacks targeting police within a 24-hour period. No
hina. There were no reported casualties in the attack. This was one of five related attacks targeting police within a 24-hour period. No gro
in, Hong Kong, China. There were no reported casualties in the attack. This was one of five related attacks targeting police within a 24-hou
rd, Hong Kong, China. There were no reported casualties in the attack. This was one of five related attacks targeting police within a 24-ho
n at the Lo Wu station in Lo Wu, Hong Kong, China. There were no reported casualties in the attack. An unidentified individual claimed re
Chi Kok, Hong Kong, China. No casualties were reported in the attack. No group claimed responsibility for the incident. Sources noted tha
in Fanling, Hong Kong, China. There were no reported casualties, but a vehicle was damaged in the attack. No group claimed responsibilit
an Chai, Hong Kong, China. There were no reported casualties in the attack. No group claimed responsibility for the incident.
ng Kong, China. There were no reported casualties in the attack. No group claimed responsibility for the incident; however, three students
ad in Tuen Mun neighborhood, Hong Kong, China. There were no reported casualties in the attack. No group claimed responsibility for th
ang Ping-keung at the police headquarters along Arsenal Street in Wan Chai neighborhood, Hong Kong, China. No group claimed respons
ue House at Lei Muk Shue Estate in Tsuen Wan, Hong Kong, China. There were no reported casualties in the attack. No group claimed resp
emorial School in Cheung Hong Estate, Tsing Yi, Hong Kong, China. There were no reported casualties in the attack. No group claimed res
ngkok, Hong Kong, China. There were no reported casualties, but three assailants were arrested in relation to the attack. No group claime
her people were injured in the attack. An Anti-Government extremist claimed responsibility for the incident.
entified individual claimed responsibility for the incident, stating that the attack was in protest of Hong Kong’s refusal to close the border
e incident. Sources noted that the attack was motivated by public calls to close Hong Kong’s borders to prevent the spread of COVID-19.
o group claimed responsibility for the incident; however, authorities detained an individual in connection with the incident.
claimed responsibility for the incident. Best Mart 360 stores have been singled out by anti-extradition law protesters as a front for Fujian
attack. No group claimed responsibility for the incident; however two students and one former student were arrested in connection with
rotesters as a front for Fujian gangs/Triads who have recently begun attacking protesters, a claim that Best Mart 360 has denied.
e arrested in connection with the incident. Authorities also suspected that the attack was carried out in order to “suspend classes or prom
to “suspend classes or prompt students to boycott classes in support of protesters.”
District
Yuen Long
North
Tai Po
Tuen Mun
Tsuen Wan
Kwai Tsing
Sha Tin
Sai Kung
Sham Shui Po
Yau Tsim Mong
Kowloon City
Wong Tai Sin
Kwun Tong
Islands
Central & Western
Wan Chai
Eastern
Southern
longitude
(western boundary),
x1
113.831
114.11
114.11
113.831
114.035
114.09
114.11
114.247
114.11
114.11
114.175
114.196
114.196
113.831
114.115
114.167
114.196
114.115
longitude
(eastern boundary),
x2
114.11
114.409
114.409
114.035
114.09
114.11
114.247
114.409
114.175
114.175
114.196
114.247
114.247
114.115
114.167
114.196
114.247
114.247
latitude
(southern boundary),
y1
22.427
22.483
22.427
22.293
22.293
22.293
22.355
22.153
22.326
22.293
22.293
22.326
22.293
22.153
22.259
22.259
22.259
22.153
latitude
(northern boundary),
y2
22.546
22.546
22.483
22.427
22.427
22.427
22.427
22.427
22.355
22.326
22.355
22.355
22.326
22.293
22.293
22.293
22.293
22.259
Area,
(x2-x1)*(y2-y1)
0.033201
0.018837
0.016744
0.027336
0.00737
0.00268
0.009864
0.044388
0.001885
0.002145
0.001302
0.001479
0.001683
0.03976
0.001768
0.000986
0.001734
0.013992
Population
639900
314500
308000
494800
310000
501100
684500
472700
434100
322300
419200
414800
687000
184300
236000
173500
538600
261000
Density in million per unit area,
(Population)/(Area*1000000)
19.27351586
16.69586452
18.39464883
18.10067311
42.0624152
186.9776119
69.39375507
10.64927458
230.2917772
150.2564103
321.9662058
280.4597701
408.1996435
4.635311871
133.4841629
175.9634888
310.6113033
18.6535163
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT6016 Spatial Data Analysis
Mini-project
Background and problem setting
The spreadsheet “Data” of the Excel file data.xlsx, extracted from Global Terrorism Database (GTD)
(https://www.start.umd.edu/data-tools/global-terrorism-database-gtd),
contains data on 34 violent incidents which occurred in Hong Kong during 2019–2020, a period of
social unrest.
Consider Hong Kong as a 2D rectangular spatial set
S = {(x, y) : 113.831 ≤ x ≤ 114.409, 22.153 ≤ y ≤ 22.546},
where x and y denote the longitude and latitude measures, respectively. We may define the “area”
R
of a sub-region R of Hong Kong to be R dx dy. Thus, the total “area” of Hong Kong is given by
(114.409 − 113.831)(22.546 − 22.153) = 0.227154. The (x, y)-coordinates of the locations of the 34
incidents are given in the dataset, which form a sample S = {S1 , . . . , S34 } of a point process on S .
Hong Kong is divided into 18 districts. In this study we assume a rectangular shape for each
district, whose four boundaries are given in the spreadsheet “18 districts” of data.xlsx, measured in
longitude and latitude. The spreadsheet also provides the area and population density (in million per
unit area) of each district. Define a covariate V (s), for s ∈ S , by
V (s) = population density of district d if s is located in district d.
Thus, V (s) has a constant value for all s belonging to the same district.
Assume that S follows a Cox point process model driven by a random intensity Λ satisfying
ln Λ(s) = ln Wα + βV (s),
s ∈ S,
where β ∈ R is an unknown coefficient and Wα denotes a gamma (α, α) random variable with an
unknown parameter α > 0 and density function
αα wα−1 e−αw
fW (w|α) =
,
Γ(α)
Note that Wα has mean 1 and variance 1/α.
1
w > 0.
Complete TASKS 1–4 with the help of a convenient computer software of your choice.
TASK 1 (4%)
Display Hong Kong as a rectangle on a 2D graph, with x- and y-axes representing longitude
and latitude, respectively.
Show on the same graph (i) the boundaries of the 18 districts, and (ii) the 34 points in S .
TASK 2 (8%)
Show that the proposed Cox point process has a parametric intensity given by
ρ(s|β) = eβV (s) ,
s ∈ S,
and a parametric conditional intensity given by
λ(s, S|α, β) =
eβV (s) (α + #S)
R
,
α + S eβV (s) ds
s ∈ S , S ∈ E (exponential space).
[Hint: derive first the density f (S) of the Cox point process, then use the fact that the conditional
intensity is given by f ({s} ∪ S)/f (S).]
With the help of a numerical optimisation package, calculate the maximum conditional
pseudo-likelihood estimates (α̂Cox , β̂Cox ) of (α, β).
Based on the above results, estimate the expected number of incidents occurring in each of
the 18 districts.
TASK 3 (8%)
Assuming a Poisson point process model for S with intensity ρ(s|β) = eβV (s) , calculate the
maximum likelihood estimate β̂P oi of β.
Generate 10000 parametric bootstrap samples from the Poisson point process model with
intensity ρ(·|β̂P oi ).
Based on each bootstrap sample, calculate the maximum conditional pseudo-likelihood
∗
estimate α̂Cox
of α, following the same procedure as described in TASK 2. Plot the
∗
empirical distribution function of the 10000 replicates of α̂Cox
thus obtained.
2
For α > 0, the Cox point process has a reweighted pair correlation function equal to a constant
1+1/α > 1, suggesting a tendency of “clusterings” of the violent incidents. As α → ∞, the reweighted
pair correlation function converges to 1 and Wα converges to a non-random constant 1. In the limiting
case α = ∞, the Cox point process reduces to a Poisson point process with intensity ρ(s|β), and the
violent incidents become independently located.
TASK 4 (5%)
With the help of the parametric bootstrap distribution found in TASK 3, suggest a
procedure for testing the null hypothesis (H0 ) that the violent incidents are independently
located, against the alternative (H1 ) that the incidents have a clustering tendency.
Report a p-value for the test.
[Hint: You may consider using α̂Cox as a test statistic, and explain why it is an appropriate choice.]
∗ Points to note ∗
• In the main text of your report, show and explain your steps, and display formulae in their
conventional mathematical form. Do not explain anything using computer code.
• Attach your computer code to your report as an appendix. Include brief comments on lines
which involve complicated operations.
********** END OF MINI-PROJECT **********
3