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MTHM017 Advanced Topics in Statistics

创建日期：2024-04-30 14:34:24

所属分类：数学mathematics

标签： MTHM017

Advanced Topics in Statistics

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MTHM017 Advanced Topics in Statistics

Assignment
The assignment has three main parts. Part A involves fitting an auto-regressive process to time series data
model using the BUGS language and assessing the effect of using different model structures on the estimation
of missing data. Part B involves using different methods for classification of data into two groups. Part C
involves producing a narrated power point presentation based on question 3 of part B.
Part A gives 50% of your final marks, Part B gives 30% of your final marks and Part C gives 20% of your
final marks. [Assignment: 160 marks in total]
A. Bayesian Inference [80 marks]
The dataset contains measurements of particulate matter (PM10) air pollution in London (measured at the
Bexley and Hounslow sites) for 2000 to 2004. The data can be found in London_Pollution.csv.
1. [4 marks] Summarise the two sets of data and calculate the number of missing data points for each
monitoring location, by year. Comment on whether the patterns of missingness have changed over time.
2. [3 marks] Plot the PM10 measurements against time for the two sites, highlighting (showing clearly)
the periods of missing data.
3. [5 marks] The locations in Eastings and Northings of the two locations are Bexley: (551862, 176380);
and Hounslow: (521070, 178480). Plot these two monitor locations on a map of London and comment
on any difference you found in the summaries of the data in the context of the geographical location of
the monitoring sites. The necessary shapefiles are on the ELE page of the course.
Considering the Bexley data, there is missing data. We are going to fit a model that allows us to estimate these
missing data by treating them as model parameters that will be estimated (and we find posterior distributions
for them). As we have time series data, we are going to use the fact that day-to-day measurements will be
correlated, i.e. today’s measurement will correlate with yesterday’s.
A random walk process of order 1, RW(1), is defined at time t as
Yt − Yt−1 = wt
Yt = Yt−1 + wt
Where wt are a set of realisations of random (or white) noise, e.g. wt ∼ N(0, σ2w). Note the first line refers to
the differences in the values at consecutive time points being white noise.
We are interested in fitting a random walk model to the Bexley data. The model will be of the following form:
Bexleyt ∼ N(Yt, σ2v)
Yt ∼ N(Yt−1, σ2w)
Where σ2w is the variance of the white noise process associated to the random walk. We then make noisy
measurements of this random walk process, thus Bexleyt, the measurement we have at time t, equals to
the true value of the underlying process Yt plus some measurement error. In the formula above, σ2v is the
variance of this measurement error.
4. [16 marks] Code this model using the model definition below in JAGS to analyse the Bexley data from
1st January 2000 to 31st December 2003 (NOTE the end year). Due to the nature of the model you
1
will have to explicitly specify a value for Y1 in the model (i.e. for the first time point as Y0 doesn’t
exist). One suggestion might be Y1 ∼ dnorm(0, 0.001). The model definition can be found below.
Run the model for 8,000 iterations, with 2 chains, discarding the first 4,000 as ‘burn-in’. Produce trace
plots for the chains and summaries for the fitted parameters (including the missing data). Hint: You
should initialise both chains. One suggestion might be using the mean and median to initialise the
missing values of Bexley, and using random uniforms (with a narrow interval centred around say 20) to
initialise Y.

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关键词一关键词二关键词三关键词四关键词五和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 EMESTER1 MAS8383 ECO 512 STAT 8310 CMN3102 MA577 CMPT 225 COMP0045 Methods Equations MATH 113 Math 3283W ICS-33 EN4302/ENT603 BIA B350F MA318 MTHM506 MECH 5315M ECONOMICS MAS8382 COM 2004 PX3142 XJEL 3662 STAT 231 MGT B399F PX4131 COM2108 30AM MSCI521 ECONM1015 ACFI304 GR5241 MATH10101 ECON 2070 COMS31900 EFIM20011 CSE 250B ACSE-5 STAT4207 SOFT2412 ELEC 331 AY2020 MSIN0209 FIT2094 CS 241L ST404 CS 411 3D CA3 INF4002 COMP3506 SIT718 CS 188 CS 170 MATH 138 CSE 251A CMT118 DATA5207 CMPT307 CMPT459 T1 PGEE11108 COSC 3P32 ME 163 MATH96007 7QQMM203 EE6227 BA 574 STA 4234 ECO206Y1Y ECO2008 MT2300 MATH 11158 CS 527 MACM 316 CSE474 2DI70 ISE 525 COMP3411 EMAT30007 7CCSMBDT MFIN704 MFIN704W21 MfIB ECE 438 CS 436 F36 CS5344 FE 621A FE621 TBA 612 ECM3151 ECMM422 MF1 MSIN0107 ESSMENT CS 5854 MFIT 5008 MIPS R4000 ENG5274 BU52018 ENG2079 BIOA02 STA2570 F0 INF553 STAT 440 STAT3008 COMP9417 COMP6451 6COM1042 BU52006 ST303 HW-1 CISC-235 CS 510 MATH3161 ECN 140 ECE391 Comp 3613 CVEN 9625 PRG455 UESTION 1 EARN 5 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