STAT2001 Mathematical Statistics
Mathematical Statistics
STAT2001/STAT2013/STAT6013 - Introductory
Mathematical Statistics (for Actuarial
Studies)/Principles of Mathematical Statistics (for
Actuarial Studies)
What is statistics? (very brief overview)
Typically statistics involves:
(1) collecting data: x1, x2, . . . , xn.
(2) presenting and describing data
(3) propose a probability model to summarise data e.g. N(µ,2).
(4) estimate parameters (quantities) in the model
µˆ =
1
n
nX
i=1
xi and ˆ2 =
1
n 1
nX
i=1
(xi x¯)2
(5) use sample statistics to do inference for parameters in model
- e.g. confidence interval for true µ
- e.g. hypothesis test µ = µ0 vs µ 6= µ0.
e.g measure heights of people
eg boxplot histogram numericalsummary
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jig a IR
ofparametersIM
with a small number
n 2 parameters
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Research led teaching (and a bit about me)
• I am a statistical scientist.
• My research focuses on developing new statistical methods for
analysing: compositional data (proportions which sum to one),
data on spheres or on more general curved surfaces (manifolds)
and data with very complex structures.
• Applications include: Paleomagnetism (study of Earth’s ancient
magnetic field), household expenditure survey data,
geochemistry (composition of rocks), Microbiome count data
(stool samples).
• See slides of my most recent work on analysing Microbiome
data and how I’ve used ideas from this course (not assessable).
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OVERVIEW
Introduction (Chapter 1 in textbook)