Erik Kusch, PhD Student
Department of Biology
Section for Ecoinformatics & Biodiversity
Center for Biodiversity Dynamics in a Changing World (BIOCHANGE)
Aarhus University
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[Study Group] Bayesian Networks 1
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[Study Group] Bayesian Networks
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[Study Group] Bayesian Networks
Discrete Continuous
Encodes…
Finite number of events Infinite number of events
Data encoding
Fixed table of values Graph of values
Characterised
by
Probability function Pr() Density function f()
Examples
-
Number rolled on a die
- Number of study group members who will
stick with it till the end
-
-
Temperature ranges
- Satisfaction rate of study group members
with the group
-
Image source
5
[00, 33] (33, 66] (66,
100]
TOTAL
[00, 20]
0% 10% 5% 15%
(20, 40]
30% 0% 5% 35%
(40, 60]
0% 5% 15% 20%
(60, 80]
5% 0% 5% 10%
(80,
100]
0% 5% 15% 20%
TOTAL
35% 20% 45% 100%
Marginal
Probability of
Marginal Probability of
Conditional Probability
of 󰇛󰇠
Joint Probability of
󰇛󰇠 󰇟󰇠
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[Study Group] Bayesian Networks
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[Study Group] Bayesian Networks
Posterior probability
Likelihood
Prior probability
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[Study Group] Bayesian Networks Image source
Prior beliefs are updated given the
observed data by finding a compromise
between the prior and the likelihood
Because Bayes is built on distributions,
parameter and belief uncertainty can be
encoded via the shape/spread of each
distribution
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Nodes / Vertices
Arc / Edge / Link
Vertices
Graph
Arcs
Tail Head
If u = v, arc = loop
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[Study Group] Bayesian Networks
Image source
Bayesian Networks
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[Study Group] Bayesian Networks
11/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 13
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[Study Group] Bayesian Networks Image source, blue
indicates observed data
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[Study Group] Bayesian Networks
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[Study Group] Bayesian Networks
Moralisation