which decreases as J gets larger. So the approximation will be more accurate as we obtain more samples. Here is an example of using Monte Carlo methods to integrate away weights in Bayesian neural networks. Let y(x) = f(x,w) for response y and input x, and let p(w) be the prior over the weights w. The posterior distribution of w given the data D is p(w|D) ∝ p(D|w)p(w) where p(D|w) is the likeli...

the probable lack of some arcs and nodes in the stochastic networks is considered in this paper, and its effect is shown as the arrival probability from a given source node to a given sink node. a discrete time markov chain with an absorbing state is established in a directed acyclic network. then, the probability of transition from the initial state to the absorbing state is computed. it is as...

background & aim: chronic diseases impact not only on patients but also on their family members’ lives. this study aims to determine dimensions of family dermatology life quality index (fdlqi) questionnaire by the use of classic and bayesian factor analysis (bfa) factor. methods & materials: in this study, fdlqi questionnaire distributed among 100 family members of dermatological patients. bfa ...

Finite, discrete-time Markov chain models of genetic algorithms have been used successfully in the past to understand the complex dynamics of a simple GA. Markov chains can exactly model the GA by accounting for all of the stochasticity introduced by various GA operators, such as initialization, selection, crossover, and mutation. Although such models quickly become unwieldy with increasing pop...

Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is hence defined and tested on some classical problems.

Free AccessImportant Keywordshttps://doi.org/10.14220/9783737013444.259SectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinkedInRedditEmail About Previous chapter Next FiguresReferencesRelatedDetails Download book coverOsnabrücker Studien zur Jüdischen und Christlichen Bibel.Volume 8 1st editionISBN: 978-3-8471-1344-7 eISBN: 978-3-7370-1344-4Hi...

Reversibility is a suucient but not necessary condition for Markov chains for use in Markov chain Monte Carlo simulation. It is necessary to select a Markov chain that has a pre-speciied distribution as its unique stationary distribution. There are many Markov chains that have such property. We give guidelines on how to rank them based on the asymptotic variance of the estimates they produce. T...

(a) If X − Y − Z −W is a Markov chain, then X − Y − Z and Y − Z −W are Markov chains. (b) If X − Y − Z and Y − Z −W are Markov chains, then X − Y − Z −W is a Markov chain. (c) If P (x, y, z, w) = P (x)p(y|x)P (z, w), then X − Y − (Z,W ) is a Markov chain. (d) If X ⊥ Y and Y ⊥ Z, then X ⊥ Z. (e) If the conditional distribution P (x|y, z) is a deterministic function of (x, y), then X − Y − Z is a...