Flaky test test/sample/test_sample.py::test_bridge_sampling

[dweindl]

For example, in https://github.com/ICB-DCM/pyPESTO/actions/runs/10882550532/job/30193828221?pr=1459:

=================================== FAILURES ===================================
_____________________________ test_bridge_sampling _____________________________

    @pytest.mark.flaky(reruns=2)
    def test_bridge_sampling():
        tol = 2
        # define problem
        objective = Objective(
            fun=lambda x: -gaussian_llh(x),
            grad=gaussian_nllh_grad,
            hess=gaussian_nllh_hess,
        )
        prior_true = NegLogParameterPriors(
            [
                {
                    "index": 0,
                    "density_fun": lambda x: (1 / (10 + 10)),
                    "density_dx": lambda x: 0,
                    "density_ddx": lambda x: 0,
                },
            ]
        )
        problem = pypesto.Problem(
            objective=AggregatedObjective([objective, prior_true]),
            lb=[-10],
            ub=[10],
            x_names=["x"],
        )
    
        # run optimization and MCMC
        result = optimize.minimize(problem, progress_bar=False, n_starts=10)
        result = sample.sample(
            problem,
            n_samples=1000,
            result=result,
        )
    
        # compute the log evidence using harmonic mean
        bridge_log_evidence = sample.evidence.bridge_sampling_log_evidence(result)
        harmonic_evidence = sample.evidence.harmonic_mean_log_evidence(result)
>       assert np.isclose(bridge_log_evidence, harmonic_evidence, atol=tol)
E       assert False
E        +  where False = <function isclose at 0x7f3c1c042bf0>(0.2670074583034374, -3.788734352667505, atol=2)
E        +    where <function isclose at 0x7f3c1c042bf0> = np.isclose

test/sample/test_sample.py:969: AssertionError
----------------------------- Captured stderr call -----------------------------

Increase number of optimizations or samples or reduce the tolerance of increase number of trials.

[PaulJonasJost]

in a quick test, neither increasing starts to 100 nor increasing samples to 5000 really helped. Results are also so far apart that no reasonable tolerance could be set IMO. Seems to be something deeper, @arrjon could you have a look at this?

[arrjon]

I will have look!