scholarly journals MCMC design-based non-parametric regression for rare event. Application to nested risk computations

2017 ◽  
Vol 23 (1) ◽  
Author(s):  
Gersende Fort ◽  
Emmanuel Gobet ◽  
Eric Moulines
Keyword(s):  
Markov Chain ◽  
Conditional Expectation ◽  
Least Squares Method ◽  
Rare Event ◽  
General Function ◽  
Ergodic Markov Chain ◽  
Parametric Regression ◽  
Asymptotic Bounds ◽  
The Mean ◽  
Non Parametric

AbstractWe design and analyze an algorithm for estimating the mean of a function of a conditional expectation when the outer expectation is related to a rare event. The outer expectation is evaluated through the average along the path of an ergodic Markov chain generated by a Markov chain Monte Carlo sampler. The inner conditional expectation is computed as a non-parametric regression, using a least-squares method with a general function basis and a design given by the sampled Markov chain. We establish non-asymptotic bounds for the

KEBANGGAAN TERHADAP BATIK MADURA BAGI WARGA SUMENEP

2014 ◽  
Vol 4 (2) ◽  
Author(s):  
Sayyida Sayyida ◽  
Nurdody Zakki
Keyword(s):  
Logistic Regression ◽  
Rural Areas ◽  
Research Method ◽  
Community Group ◽  
Parametric Regression ◽  
Logit Function ◽  
The Village ◽  
The City ◽  
Level Of Risk ◽  
Non Parametric

Diversity of Indonesian Batik hanging area. One of the very well-known Indonesian batik is Batik Madura. Batik Madura has become a pride for Indonesia, especially for Madura. The purpose of the study is to model the Sumenep pride to Batik Madura and to see the level of risk or tendency of batik madura pride for the community group Sumenep. This research method uses a non parametric regression used a non-parametric regression because the dependent variable in this study is the variable Y are variables not normally distributed. The results of this study states that the level of risk of the village in Sumenep proud of batik is almost 5 times higher than the islands while people in this city who live in the district town at risk Sumenep proud of Batik Madura 8-fold compared to the archipelago. So it can be concluded that the city is much more proud of batik than those who reside in rural areas especially those who reside in the islands. This study uses data from 100 questionnaires were analyzed using logistic regression analysis. The conclusion of this study is the pride of the batik model as follows: Function logistic regression / logit function: g (x) = 0,074 + 1,568X4(1)+2,159X4(2 this is case the islands as a comparison, X4(1)  is the place to stay in the village and X4(2)  is the place to stay in town, so the Model Opportunities p(x) = EXP(g(x))/1+EXP(g(x)).  Hopes for further research is to conduct research on the development of batik in an integrated region, the need to be disseminated to potential areas of particular potential in Madura batik, especially for residents who reside in the Islands.Keywords: Pride, Batik, Sumenep.

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

scholarly journals VARIABILITY OF EVOLUTIONARY RATES OF DNA

Genetics ◽  
1986 ◽  
Vol 113 (4) ◽  
pp. 1077-1091
Author(s):  
John H Gillespie
Keyword(s):  
Dna Sequences ◽  
Significant Excess ◽  
Ergodic Markov Chain ◽  
The Third ◽  
Markov Chain Models ◽  
Rate Of Molecular Evolution ◽  
The Mean ◽  
Nuclear Loci ◽  
The Individual ◽  
Evolution Of Proteins

ABSTRACT A statistical analysis of DNA sequences from four nuclear loci and five mitochondrial loci from different orders of mammals is described. A major aim of the study is to describe the variation in the rate of molecular evolution of proteins and DNA. A measure of rate variability is the statistic R, the ratio of the variance in the number of substitutions to the mean number. For proteins, R is found to be in the range 0.16 < R < 35.55, thus extending in both directions the values seen in previous studies. An analysis of codons shows that there is a highly significant excess of double substitutions in the first and second positions, but not in the second and third or first and third positions. The analysis of the dynamics of nucleotide evolution showed that the ergodic Markov chain models that are the basis of most published formulas for correcting for multiple substitutions are incompatible with the data. A bootstrap procedure was used to show that the evolution of the individual nucleotides, even the third positions, show the same variation in rates as seen in the proteins. It is argued that protein and silent DNA evolution are uncoupled, with the evolution at both levels showing patterns that are better explained by the action of natural selection than by neutrality. This conclusion is based primarily on a comparison of the nuclear and mitochondrial results.

An extension of a theorem concerning an interesting Markov chain

1973 ◽  
Vol 10 (4) ◽  
pp. 886-890 ◽  
Author(s):  
W. J. Hendricks
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Ergodic Markov Chain ◽  
The Right

In a single-shelf library of N books we suppose that books are selected one at a time and returned to the kth position on the shelf before another selection is made. Books are moved to the right or left as necessary to vacate position k. The probability of selecting each book is assumed to be known, and the N! arrangements of the books are considered as states of an ergodic Markov chain for which we find the stationary distribution.

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