29,150 research outputs found
Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster
Background: Reaction-diffusion systems are frequently used in systems biology to model developmental and signalling processes. In many applications, count numbers of the diffusing molecular species are very low, leading to the need to explicitly model the inherent variability using stochastic methods. Despite their importance and frequent use, parameter estimation for both deterministic and stochastic reaction-diffusion systems is still a challenging problem.
Results: We present a Bayesian inference approach to solve both the parameter and state estimation problem for stochastic reaction-diffusion systems. This allows a determination of the full posterior distribution of the parameters (expected values and uncertainty). We benchmark the method by illustrating it on a simple synthetic experiment. We then test the method on real data about the diffusion of the morphogen Bicoid in Drosophila melanogaster. The results show how the precision with which parameters can be inferred varies dramatically, indicating that the ability to infer full posterior distributions on the parameters can have important experimental design consequences.
Conclusions: The results obtained demonstrate the feasibility and potential advantages of applying a Bayesian approach to parameter estimation in stochastic reaction-diffusion systems. In particular, the ability to estimate credibility intervals associated with parameter estimates can be precious for experimental design. Further work, however, will be needed to ensure the method can scale up to larger problems
Enhanced Welding Operator Quality Performance Measurement: Work Experience-Integrated Bayesian Prior Determination
Measurement of operator quality performance has been challenging in the
construction fabrication industry. Among various causes, the learning effect is
a significant factor, which needs to be incorporated in achieving a reliable
operator quality performance analysis. This research aims to enhance a
previously developed operator quality performance measurement approach by
incorporating the learning effect (i.e., work experience). To achieve this
goal, the Plateau learning model is selected to quantitatively represent the
relationship between quality performance and work experience through a
beta-binomial regression approach. Based on this relationship, an informative
prior determination approach, which incorporates operator work experience
information, is developed to enhance the previous Bayesian-based operator
quality performance measurement. Academically, this research provides a
systematic approach to derive Bayesian informative priors through integrating
multi-source information. Practically, the proposed approach reliably measures
operator quality performance in fabrication quality control processes.Comment: 8 pages, 5 figures, 2 tables, i3CE 201
Dose Finding with Escalation with Overdose Control (EWOC) in Cancer Clinical Trials
Traditionally, the major objective in phase I trials is to identify a
working-dose for subsequent studies, whereas the major endpoint in phase II and
III trials is treatment efficacy. The dose sought is typically referred to as
the maximum tolerated dose (MTD). Several statistical methodologies have been
proposed to select the MTD in cancer phase I trials. In this manuscript, we
focus on a Bayesian adaptive design, known as escalation with overdose control
(EWOC). Several aspects of this design are discussed, including large sample
properties of the sequence of doses selected in the trial, choice of prior
distributions, and use of covariates. The methodology is exemplified with
real-life examples of cancer phase I trials. In particular, we show in the
recently completed ABR-217620 (naptumomab estafenatox) trial that omitting an
important predictor of toxicity when dose assignments to cancer patients are
determined results in a high percent of patients experiencing severe side
effects and a significant proportion treated at sub-optimal doses.Comment: Published in at http://dx.doi.org/10.1214/10-STS333 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Bayesian-Based Approach for Public Sentiment Modeling
Public sentiment is a direct public-centric indicator for the success of
effective action planning. Despite its importance, systematic modeling of
public sentiment remains untapped in previous studies. This research aims to
develop a Bayesian-based approach for quantitative public sentiment modeling,
which is capable of incorporating uncertainty and guiding the selection of
public sentiment measures. This study comprises three steps: (1) quantifying
prior sentiment information and new sentiment observations with Dirichlet
distribution and multinomial distribution respectively; (2) deriving the
posterior distribution of sentiment probabilities through incorporating the
Dirichlet distribution and multinomial distribution via Bayesian inference; and
(3) measuring public sentiment through aggregating sampled sets of sentiment
probabilities with an application-based measure. A case study on Hurricane
Harvey is provided to demonstrate the feasibility and applicability of the
proposed approach. The developed approach also has the potential to be
generalized to model various types of probability-based measures
Noncommutative Bayesian Statistical Inference from a wedge of a Bifurcate Killing Horizon
Expanding a remark of my PHD-thesis the noncommutative bayesian statistical
inference from one wedge of a bifurcate Killing horizon is analyzed looking at
its inter-relation with the Unruh effectComment: some correction performed; to appear in "International Journal of
Theoretical Physics
Bayesian Nonstationary Spatial Modeling for Very Large Datasets
With the proliferation of modern high-resolution measuring instruments
mounted on satellites, planes, ground-based vehicles and monitoring stations, a
need has arisen for statistical methods suitable for the analysis of large
spatial datasets observed on large spatial domains. Statistical analyses of
such datasets provide two main challenges: First, traditional
spatial-statistical techniques are often unable to handle large numbers of
observations in a computationally feasible way. Second, for large and
heterogeneous spatial domains, it is often not appropriate to assume that a
process of interest is stationary over the entire domain.
We address the first challenge by using a model combining a low-rank
component, which allows for flexible modeling of medium-to-long-range
dependence via a set of spatial basis functions, with a tapered remainder
component, which allows for modeling of local dependence using a compactly
supported covariance function. Addressing the second challenge, we propose two
extensions to this model that result in increased flexibility: First, the model
is parameterized based on a nonstationary Matern covariance, where the
parameters vary smoothly across space. Second, in our fully Bayesian model, all
components and parameters are considered random, including the number,
locations, and shapes of the basis functions used in the low-rank component.
Using simulated data and a real-world dataset of high-resolution soil
measurements, we show that both extensions can result in substantial
improvements over the current state-of-the-art.Comment: 16 pages, 2 color figure
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