Research, software, data and methods. Inspect the context, compare your options, and take a useful next step.
SciPy documentation
A solver-selection guide spanning local and global optimization, roots, constrained problems, linear programming and assignment.
Investigate Which solver classes satisfy a fixed accuracy and feasibility target on a small declared suite of smooth and constrained problems?
Stan User's Guide / Stan Development Team
A guide to using ODE models in inference, including solver choices, stiffness, tolerances, parameter estimation and adjoint methods.
Investigate How much do inferred parameters shift as ODE tolerances are tightened for a harmonic oscillator with synthetic observations?
SciPy documentation
A reference for permutation tests that distinguishes exchangeability structures, exact enumeration and randomized null sampling.
Investigate For a small paired dataset, does the randomized test approach an independently enumerated exact null distribution?
Stan User's Guide / Stan Development Team
A guide to prior and posterior predictive checks that compare replicated-data summaries with chosen aspects of observed data.
Investigate Which discrepancies detect a known tail-shape mismatch that a mean-only predictive check misses?
SciPy documentation
A guide to quasi-Monte Carlo sampling, discrepancy, scrambling and practical use of sampling engines.
Investigate How does scrambled low-discrepancy sampling compare with independent random sampling on bounded smooth and discontinuous integrands?
Stan User's Guide / Stan Development Team
A guide distinguishing reparameterizations from changes of variables and explaining when log-Jacobian adjustments are required.
Investigate Does a transformed one-dimensional density normalize correctly and recover known moments with the required Jacobian?
SciPy documentation
A signal-processing guide covering convolution, filtering, spectral estimation and short-time Fourier transforms.
Investigate How do window and padding choices affect recovered amplitude and spectral leakage for a known multitone signal?
Stan User's Guide / Stan Development Team
A guide to checking Bayesian inference algorithms by simulating parameters and datasets from a model and examining posterior ranks or coverage.
Investigate Can a deliberately biased posterior sampler be distinguished from an exact conjugate sampler by a prespecified rank-uniformity diagnostic?
SciPy documentation
A tutorial on extracting a few eigenpairs from sparse operators, including shift-invert mode and matrix-free interfaces.
Investigate How do the requested spectrum region and tolerance affect convergence and residuals for a sparse matrix with known eigenvalues?
SciPy documentation
A computational-geometry reference covering Delaunay triangulations, convex hulls, Voronoi structures and degenerate point configurations.
Investigate Which geometric invariants remain valid when the input contains duplicates or nearly coplanar points?
statsmodels documentation
A state-space modeling guide covering filtering, smoothing, latent-state uncertainty, time-series models and residual diagnostics.
Investigate Can a small linear-Gaussian model recover known Kalman-filter states and covariances under missing observations?
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