Integrating science through Bayesian Belief Networks : case study of Lyngbya in Moreton Bay

Bayesian Belief Networks (BBNs) are emerging as valuable tools for investigating complex ecological problems. In a BBN, the important variables in a problem are identified and causal relationships are represented graphically. Underpinning this is the probabilistic framework in which variables can take on a finite range of mutually exclusive states. Associated with each variable is a conditional probability table (CPT), showing the probability of a variable attaining each of its possible states conditioned on all possible combinations of it parents. Whilst the variables (nodes) are connected, the CPT attached to each node can be quantified independently. This allows each variable to be populated with the best data available, including expert opinion, simulation results or observed data. It also allows the information to be easily updated as better data become available ----- ----- This paper reports on the process of developing a BBN to better understand the initial rapid growth phase (initiation) of a marine cyanobacterium, Lyngbya majuscula, in Moreton Bay, Queensland. Anecdotal evidence suggests that Lyngbya blooms in this region have increased in severity and extent over the past decade. Lyngbya has been associated with acute dermatitis and a range of other health problems in humans. Blooms have been linked to ecosystem degradation and have also damaged commercial and recreational fisheries. However, the causes of blooms are as yet poorly understood.

Sampling designs on stream networks using the pseudo-Bayesian approach

Monitoring stream networks through time provides important ecological information. The sampling design problem is to choose locations where measurements are taken so as to maximise information gathered about physicochemical and biological variables on the stream network. This paper uses a pseudo-Bayesian approach, averaging a utility function over a prior distribution, in finding a design which maximizes the average utility. We use models for correlations of observations on the stream network that are based on stream network distances and described by moving average error models. Utility functions used reflect the needs of the experimenter, such as prediction of location values or estimation of parameters. We propose an algorithmic approach to design with the mean utility of a design estimated using Monte Carlo techniques and an exchange algorithm to search for optimal sampling designs. In particular we focus on the problem of finding an optimal design from a set of fixed designs and finding an optimal subset of a given set of sampling locations. As there are many different variables to measure, such as chemical, physical and biological measurements at each location, designs are derived from models based on different types of response variables: continuous, counts and proportions. We apply the methodology to a synthetic example and the Lake Eacham stream network on the Atherton Tablelands in Queensland, Australia. We show that the optimal designs depend very much on the choice of utility function, varying from space filling to clustered designs and mixtures of these, but given the utility function, designs are relatively robust to the type of response variable.

Bayesian filtering over compressed appearance states

This paper presents a framework for performing real-time recursive estimation of landmarks’ visual appearance. Imaging data in its original high dimensional space is probabilistically mapped to a compressed low dimensional space through the definition of likelihood functions. The likelihoods are subsequently fused with prior information using a Bayesian update. This process produces a probabilistic estimate of the low dimensional representation of the landmark visual appearance. The overall filtering provides information complementary to the conventional position estimates which is used to enhance data association. In addition to robotics observations, the filter integrates human observations in the appearance estimates. The appearance tracks as computed by the filter allow landmark classification. The set of labels involved in the classification task is thought of as an observation space where human observations are made by selecting a label. The low dimensional appearance estimates returned by the filter allow for low cost communication in low bandwidth sensor networks. Deployment of the filter in such a network is demonstrated in an outdoor mapping application involving a human operator, a ground and an air vehicle.

Eliciting and encoding expert knowledge on variable selection into classical or Bayesian species distribution models

The quality of species distribution models (SDMs) relies to a large degree on the quality of the input data, from bioclimatic indices to environmental and habitat descriptors (Austin, 2002). Recent reviews of SDM techniques, have sought to optimize predictive performance e.g. Elith et al., 2006. In general SDMs employ one of three approaches to variable selection. The simplest approach relies on the expert to select the variables, as in environmental niche models Nix, 1986 or a generalized linear model without variable selection (Miller and Franklin, 2002). A second approach explicitly incorporates variable selection into model fitting, which allows examination of particular combinations of variables. Examples include generalized linear or additive models with variable selection (Hastie et al. 2002); or classification trees with complexity or model based pruning (Breiman et al., 1984, Zeileis, 2008). A third approach uses model averaging, to summarize the overall contribution of a variable, without considering particular combinations. Examples include neural networks, boosted or bagged regression trees and Maximum Entropy as compared in Elith et al. 2006. Typically, users of SDMs will either consider a small number of variable sets, via the first approach, or else supply all of the candidate variables (often numbering more than a hundred) to the second or third approaches. Bayesian SDMs exist, with several methods for eliciting and encoding priors on model parameters (see review in Low Choy et al. 2010). However few methods have been published for informative variable selection; one example is Bayesian trees (O’Leary 2008). Here we report an elicitation protocol that helps makes explicit a priori expert judgements on the quality of candidate variables. This protocol can be flexibly applied to any of the three approaches to variable selection, described above, Bayesian or otherwise. We demonstrate how this information can be obtained then used to guide variable selection in classical or machine learning SDMs, or to define priors within Bayesian SDMs.