Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.Comment: 26 pages, 2 figures, accepted in Journal of Computational and Graphical Statistics (http://www.amstat.org/publications/jcgs.cfm

Bayesian model comparison with un-normalised likelihoods

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalizing constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes’ factors for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates

Bayesian Computation with Intractable Likelihoods

This article surveys computational methods for posterior inference with intractable likelihoods, that is where the likelihood function is unavailable in closed form, or where evaluation of the likelihood is infeasible. We review recent developments in pseudo-marginal methods, approximate Bayesian computation (ABC), the exchange algorithm, thermodynamic integration, and composite likelihood, paying particular attention to advancements in scalability for large datasets. We also mention R and MATLAB source code for implementations of these algorithms, where they are available.Comment: arXiv admin note: text overlap with arXiv:1503.0806

A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation.

As modeling becomes a more widespread practice in the life sciences and biomedical sciences, researchers need reliable tools to calibrate models against ever more complex and detailed data. Here we present an approximate Bayesian computation (ABC) framework and software environment, ABC-SysBio, which is a Python package that runs on Linux and Mac OS X systems and that enables parameter estimation and model selection in the Bayesian formalism by using sequential Monte Carlo (SMC) approaches. We outline the underlying rationale, discuss the computational and practical issues and provide detailed guidance as to how the important tasks of parameter inference and model selection can be performed in practice. Unlike other available packages, ABC-SysBio is highly suited for investigating, in particular, the challenging problem of fitting stochastic models to data. In order to demonstrate the use of ABC-SysBio, in this protocol we postulate the existence of an imaginary reaction network composed of seven interrelated biological reactions (involving a specific mRNA, the protein it encodes and a post-translationally modified version of the protein), a network that is defined by two files containing 'observed' data that we provide as supplementary information. In the first part of the PROCEDURE, ABC-SysBio is used to infer the parameters of this system, whereas in the second part we use ABC-SysBio's relevant functionality to discriminate between two different reaction network models, one of them being the 'true' one. Although computationally expensive, the additional insights gained in the Bayesian formalism more than make up for this cost, especially in complex problems

Increasing Costs Due to Ocean Acidification Drives Phytoplankton to Be More Heavily Calcified: Optimal Growth Strategy of Coccolithophores

Ocean acidification is potentially one of the greatest threats to marine ecosystems and global carbon cycling. Amongst calcifying organisms, coccolithophores have received special attention because their calcite precipitation plays a significant role in alkalinity flux to the deep ocean (i.e., inorganic carbon pump). Currently, empirical effort is devoted to evaluating the plastic responses to acidification, but evolutionary considerations are missing from this approach. We thus constructed an optimality model to evaluate the evolutionary response of coccolithophorid life history, assuming that their exoskeleton (coccolith) serves to reduce the instantaneous mortality rates. Our model predicted that natural selection favors constructing more heavily calcified exoskeleton in response to increased acidification-driven costs. This counter-intuitive response occurs because the fitness benefit of choosing a better-defended, slower growth strategy in more acidic conditions, outweighs that of accelerating the cell cycle, as this occurs by producing less calcified exoskeleton. Contrary to the widely held belief, the evolutionarily optimized population can precipitate larger amounts of CaCO3 during the bloom in more acidified seawater, depending on parameter values. These findings suggest that ocean acidification may enhance the calcification rates of marine organisms as an adaptive response, possibly accompanied by higher carbon fixation ability. Our theory also provides a compelling explanation for the multispecific fossil time-series record from ∼200 years ago to present, in which mean coccolith size has increased along with rising atmospheric CO2 concentration

A magnetic circuits\u27 optimisation algorithm for MR devices

This paper presents a new algorithm to be used for torque to mass ratio optimisation of a magneto-rheological device. A complex combination of optimisation algorithm and equations based on the magnetic circuit is detailled. It takes into account magnetic saturation properties of the fluid and different parts in a novel way that led to great improvement. While a double loop optimization process allocated to Matlab, Finite Element simulations were conducted on Ansys. The proposed brake illustrates the strength by greatly increasing its performances in terms of resultant torque and material consumption. Compared to market available MR brakes, the torque to mass ratio has more than doubled

Enhanced E. huxleyi carbonate counterpump as a positive feedback to increase deglacial pCO2sw in the Eastern Equatorial Pacific

The modern Eastern Equatorial Pacific (EEP) Ocean is a high nutrient low chlorophyll (HNLC) upwelling region and a large oceanic source of carbon to the atmosphere. During the last deglaciation, the EEP played a major role in the outgassing of carbon dioxide into the atmosphere from the upwelling surface water system of CO2-enriched deep-water masses originating from the Southern Ocean. The EEP upwelling system is also fertilizing the surface waters and enhancing the biological pump. Here we present data on the mass and calcification dynamics of the coccolithophore species Emiliania huxleyi spanning the last 30 ky at Site ODP 1238 (1\ub052.310\u2032S, 82\ub046.934\u2032W; 2203 m) in the EEP. Our results show an increased coccolith calcification degree during times of high pCO2 and low surface water pH conditions; this unexpected result is tentatively explained as related to changes in homeostasis equilibrium at the site of calcification and between the cell and the seawater environment. We estimated the E. huxleyi particulate inorganic to organic carbon ratio (PIC:POC) in order to detect changes in the carbonate counter-pump to carbon pump activity, which can act as either a positive or negative feedback to atmospheric CO2 modulating air-sea gas exchange. Our study indicates an enhanced coccolithophore biological pump during the last glacial that could have buffered, at least partially, the excess of pCO2atm via absorption into the ocean. Finally, during the last deglaciation, the enhanced carbonate counter pump was a major source of high pCO2sw in the EEP surface ocean