Bayesian analysis for reversible Markov chains

We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from P\'{o}lya's urn. We give closed form normalizing constants, a simple method of simulation from the posterior and a characterization along the lines of W. E. Johnson's characterization of the Dirichlet prior.Comment: Published at http://dx.doi.org/10.1214/009053606000000290 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spontaneous breaking of rotational symmetry in the presence of defects

We prove a strong form of spontaneous breaking of rotational symmetry for a simple model of two-dimensional crystals with random defects in thermal equilibrium at low temperature. The defects consist of isolated missing atoms.Comment: 18 page

Edge-reinforced random walk on a ladder

We prove that the edge-reinforced random walk on the ladder ${\mathbb{Z}\times\{1,2\}}$ with initial weights $a>3/4$ is recurrent. The proof uses a known representation of the edge-reinforced random walk on a finite piece of the ladder as a random walk in a random environment. This environment is given by a marginal of a multicomponent Gibbsian process. A transfer operator technique and entropy estimates from statistical mechanics are used to analyze this Gibbsian process. Furthermore, we prove spatially exponentially fast decreasing bounds for normalized local times of the edge-reinforced random walk on a finite piece of the ladder, uniformly in the size of the finite piece.Comment: Published at http://dx.doi.org/10.1214/009117905000000396 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic behavior of edge-reinforced random walks

In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given by random weights on the edges. The edge weights decay exponentially in space. The process converges to a stationary process. We provide asymptotic bounds for the range of the random walker up to a given time, showing that it localizes much more than an ordinary random walker. The random environment is described in terms of an infinite-volume Gibbs measure.Comment: Published at http://dx.doi.org/10.1214/009117906000000674 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Linearly edge-reinforced random walks

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the random walk on infinite graphs. On trees, one has a representation as a random walk in an independent random environment. We review recent results for the random walk on ladders: recurrence, a representation as a random walk in a random environment, and estimates for the position of the random walker.Comment: Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Model Aktivitas Praktikum Lapangan Berbasis Ergonomi (Apelerg) Memperbaiki Respon Fisiologis Tubuh, Menurunkan Kelelahan, dan Meningkatkan Kinerja, Dibandingkan dengan Model Lama (Apel), pada Mahasiswa Fmipa Unima

Aktivitas praktikum lapangan merupakan kegiatan yang dilakukan sebagaiimplementasi kurikulum akademik di Jurusan Fisika FMIPA UNIMA. Sebagaiimplementasi kurikulum tersebut telah dibuat model aktivitas praktikum lapangan (modelAPeL) dan telah digunakan sejak tahun 2001. Namun model APeL ternyata menimbulkanrisiko yang merugikan bagi mahasiswa dilihat dari respon fisiologis dan kelelahansehingga mahasiswa belum dapat mencapai kinerja yang diharapkan. Untuk itu telahdiupayakan dengan penerapan pendekatan ergonomi total (PET) suatu model baru yaitumodel APeLErg. Untuk menguji keandalan model APeLErg dibandingkan dengan modelAPeL, telah dilakukan penelitian dengan hipotesis: model APeLErg, dibandingkan denganmodel APeL; memperbaiki respon fisiologis tubuh; menurunkan kelelahan; danmeningkatkan kinerja mahasiswa di daerah dataran rendah/panas dan di daerah datarantinggi/dingin. Penelitian ini dilakukan dalam dua tahap dengan menggunakan rancangansama subjek. Penelitian pada tahap pertama dilakukan di daerah panas denganmenggunakan 15 orang subjek sedangkan penelitian tahap kedua di daerah dinginmenggunakan 18 orang subjek. Hasil penelitian tahap I dan tahap II menunjukkan bahwaaktivitas dengan model APeLErg dapat: memperbaiki respon fisiologis mahasiswa secarasignifikan (p<0,05); menurunkan rata-rata skor kelelahan umum secara signifikan(p<0,05); meningkatkan kecepatan, kekonstanan dan ketelitian mahasiswa secarasignifikan (p<0,05); dan meningkatkan kinerja mahasiswa secara signifikan (p<0,05). Darihasil penelitian ini dapat disimpulkan bahwa model APeLErg dapat: memperbaiki responfisiologis mahasiswa; menurunkan tingkat kelelahan mahasiswa; dan meningkatkankinerja mahasiswa dalam melakukan aktivitas praktikum lapangan