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Right now, we assume an observation at t_0 = obs_times[0]. This is potentially unintuitive, especially for continuous-time models. We should probably instead
Infer t_0 = obs_times[0] if and only if it is not specified
Properly compute the transition $p(x(t_1)) = \int p(x(t_1) | x(t_0)) p(x(t_0)) , dt$ if $t_0$ is specified and differs from t_1 := obs_times[0].
a. This is a bit different for continuous and discrete time, but should be done for both (and for discrete time, will depend on how Figure Out How Times Are Handled in Discrete Time #206) is handled.
Right now, we assume an observation at
t_0 = obs_times[0]. This is potentially unintuitive, especially for continuous-time models. We should probably insteadt_0 = obs_times[0]if and only if it is not specifiedt_1 := obs_times[0].a. This is a bit different for continuous and discrete time, but should be done for both (and for discrete time, will depend on how Figure Out How Times Are Handled in Discrete Time #206) is handled.