30  References

Adelson-Velsky, Georgy M., and Evgenii M. Landis. 1962. “An Algorithm for the Organization of Information.” Soviet Mathematics Doklady 3: 1259–63.
Amestoy, Patrick R., Timothy A. Davis, and Iain S. Duff. 1996. “An Approximate Minimum Degree Ordering Algorithm.” SIAM Journal on Matrix Analysis and Applications 17 (4): 886–905. https://doi.org/10.1137/S0895479894278952.
Baydin, Atilim Gunes, Barak A. Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind. 2018. “Automatic Differentiation in Machine Learning: A Survey.” Journal of Machine Learning Research 18 (153): 1–43.
Bladt, Mogens, and Bo Friis Nielsen. 2017. Matrix-Exponential Distributions in Applied Probability. Vol. 81. Probability Theory and Stochastic Modelling. Springer. https://doi.org/10.1007/978-1-4939-7049-0.
Bradbury, James, Roy Frostig, Peter Hawkins, et al. 2018. JAX: Composable Transformations of Python+NumPy Programs. V. 0.3.13. Released. http://github.com/jax-ml/jax.
Cormen, Thomas H., Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2009. Introduction to Algorithms. 3rd ed. MIT Press.
Doob, Joseph L. 1957. “Conditional Brownian Motion and the Boundary Limits of Harmonic Functions.” Bulletin de La Société Mathématique de France 85: 431–58. https://doi.org/10.24033/bsmf.1494.
Gelman, Andrew. 2006. “Prior Distributions for Variance Parameters in Hierarchical Models.” Bayesian Analysis 1 (3): 515–34. https://doi.org/10.1214/06-BA117A.
Gelman, Andrew, and Donald B. Rubin. 1992. “Inference from Iterative Simulation Using Multiple Sequences.” Statistical Science 7 (4): 457–72. https://doi.org/10.1214/ss/1177011136.
George, Alan. 1973. “Nested Dissection of a Regular Finite Element Mesh.” SIAM Journal on Numerical Analysis 10 (2): 345–63. https://doi.org/10.1137/0710032.
George, Alan, and Joseph W. H. Liu. 1981. Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall.
Gillespie, Daniel T. 1977. “Exact Stochastic Simulation of Coupled Chemical Reactions.” Journal of Physical Chemistry 81 (25): 2340–61. https://doi.org/10.1021/j100540a008.
Griewank, Andreas, and Andrea Walther. 2008. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. 2nd ed. SIAM. https://doi.org/10.1137/1.9780898717761.
Haario, Heikki, Eero Saksman, and Johanna Tamminen. 2001. “An Adaptive Metropolis Algorithm.” Bernoulli 7 (2): 223–42. https://doi.org/10.2307/3318737.
Hansen, Lars Peter. 1982. “Large Sample Properties of Generalized Method of Moments Estimators.” Econometrica 50 (4): 1029–54. https://doi.org/10.2307/1912775.
Hastings, W. Keith. 1970. Monte Carlo Sampling Methods Using Markov Chains and Their Applications.” Biometrika 57 (1): 97–109. https://doi.org/10.1093/biomet/57.1.97.
Higham, Nicholas J. 2002. Accuracy and Stability of Numerical Algorithms. 2nd ed. SIAM. https://doi.org/10.1137/1.9780898718027.
Hobolth, Asger, Iker Rivas-González, Mogens Bladt, and Andreas Futschik. 2024. “Phase-Type Distributions in Mathematical Population Genetics: An Emerging Framework.” Theoretical Population Biology 157: 14–32. https://doi.org/10.1016/j.tpb.2024.03.001.
Hudson, Richard R. 1983. “Properties of a Neutral Allele Model with Intragenic Recombination.” Theoretical Population Biology 23 (2): 183–201. https://doi.org/10.1016/0040-5809(83)90013-8.
Jensen, Arne. 1953. “Markoff Chains as an Aid in the Study of Markoff Processes.” Skandinavisk Aktuarietidskrift 36: 87–91. https://doi.org/10.1080/03461238.1953.10419459.
Kahan, William. 1965. “Pracniques: Further Remarks on Reducing Truncation Errors.” Communications of the ACM 8 (1): 40. https://doi.org/10.1145/363707.363723.
Kahn, Arthur B. 1962. “Topological Sorting of Large Networks.” Communications of the ACM 5 (11): 558–62. https://doi.org/10.1145/368996.369025.
Kingma, Diederik P., and Jimmy Ba. 2015. “Adam: A Method for Stochastic Optimization.” Proceedings of the 3rd International Conference on Learning Representations (ICLR).
Kingman, John F. C. 1982. “The Coalescent.” Stochastic Processes and Their Applications 13 (3): 235–48. https://doi.org/10.1016/0304-4149(82)90011-4.
Kulkarni, Vidyadhar G. 1989. “A New Class of Multivariate Phase Type Distributions.” Operations Research 37 (1): 151–58. https://doi.org/10.1287/opre.37.1.151.
Lipton, Richard J., Donald J. Rose, and Robert Endre Tarjan. 1979. “Generalized Nested Dissection.” SIAM Journal on Numerical Analysis 16 (2): 346–58. https://doi.org/10.1137/0716027.
Lipton, Richard J., and Robert Endre Tarjan. 1979. “A Separator Theorem for Planar Graphs.” SIAM Journal on Applied Mathematics 36 (2): 177–89. https://doi.org/10.1137/0136016.
Liu, Qiang, and Dilin Wang. 2016. “Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm.” Advances in Neural Information Processing Systems 29: 2378–86.
Metropolis, Nicholas, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. 1953. “Equation of State Calculations by Fast Computing Machines.” Journal of Chemical Physics 21 (6): 1087–92. https://doi.org/10.1063/1.1699114.
National Institute of Standards and Technology. 2015. Secure Hash Standard (SHS). FIPS PUB 180-4. U.S. Department of Commerce. https://doi.org/10.6028/NIST.FIPS.180-4.
Neal, Radford M. 2011. MCMC Using Hamiltonian Dynamics.” Chap. 5 in Handbook of Markov Chain Monte Carlo, edited by Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng. Chapman; Hall/CRC.
Neuts, Marcel F. 1981. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press.
Newey, Whitney K., and Daniel McFadden. 1994. “Large Sample Estimation and Hypothesis Testing.” In Handbook of Econometrics, edited by Robert F. Engle and Daniel McFadden, vol. 4. Elsevier. https://doi.org/10.1016/S1573-4412(05)80005-4.
Nocedal, Jorge, and Stephen J. Wright. 2006. Numerical Optimization. 2nd ed. Springer Series in Operations Research. Springer. https://doi.org/10.1007/978-0-387-40065-5.
Norris, James R. 1997. Markov Chains. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press. https://doi.org/10.1017/CBO9780511810633.
Patel, Amit. 2013. Hexagonal Grids. Red Blob Games. https://www.redblobgames.com/grids/hexagons/.
Robbins, Herbert, and Sutton Monro. 1951. “A Stochastic Approximation Method.” Annals of Mathematical Statistics 22 (3): 400–407. https://doi.org/10.1214/aoms/1177729586.
Roberts, Gareth O., Andrew Gelman, and Walter R. Gilks. 1997. “Weak Convergence and Optimal Scaling of Random Walk Metropolis Algorithms.” Annals of Applied Probability 7 (1): 110–20. https://doi.org/10.1214/aoap/1034625254.
Roberts, Gareth O., and Jeffrey S. Rosenthal. 2007. “Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms.” Journal of Applied Probability 44 (2): 458–75. https://doi.org/10.1239/jap/1183667414.
Rogers, L. C. G., and David Williams. 2000. Diffusions, Markov Processes and Martingales. 2nd ed. 1: Foundations. Cambridge University Press. https://doi.org/10.1017/CBO9781107590120.
Røikjer, Thomas, Asger Hobolth, and Kasper Munch. 2022. “Graph-Based Algorithms for Phase-Type Distributions.” Statistics and Computing 32 (6): 85. https://doi.org/10.1007/s11222-022-10155-6.
Rose, Donald J. 1970. “Triangulated Graphs and the Elimination Process.” Journal of Mathematical Analysis and Applications 32: 597–609. https://doi.org/10.1016/0022-247X(70)90282-9.
Rose, Donald J., and Robert Endre Tarjan. 1978. “Algorithmic Aspects of Vertex Elimination on Directed Graphs.” SIAM Journal on Applied Mathematics 34 (1): 176–97. https://doi.org/10.1137/0134014.
Schauer, Moritz, Frank van der Meulen, and Harry van Zanten. 2017. “Guided Proposals for Simulating Multi-Dimensional Diffusion Bridges.” Bernoulli 23 (4A): 2917–50. https://doi.org/10.3150/16-BEJ833.
Stein, Charles. 1972. “A Bound for the Error in the Normal Approximation to the Distribution of a Sum of Dependent Random Variables.” Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability 2: 583–602.
Tarjan, Robert. 1972. “Depth-First Search and Linear Graph Algorithms.” SIAM Journal on Computing 1 (2): 146–60. https://doi.org/10.1137/0201010.
Tinney, William F., and John W. Walker. 1967. “Direct Solutions of Sparse Network Equations by Optimally Ordered Triangular Factorization.” Proceedings of the IEEE 55 (11): 1801–9. https://doi.org/10.1109/PROC.1967.6011.
van der Vaart, Aad W. 1998. Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press. https://doi.org/10.1017/CBO9780511802256.
Van Loan, Charles F. 1978. “Computing Integrals Involving the Matrix Exponential.” IEEE Transactions on Automatic Control 23 (3): 395–404. https://doi.org/10.1109/TAC.1978.1101743.
Weisfeiler, Boris, and Andrei Leman. 1968. “A Reduction of a Graph to a Canonical Form and an Algebra Arising During This Reduction.” Nauchno-Technicheskaya Informatsia 2 (9): 12–16.
Wiuf, Carsten, and Jotun Hein. 1999. “Recombination as a Point Process Along Sequences.” Genetics 153 (2): 999–1012. https://doi.org/10.1093/genetics/153.2.999.
Yannakakis, Mihalis. 1981. “Computing the Minimum Fill-in Is NP-Complete.” SIAM Journal on Algebraic Discrete Methods 2 (1): 77–79. https://doi.org/10.1137/0602010.