Getting Started

Installation

EnhancedBayesianNetworks.jl is not yet registered in Julia's General registry, so install it directly from its GitHub repository. From the Julia REPL, enter the package manager with ] and add it by URL:

pkg> add https://github.com/JuliaUQ/EnhancedBayesianNetworks.jl

or, equivalently, from code:

using Pkg
Pkg.add(url = "https://github.com/JuliaUQ/EnhancedBayesianNetworks.jl")

Then load it — this also brings in the re-exported UncertaintyQuantification.jl types (Model, Parameter, RandomVariable, Interval, ProbabilityBox, the simulation methods) and the distributions used to define nodes:

using EnhancedBayesianNetworks

Your first Bayesian network

Building a network always follows the same three steps: construct the nodes, wire the edges with add_child!, and finalize with order!. Here is a two-node weather/sprinkler model — a root node W and a child S whose CPT is conditioned on it:

W = DiscreteNode(:W)
W[:W => :sunny]  = 0.5
W[:W => :cloudy] = 0.5

S = DiscreteNode(:S, [:W])
S[:W => :sunny,  :S => :on] = 0.9; S[:W => :sunny,  :S => :off] = 0.1
S[:W => :cloudy, :S => :on] = 0.2; S[:W => :cloudy, :S => :off] = 0.8

bn = BayesianNetwork([W, S])
add_child!(bn, :W, :S)
order!(bn)

Now query it. infer returns the posterior over a query variable given some evidence:

infer(bn, :S, Evidence(:W => :sunny))       # P(S | W = sunny)

Posterior P(S | W=sunny)

S	Probability
------------------------
on	0.9
off	0.1

With no evidence you get the prior marginal:

infer(bn, :S, Evidence())                   # P(S)

Posterior P(S)

S	Probability
------------------------
on	0.55
off	0.45

A first enhanced Bayesian network

The real power of the package is mixing in continuous and functional nodes — a node whose conditional table comes from a reliability analysis rather than being tabulated. The enhanced network is reduced to a discrete one with reduce, then queried exactly as above:

Load = DiscreteNode(:Load, [:low => [Parameter(1.0, :Load)], :high => [Parameter(3.0, :Load)]])
Load[:Load => :low] = 0.7; Load[:Load => :high] = 0.3
R = ContinuousNode(:R, Normal(3.0, 0.5))                 # a continuous resistance
model = Model(df -> df.R .- df.Load, :g)                 # limit state g = R - Load
F = DiscreteFunctionalNode(:F, [model], df -> df.g, MonteCarlo(2000))

ebn = EnhancedBayesianNetwork([Load, R, F])
add_child!(ebn, :Load, :F); add_child!(ebn, :R, :F); order!(ebn)

reduced = reduce(ebn)                                    # -> BayesianNetwork
infer(reduced, :F, Evidence(:Load => :high))            # failure probability given a high load

Making the resistance imprecise — ContinuousNode(:R, Interval(2.0, 4.0)) with a DoubleLoop(MonteCarlo(1000)) simulation — turns the result into interval bounds and reduces to a CredalNetwork instead. See Reduction & Reliability Analysis for the full story.

Where to next

• Introduction — the concepts behind enhanced Bayesian networks.

• Nodes and Networks — the building blocks in depth.

• Reduction & Reliability Analysis — evaluating enhanced networks, with and without imprecision.

• Inference, Parameter Learning, and Plotting.