DATA
ANALYSIS (DA_2024) SYLLABUS
Academic
Year 2023-2024, 6 ECTS.
A course for the Master
Programs in Genetics and Molecular Biology and Neurobiology, given in the 2nd semester.
Instructor:
Prof.Andrea Giansanti, Sapienza University
of Rome, Department of Physics, (Marconi Building (CU013), 2nd floor,
room 211) tel. 0649914367 (3385075611)
andrea.giansanti@roma1.infn.it
Evaluation: based on the discussion of a
research/methodological paper, written essays, written tests, home-works
and participation to discussions : 40%. Final oral exam: 60%.
Recommended textbooks
[R]Bernard Rosner - Fundamentals of Biostatistics-Brooks
Cole (2015).
[WS] Michael C.
Whitlock and Dolph Schluter - The
Analysis of Biological Data-W. H. Freeman and Company (2015)
Note: STUDY
MATERIALS, LECTURE OUTLINES & NOTES, SLIDES CAN BE FOUND ON THE
e-learning Sapienza Platform: (course DA_2024)
Access to the recordings of the lectures, for strict personal use, can be requested
from the instructor
0. INTRODUCTION (see also the inaugural
lecture DA_2024_inaugural_lecture.pdf)
Data, Metadata, Ontologies.
Data/Models/Computation/Simulation
Facts/things (Wittgenstein redux: 1.1 the world is the totality of
facts not of things)
Data tables (objects/descriptors)
Galilei's remouval of the animal at the origin of moderm science, based
on physics
Styles of physics and styles of biology: "geometry vs. stamp collection"
Randomness, noise
Evolution and randomness: the case of surviving war planes
Elements of the scientific method: observations/models
The universal structure of a scientific paper
Forms of
reasoning: deduction, induction, abduction.
The
issue of reproducibility
Science
before and after the computer era
The birth of
computational (in silico) biology
Computational
systems biology/medicine
Numeracy
(Cell biology by the numbers)
The Biological
Bayesian revolution.
2. DATA AND THEIR REPRESENTATION (WS
chap. 2, R 2.8)
types of data and
variables (categorical, numerical)
displaying the data
(scatter plots, bar graphs,
pie charts, strip charts, box plots, frequency tables,
histograms: binning and
resolution)
3.
DESCRIPTIVE STATISTICS (R 2.1-2.6, W&S chap.3 (to be used as
a rewiew reading))
measures of
location (aritmetic mean, median, mode, mean vs median)
measures of spread (range,
quantiles, variance and standard deviation, coefficient of variation)
Chisini's principles for the means
[Graziani2009]
4.
PROBABILISTIC REASONING (R 3.1-3.8, W&S chap. 5)
uncertainty and decisions
events, trials,
uncertainty, probability
definitions of probabilities: classic, frequentist, subjective
graphical
representations through Venn diagrams
dependent/independent events
addition and multiplication formulas
conditional probabilities
Bayes’ theorem and
its relevance (subjective/objective, a fair representation of knowledge
accumulation) [Puga2015]
Eikosograms (RW
Oldford)[ https://cran.r-project.org/web/packages/eikosograms/vignettes/Introduction.html ]
5.
BAYES’ THEOREM AND TESTS (see lecture n.10)
Clinical tests as
binary classifications (R 3.7)
Clinical tests and
conditional probabilities (R 3.8)
A bayesian
classifier of protein sequences [Bulashevska2008]
ROC curves (R 3.9,
see also [Fawcett2006])
Confusion matrices
Relative risk
6.
PROBABILITY DISTRIBUTIONS
random variables (R
4.1- 4.6)
Probability distributions:
discrete/continuous (R 5.1-5.4)
Moments of a
probability distribution
The normal
distribution (R 5.3-5.4, W&S chap. 10 suggested recapitulation reading)
Linear combinations
of random variables (R 5.6)
Z-transform and
percentiles of N(0,1) (R 5.5)
7.
INFERENTIAL STATISTICS AND ESTIMATION (R 6.1-6.7 )
Population and
samples moments and estimators
The arithmetic mean as maximum likelihood estimator of the first
moment of a gaussian distribution [see notes DA_2020_L12_notes]
Random
samples (tables of random numbers)
Biased/unbiased
estimators
Point estimation of
the mean
Standard error of
the mean
Error bars [https://www.nature.com/articles/nmeth.2659
]
Central limit theorem
Interval estimation
t-distribution, degrees
of freedom
Confidence intervals for
the mean of anormal distribution
Point estimator of the
variance
Chi-square distribution,
degrees of freedom
Interval estimation for
the variance of a normal distribution
The bootstrap (R
6.11, [https://www.nature.com/articles/nmeth.3414])
8. HYPOTHESIS TESTING (one/two samples) ( R 7.1-
7.6; 8.1-8.4, 8.6 ,W&S chap. 6)
Formal aspects (see
lecture notes included in L 14 slides)
Null hypothesis and
alternative hypothesis.
Errors of Type I and
Type II.
Confidence levels
Acceptance-rejection
regions
p-value.
Power
One sample/two sample tests
One sided test/two sided test
Longitudinal/cross-sectional studies
Testing for the equality of two variances
F distribution
F test
9. NON PARAMETRIC TESTS (R 9.1-9.2; 9.4
,W&S chap.13)
The problem of non-normal distributed data
Lognormal distribution
Tests of normality
Ranks
Sign test
Wilcoxon rank-sum test (Mann-Whitney U test)
10. MULTIPLE PARAMETRIC/NON PARAMETRIC TESTS
(R 12.1-12-4; 12.7)
Whitin
group/between-group variability
One-way ANOVA
Bonferroni correction
Kruskal-Wallis test
11. CORRELATION AND
REGRESSION (R 11.1-11-5 ; 11.7, W&S chapp. 16 and 17 )
Association of variables, correlations/dependencies
Correlation is not
causation [https://www.nature.com/articles/nmeth.3587]
The mathematics of linearity: vectors, matrices, linear
transformations
Linear regression analysis independent/dependent variables
Least squares method [see handout SJ Miller]]
The correlation coefficient
Principal
component analysis (PCA) [see Higgs&Attwood chap. 2]
- Docente: ANDREA GIANSANTI