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lowerBound may be -inf and upperBound may be inf. inf as a lower bound and -inf as an upper bound are invalid.
If priors are specified for any parameter, every estimated parameter with an infinite bound must have an explicit proper prior. The default uniform(lowerBound, upperBound) would be improper.
The current state of petab.v2:
Parameter.lb/ub are plain floats without a finiteness check (core.py#L1048-L1055). lb == ub == inf passes validation, because Parameter._validate only checks lb > ub (core.py#L1136). The existing _is_finite_or_neg_inf / _is_finite_or_pos_inf validators for time could be reused here.
There is no check that parameters with infinite bounds have an explicit prior when the problem has a MAP objective. Problem.get_priors creates Uniform(p.lb, p.ub) for parameters without a prior, which may be infinite (core.py#L2083).
Problem.get_startpoint_distributions creates the same default uniform distribution, also for maximum likelihood problems (core.py#L2101). Start points can't be sampled for parameters with infinite bounds and no prior. This should raise an informative error, or the caller should be able to provide a fallback distribution.
To do:
Restrict lb to finite or -inf and ub to finite or inf.
Add a validation task: if has_map_objective, every estimated parameter with an infinite bound needs an explicit priorDistribution. Whether the specified prior is proper, e.g. uniform with infinite priorParameters, is still open in the spec. This could be checked together with the existing TODO in CheckPriorDistribution (lint.py#L819).
Handle infinite bounds in start point sampling.
Test that prior truncation works with one-sided infinite bounds (e.g., log-normal with bounds 0/inf), i.e., that it is a no-op where the bounds match the prior's domain.
Nominal values: no change for now. Pending v2: Allow infinite nominalValue PEtab#685, which proposes allowing inf/-inf. Currently, infinite nominal values are not rejected.
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