Environmental statistics
Lecture 1
Marian Scott
room 220
session 14/15
Outline of course
There
are a variety of assessments depending
on which programme you are studying (M level
and MSc have an addi
Bayesian Statistics
Lecture 5
Vincent Macaulay
School of Mathematics and Statistics
University of Glasgow
Lecture 5
Central posterior intervals and HPDRs
Central posterior intervals and HPDRs
Central
7
Modeling Extreme Climate Events:
Two Case Studies in Mexico
O. Rafael GarcaCueto and Nstor SantillnSoto
Universidad Autnoma de Baja California
Instituto de Ingeniera
Mxico
1. Introduction
The most
Environmental statistics
Lecture 1
Marian Scott
room 220
session 15/16
Outline of course
Tues
lecture Maths Building 326, Thurs lecture,
James watt south, 355 now moved to Maths
Building , room 516
Environmental statisticslecture 3/4
Modelling variability and handling
uncertainty
Marian Scott
room 220
session 15/16
what we will cover
Distributions:
Normal, Poisson, lognormal
extreme value di
Introduction to modelling extremes
Marian Scott
(with thanks to Clive Anderson, Trevor Hoey)
Introduction
Examples of extremes in environmental
contexts
Some statistical models for extremes
Block m
Environmental statistics extremes
Marian Scott
room 220
session 15/16
what we will cover
Distributions
standard distributions
The very standard distributions
continuous
Normal, X~ N(, 2), X
log Norm
Environmental statistics
Summary points
what have we covered and what
should you know?
Outline
You will have statistical tables,
the Env Stats formula sheet will be provided attached
to the exam paper
Wednesday, 7th May 2014
09.30 am 11.00 am
EXAMINATION FOR THE DEGREES OF M.A., M.SCI AND B.SC. (SCIENCE)
ENVIRONMENTAL STATISTICS
Hand calculators with simple basic functions (log, exp, square root, e
Example sheet 1, solutions for Qns 4
4 general approach would be to used a a formula for the approximate variance of a function
of random van'ables
Y= f(X1, ...,Xn), then the approximate variance o
Environmental statisticslecture 3/4
Modelling variability and handling
uncertainty
Marian Scott
room 220
session 14/15
what we will cover
Distributions:
Normal, Poisson, lognormal
extreme value di
Spatial point processes
A Spatial point process is a set of locations, irregularly distributed
within a designated region and presumed to have been generated
by some form of stochastic (random) mechan
School of Mathematics and Statistics
Environmental Statistics
Session 14/15
Example sheet 1: Censoring, uncertainty, limits of detection
A: censoring and uncertainty calculations
1. Limits of detectio
STATISTICS 4H/M
Environmental Statistics Practical 1
Session 14/15
Aims and intended learning outcomes
To explore graphically some environmental data sets
To consider graphical representations of some
School of Mathematics and Statistics
Session 14/15
Example sheet 2: Environmental Statistics
Several of these examples are similar in nature to exam questions, in that you are
asked to comment on stat
STATISTICS 4H/M
Environmental Statistics Practical 2
Session 14/15
Spatial analysis and dealing with extremes
Aims and intended learning outcomes
To explore a quantile regression example and to interp
Solutions to Env Stats 2014 (level H and M)
1 a) Trend has been defined in a variety of ways
A longterm change in the mean level
Longterm movement
The nonrandom function (t)= E (Y(t)
Trend is a
?
?
EXAMINATION FOR THE DEGREE OF M.SC. (TAUGHT)
ENVIRONMENTAL STATISTICS Aquatic and Freshwater Sciences
Hand calculators with simple basic functions (log, exp, square root, etc.) may be used in
exam
Some real life changepoint
issues
Whitelees wind farm with Susan
Waldron, Helen Murray and
Fraser Tough
The site
Outline
key question:what is the effect of the
windfarm development?
A) impact assess
Additional formula sheet for Environmental Statistics, 20142015
Probability distributions for Extremes
Generalised Extreme Value (GEV) distribution, has three parameters, location, scale
and shape (u
Spatial modelling
Lecture
what
11/12
will we cover?
types of spatial data
spatial correlations
statistical models for spatial data
mapping
some examples
Case
1: point processes (like location o
~W (1) in ecological sciences in time

A simple trend line
A pvalue or a 95% confidence interval for the slope
A smooth curve
The relative change in an index between two time points(%)
A linear regr
some more information about
indicators
Measuring biodiversity
Composite indices
The 2010 Biodiversity target
To
significantly reduce the rate of biodiversity
loss by 2010
European Member States went
Sampling and monitoring (contd)
B:
designing monitoring experiments
Outline
goals:
to detect unexpected changes and
trends
standard
statistical sampling schemes are
adequate, but there are special
School of Mathematics and Statistics
Session 14/15
Example sheet 3: Environmental Statistics
1. If X1,., is a sequence of independent standard exponential Exp(1) variables,
a. show that F(x)= 1ex fo
Example sheet 1, solutions for Qns 4
4 general approach would be to used a a formula for the approximate variance of a function
of random variables
Y= f(X1, ,Xn), then the approximate variance of Y is
Uncertainties
Example
IPCC produced guidelines on two approaches to the
uncertainty calculations for greenhouse gas emissions.
Total greenhouse gas emissions, C, for a given year
are calculated as
C
DetectionandEstimation
Detection
MannKendall statistic
Seasonal Kendall trend test
Heterogeneity
Serial Correlation
1
FromEEA,2013,ozonetrends
2
The MannKendall statistic for season j
sgn(x) =1 if x