2,416 research outputs found
Evaluating Stationary Distribution of the Binary GA Markov Chain in Special Cases
The evolutionary algorithm stochastic process is well-known to be
Markovian. These have been under investigation in much of the
theoretical evolutionary computing research. When mutation rate is
positive, the Markov chain modeling an evolutionary algorithm is
irreducible and, therefore, has a unique stationary distribution,
yet, rather little is known about the stationary distribution. On the other
hand, knowing the stationary distribution may provide
some information about the expected times to hit optimum, assessment of the biases due to recombination and is of importance in population
genetics to assess what\u27s called a ``genetic load" (see the
introduction for more details). In this talk I will show how the quotient
construction method can be exploited to derive rather explicit bounds on the ratios of the stationary distribution values of various subsets of
the state space. In fact, some of the bounds obtained in the current
work are expressed in terms of the parameters involved in all the
three main stages of an evolutionary algorithm: namely selection,
recombination and mutation. I will also discuss the newest developments which may allow for further improvements of the bound
A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters
Markov Chain Monte Carlo (MCMC) methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models. However, MCMC methods require the a priori definition of a proposal or sampling distribution, which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the Markov Chain and its rate of convergence. In this paper we present an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), which is well suited to infer the posterior distribution of hydrologic model parameters. The SCEM-UA algorithm is a modified version of the original SCE-UA global optimization algorithm developed by Duan et al. [1992]. The SCEM-UA algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Three case studies demonstrate that the adaptive capability of the SCEM-UA algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional Metropolis-Hastings samplers
Coherent Bayesian analysis of inspiral signals
We present in this paper a Bayesian parameter estimation method for the
analysis of interferometric gravitational wave observations of an inspiral of
binary compact objects using data recorded simultaneously by a network of
several interferometers at different sites. We consider neutron star or black
hole inspirals that are modeled to 3.5 post-Newtonian (PN) order in phase and
2.5 PN in amplitude. Inference is facilitated using Markov chain Monte Carlo
methods that are adapted in order to efficiently explore the particular
parameter space. Examples are shown to illustrate how and what information
about the different parameters can be derived from the data. This study uses
simulated signals and data with noise characteristics that are assumed to be
defined by the LIGO and Virgo detectors operating at their design
sensitivities. Nine parameters are estimated, including those associated with
the binary system, plus its location on the sky. We explain how this technique
will be part of a detection pipeline for binary systems of compact objects with
masses up to 20 \sunmass, including cases where the ratio of the individual
masses can be extreme.Comment: Accepted for publication in Classical and Quantum Gravity, Special
issue for GWDAW-1
Accelerating delayed-acceptance Markov chain Monte Carlo algorithms
Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a
probability distribution via a two-stages version of the Metropolis-Hastings
algorithm, by combining the target distribution with a "surrogate" (i.e. an
approximate and computationally cheaper version) of said distribution. DA-MCMC
accelerates MCMC sampling in complex applications, while still targeting the
exact distribution. We design a computationally faster, albeit approximate,
DA-MCMC algorithm. We consider parameter inference in a Bayesian setting where
a surrogate likelihood function is introduced in the delayed-acceptance scheme.
When the evaluation of the likelihood function is computationally intensive,
our scheme produces a 2-4 times speed-up, compared to standard DA-MCMC.
However, the acceleration is highly problem dependent. Inference results for
the standard delayed-acceptance algorithm and our approximated version are
similar, indicating that our algorithm can return reliable Bayesian inference.
As a computationally intensive case study, we introduce a novel stochastic
differential equation model for protein folding data.Comment: 40 pages, 21 figures, 10 table
A Version of Geiringer-like Theorem for Decision Making in the Environments with Randomness and Incomplete Information
Purpose: In recent years Monte-Carlo sampling methods, such as Monte Carlo
tree search, have achieved tremendous success in model free reinforcement
learning. A combination of the so called upper confidence bounds policy to
preserve the "exploration vs. exploitation" balance to select actions for
sample evaluations together with massive computing power to store and to update
dynamically a rather large pre-evaluated game tree lead to the development of
software that has beaten the top human player in the game of Go on a 9 by 9
board. Much effort in the current research is devoted to widening the range of
applicability of the Monte-Carlo sampling methodology to partially observable
Markov decision processes with non-immediate payoffs. The main challenge
introduced by randomness and incomplete information is to deal with the action
evaluation at the chance nodes due to drastic differences in the possible
payoffs the same action could lead to. The aim of this article is to establish
a version of a theorem that originated from population genetics and has been
later adopted in evolutionary computation theory that will lead to novel
Monte-Carlo sampling algorithms that provably increase the AI potential. Due to
space limitations the actual algorithms themselves will be presented in the
sequel papers, however, the current paper provides a solid mathematical
foundation for the development of such algorithms and explains why they are so
promising.Comment: 53 pages in size. This work has been recently submitted to the IJICC
(International Journal on Intelligent Computing and Cybernetics
Evolutionary Inference via the Poisson Indel Process
We address the problem of the joint statistical inference of phylogenetic
trees and multiple sequence alignments from unaligned molecular sequences. This
problem is generally formulated in terms of string-valued evolutionary
processes along the branches of a phylogenetic tree. The classical evolutionary
process, the TKF91 model, is a continuous-time Markov chain model comprised of
insertion, deletion and substitution events. Unfortunately this model gives
rise to an intractable computational problem---the computation of the marginal
likelihood under the TKF91 model is exponential in the number of taxa. In this
work, we present a new stochastic process, the Poisson Indel Process (PIP), in
which the complexity of this computation is reduced to linear. The new model is
closely related to the TKF91 model, differing only in its treatment of
insertions, but the new model has a global characterization as a Poisson
process on the phylogeny. Standard results for Poisson processes allow key
computations to be decoupled, which yields the favorable computational profile
of inference under the PIP model. We present illustrative experiments in which
Bayesian inference under the PIP model is compared to separate inference of
phylogenies and alignments.Comment: 33 pages, 6 figure
Bayesian phylogenetic modelling of lateral gene transfers
PhD ThesisPhylogenetic trees represent the evolutionary relationships between a set of species.
Inferring these trees from data is particularly challenging sometimes since the transfer
of genetic material can occur not only from parents to their o spring but also
between organisms via lateral gene transfers (LGTs). Thus, the presence of LGTs
means that genes in a genome can each have di erent evolutionary histories, represented
by di erent gene trees.
A few statistical approaches have been introduced to explore non-vertical evolution
through collections of Markov-dependent gene trees. In 2005 Suchard described
a Bayesian hierarchical model for joint inference of gene trees and an underlying
species tree, where a layer in the model linked gene trees to the species tree via a
sequence of unknown lateral gene transfers. In his model LGT was modeled via a
random walk in the tree space derived from the subtree prune and regraft (SPR)
operator on unrooted trees. However, the use of SPR moves to represent LGT in an
unrooted tree is problematic, since the transference of DNA between two organisms
implies the contemporaneity of both organisms and therefore it can allow unrealistic
LGTs.
This thesis describes a related hierarchical Bayesian phylogenetic model for
reconstructing phylogenetic trees which imposes a temporal constraint on LGTs,
namely that they can only occur between species which exist concurrently. This is
achieved by taking into account possible time orderings of divergence events in trees,
without explicitly modelling divergence times. An extended version of the SPR operator
is introduced as a more adequate mechanism to represent the LGT e ect in a
tree. The extended SPR operation respects the time ordering. It additionaly di ers
from regular SPR as it maintains a 1-to-1 correspondence between points on the
species tree and points on each gene tree. Each point on a gene tree represents the
existence of a population containing that gene at some point in time. Hierarchical
phylogenetic models were used in the reconstruction of each gene tree from its
corresponding gene alignment, enabling the pooling of information across genes. In
addition to Suchard's approach, we assume variation in the rate of evolution between
di erent sites. The species tree is assumed to be xed.
A Markov Chain Monte Carlo (MCMC) algorithm was developed to t the model
in a Bayesian framework. A novel MCMC proposal mechanism for jointly proposing
the gene tree topology and branch lengths, LGT distance and LGT history has been
developed as well as a novel graphical tool to represent LGT history, the LGT Biplot.
Our model was applied to simulated and experimental datasets. More speci cally we
analysed LGT/reassortment presence in the evolution of 2009 Swine-Origin In
uenza
Type A virus. Future improvements of our model and algorithm should include joint
inference of the species tree, improving the computational e ciency of the MCMC
algorithm and better consideration of other factors that can cause discordance of
gene trees and species trees such as gene loss
Report on the second Mock LISA Data Challenge
The Mock LISA Data Challenges are a program to demonstrate LISA data-analysis capabilities and to encourage their development. Each round of challenges consists of several data sets containing simulated instrument noise and gravitational-wave sources of undisclosed parameters. Participants are asked to analyze the data sets and report the maximum information about source parameters. The challenges are being released in rounds of increasing complexity and realism: in this proceeding we present the results of Challenge 2, issued in January 2007, which successfully demonstrated the recovery of signals from supermassive black-hole binaries, from ~20,000 overlapping Galactic white-dwarf binaries, and from the extreme-mass-ratio inspirals of compact objects into central galactic black holes
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