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.