Homework 5

Space/time covariance models

**Date given: **10/10

**Due: **10/22
noon

** **

**Part 1** (20 points)

Consider the space/time random
field (S/TRF) *X( p)*, with

*c _{X}*(

where *r* is the spatial lag
(*Km)*, *t* is the temporal
lag (day), and the covariance parameters are *c _{01}*=1.5

1) Can this field be assumed to
be homogeneous/stationary? Can you express this covariance model as a
space/time separable model? What is the variance of *X( p)*? Describe
physically the covariance model and each of its coefficients

2) Write the
expression the covariance when the temporal lag *t *is zero:

*c** _{X}*(

3) Write the
expression the covariance when the spatial lag *r *is zero:

*c** _{X}*(

**Part2** (30 points)

1) Consider a homogenous
space/time random field (S/TRF) *X( p)* where we know that it’s
covariance model verifies the following two expressions

*c _{X}*(

*c _{X}*(

where var* _{X}*=2.0

2) Now consider the following two expressions

*c _{X}*(

*c _{X}*(

where var* _{X}*=2.0

**Part 3** (25 points)

1) Model the space/time covariance of the Arsenic dataset dataAS.txt. Do an exploratory analysis of this data and model its covariance model. Provide a write up describing your analysis. This write up should describe the distribution of the data (is it normal?), it should have a figure showing the experimental and model covariance, it should provide the mathematical expression of the spatial and temporal components of your s/t covariance, and it should provide the expression for the full s/t covariance model.

2) Do the same analysis for the Flu dataset dataFLU.txt.

**Part 4** (25 points)

Model the space/time covariance for your __project dataset__ and add
this to your growing project report. This write-up should include what you
have produced in previous homework, i.e. it should lay out your research
question with relevant citations, it should have an exploratory data analysis
showing your project data, it should include your covariance analysis, your covariance
model (including a figure of the covariance model on top of your experimental
covariance values), and its interpretation. Provide citations that either relates
your covariance modeling with previous works, or write something up claiming
you are generating novel covariance results. This write-up will serve as a
part of your final project report.

Submit parts 1, 2 and 3 as a well-written word document named yourfirstname_yourlastname_hwk5_part123.docx that you send to the instructor. Submit part 4 separately as a well-written word document named yourfirstname_yourlastname_hwk5_part4.docx that you also send to the instructor.