Implement dependent parameters feature for FreeParameters

[glwagner]

Usage is something like

priors = (a=Normal(0, 1), b=Normal(0, 1)) # free parameters
c(p) = p.a + p.b # compute a third dependent parameter `c` as a function of `a` and `b`
parameters = FreeParameters(priors, dependent_parameters=(; c))

Closes #269

[navidcy]

Can you create another simple example in FreeParameters docstring that demonstrates the dependent_parameters kwarg?

[navidcy]

a bit further down there is a redefinition of this method:

observation_map(map::ConcatenatedVectorNormMap, observations) = hcat(0.0)

which one we want?

[navidcy]

is it because of this that docs fail?

** incremental compilation may be fatally broken for this module **

[navidcy]

We also need to update show(io::IO, p::FreeParameters)

[navidcy]

I gave it a crack but it could be done better :)

julia> priors = (ν = Normal(1e-4, 1e-5), κ = Normal(1e-3, 1e-5))
(ν = Normal{Float64}(μ=0.0001, σ=1.0e-5), κ = Normal{Float64}(μ=0.001, σ=1.0e-5))

julia> free_parameters = FreeParameters(priors)
FreeParameters with 2 parameters
├── names: (:ν, :κ)
├── priors: Dict{Symbol, Any}
│   ├── ν => Normal{Float64}(μ=0.0001, σ=1.0e-5)
│   └── κ => Normal{Float64}(μ=0.001, σ=1.0e-5)
└── dependent parameters: Dict{Symbol, Any}

julia> c(p) = p.ν + p.κ # compute a third dependent parameter `c` as a function of `ν` and `κ`
c (generic function with 1 method)

julia> free_parameters_with_a_dependent = FreeParameters(priors, dependent_parameters=(; c))
FreeParameters with 2 parameters and 1 dependent parameters
├── names: (:ν, :κ)
├── priors: Dict{Symbol, Any}
│   ├── ν => Normal{Float64}(μ=0.0001, σ=1.0e-5)
│   └── κ => Normal{Float64}(μ=0.001, σ=1.0e-5)
└── dependent parameters: Dict{Symbol, Any}
    └── c => c

[navidcy]

docs seems to fails at https://github.com/CliMA/ParameterEstimocean.jl/runs/6742066654?check_suite_focus=true#step:6:939
strange...

[navidcy]

I gave it a crack but it could be done better :)

julia> priors = (ν = Normal(1e-4, 1e-5), κ = Normal(1e-3, 1e-5))
(ν = Normal{Float64}(μ=0.0001, σ=1.0e-5), κ = Normal{Float64}(μ=0.001, σ=1.0e-5))

julia> free_parameters = FreeParameters(priors)
FreeParameters with 2 parameters
├── names: (:ν, :κ)
├── priors: Dict{Symbol, Any}
│   ├── ν => Normal{Float64}(μ=0.0001, σ=1.0e-5)
│   └── κ => Normal{Float64}(μ=0.001, σ=1.0e-5)
└── dependent parameters: Dict{Symbol, Any}

julia> c(p) = p.ν + p.κ # compute a third dependent parameter `c` as a function of `ν` and `κ`
c (generic function with 1 method)

julia> free_parameters_with_a_dependent = FreeParameters(priors, dependent_parameters=(; c))
FreeParameters with 2 parameters and 1 dependent parameters
├── names: (:ν, :κ)
├── priors: Dict{Symbol, Any}
│   ├── ν => Normal{Float64}(μ=0.0001, σ=1.0e-5)
│   └── κ => Normal{Float64}(μ=0.001, σ=1.0e-5)
└── dependent parameters: Dict{Symbol, Any}
    └── c => c

it'd be nice if we can print something related to the dependent parameters... but I don't know what? if c was defined as a function then there is nothing to print out...

[glwagner]

it'd be nice if we can print something related to the dependent parameters... but I don't know what? if c was defined as a function then there is nothing to print out...

we can use Oceananigans' prettysummary to print function information. But as you say this doesn't give much additional info; it just prints the name of the function and optionally how many methods are defined for it.

[navidcy]

I'll try to build the docs locally to see if I run into same issue(s).