The spectrum of the independent Metropolis-Hastings algorithm. (English) Zbl 1106.60060
Summary: We perform a spectral analysis for the kernel operator associated with the transition kernel for the Metropolis-Hastings algorithm that uses a fixed, location independent proposal distribution. Our main result is to establish the spectrum of the kernel operator \(T\) in the continuous case, thereby generalizing the results obtained by J. S. Liu [Stat. Comput. 6, 113–119 (1996)] for the finite case.
MSC:
| 60J22 | Computational methods in Markov chains |
References:
| [1] | Gåsemyr, J. (2005). A theoretical analysis of the performance of the independent Metropolis–Hastings algorithm on continuous state spaces. (In progress). |
| [2] | Hauge, R. (2002). On convergence of independent Metropolis–Hastings. Norwegian Computing Center, P. O. Box 114 Blindern, N–0314 Oslo, Norway. |
| [3] | Holden, L., Hauge, R., and Holden, M. (2002). Adaptive independent Metropolis–Hastings. Norwegian Computing Center, P. O. Box 114 Blindern, N–0314 Oslo, Norway. · Zbl 1192.65009 |
| [4] | Hastings W.K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrica 57:97–109 · Zbl 0219.65008 · doi:10.1093/biomet/57.1.97 |
| [5] | Liu J.S. (1996). Metropolized independent sampling with comparison to rejection sampling and importance sampling. Statist. Comput. 6:113–119 · doi:10.1007/BF00162521 |
| [6] | Metropolis M., Rosenbluth A.W., Rosenbluth M.N., Teller A., and Teller E. (1953). Equation of state calculations by fast computing machines. J. Chem. Phys. 21:1087–1092 · doi:10.1063/1.1699114 |
| [7] | Smith R.L., and Tierney L. (1996). Exact transition probabilities for the independence Metropolis sampler. Technical report, Department of Statistics, University of North Carolina, Chapel Hill, N.C. 27599–3260, USA |
| [8] | Tierney L. (1994). Markov chains for exploring posterior distributions. Ann. Statistics 22:1701–1762 · Zbl 0829.62080 · doi:10.1214/aos/1176325750 |
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