Interval indexing in Bayesian Survival Analysis

[JulietteOrtholand]

Notebook title: Bayesian Survival Analysis
Notebook url: https://www.pymc.io/projects/examples/en/latest/survival_analysis/survival_analysis.html

Issue description

The baseline hazard is computed over $K$ intervals indexed by $k$, thanks to $\lambda(t) = \lambda_k$ for $t \in [\tau_{k-1},\tau_k]$. This value is saved under the variable base_hazard and is of size $K$: $[\lambda_1, ...., \lambda_K]$. Yet there is another variable interval_bounds that stores $[\tau_0, ..., \tau_K ]$, thus of size $K+1$.
The cumulative baseline hazard, which is $\int_{\tau_0}^t \lambda(t)$ is estimated as (interval_length * hazard).cumsum(axis=-1), thus still a variable of size $K$. At a certain point, the cumulative hazard is plotted depending on the interval_bounds variables. The two objects do not have the same size, and the choice in the notebook was to use interval_bounds[:-1]. So this means that at time $\tau_0$, the variables is equal $(\tau_1-\tau_0)\lambda_1$, yet at time the cumulative baseline hazard equal $\int_{\tau_0}^{\tau_0} \lambda(t) = 0$.

Expected output

Thus I think, interval_bounds[:-1] in plots should be replaced by interval_bounds[1:]

Proposed solution

Let me know if you agree. Then, I can make a PR and check that this issue "only" occurs in plots.