Error small Variance

[johannesgiersdorf]

The estimated variance is sometimes to small, so the Normal distribution can't be constructed.

Error message

ERROR: LoadError: ArgumentError: Normal: the condition σ >= zero(σ) is not satisfied.
Stacktrace:
 [1] macro expansion
   @ ~/.julia/packages/Distributions/cNe2C/src/utils.jl:6 [inlined]
 [2] #Normal#112
   @ ~/.julia/packages/Distributions/cNe2C/src/univariate/continuous/normal.jl:37 [inlined]
 [3] Normal(μ::Float64, σ::Float64)
   @ Distributions ~/.julia/packages/Distributions/cNe2C/src/univariate/continuous/normal.jl:37
 [4] quadrature(bquad::BayesQuad{SqExponentialKernel, Float64, Float64}, model::BayesModel{ZeroMeanDiagNormal{Tuple{Base.OneTo{Int64}}}, typeof(log_f)}, samples::Vector{Vector{Float64}})
   @ BayesianQuadrature ~/.julia/packages/BayesianQuadrature/eNnqB/src/bayesquads/bayesquad.jl:58
 [5] (::BayesQuad{SqExponentialKernel, Float64, Float64})(rng::MersenneTwister, model::BayesModel{ZeroMeanDiagNormal{Tuple{Base.OneTo{Int64}}}, typeof(log_f)}, sampler::PriorSampling; x_init::Vector{Any}, nsamples::Int64, callback::Nothing)
   @ BayesianQuadrature ~/.julia/packages/BayesianQuadrature/eNnqB/src/interface.jl:10
 [6] top-level scope
   @ ~/Documents/uni/master/master-thesis-code-base/src/min_example_normal.jl:13
 [7] include(fname::String)
   @ Base.MainInclude ./client.jl:444
 [8] top-level scope
   @ REPL[8]:1

Example

using BayesianQuadrature
using Distributions
using KernelFunctions
using Random

rng = Random.MersenneTwister(42)

p_0 = MvNormal(ones(2)) # As for now the prior must be a MvNormal
log_f(x) = logpdf(MvNormal(0.5 * ones(2)), x) 
m = BayesModel(p_0, log_f) 
bquad = BayesQuad(SEKernel(); l=10.0, σ=1.0) 
sampler = PriorSampling() 
p_I, _ = bquad(rng, m, sampler; nsamples=200) # Returns a Normal distribution
@show p_I 

[johannesgiersdorf]

It is possible to create a Normal with no checks. It seems that the estimated sigma is sometimes negative. On first glace it seems this happens less often using the test environment. I tested different seeds in the unit test vs just calling it directly (where i got negative values for different seeds)

vals = [std(bquad(Random.MersenneTwister(i), m, sampler; nsamples=200)[1]) for i in 1:300] 
> sum(vals .<= 0)/length(vals) = 0.7866666666666666 #pakage environment
> sum(vals .<= 0)/length(vals) = 0.07333333333333333 #test environment

[johannesgiersdorf]

It seems to me to be a numerical error in evaluate_var. The easiest fix should be to take 0 instead of a negative value.

[johannesgiersdorf]

For now added a warning in case of numerical error #25