Let's talk about health: shoppers' discourse regarding health while food shopping

Objective: The present study aimed to examine the role of health in consumers’ food purchasing decisions through investigating the nature of people’s discourse regarding health while conducting their food shopping.

Design: The study employed the think-aloud technique as part of an accompanied shop. All mentions of health and terms relating to health were identified from the data set. Inductive thematic analysis was conducted to examine how health was talked about in relation to people’s food choice decisions.

Setting: Supermarkets in Dublin, Republic of Ireland and Belfast, Northern Ireland.

Subjects Participants: (n 50) were aged over 18 years and represented the main household shopper.

Results: Responsibility for others and the perceived need to illicit strict control to avoid ‘unhealthy’ food selections played a dominant role in how health was talked about during the accompanied shop. Consequently healthy shopping was viewed as difficult and effort was required to make the healthy choice, with shoppers relating to product-based inferences to support their decisions.

Conclusions: This qualitative exploration has provided evidence of a number of factors influencing the consideration of health during consumers’ food shopping. These results highlight opportunities for stakeholders such as public health bodies and the food industry to explore further ways to help enable consumers make healthy food choices.

A necessarily complex model to explain the biogeography of the amphibians and reptiles of Madagascar

Pattern and process are inextricably linked in biogeographic analyses, though we can observe pattern, we must infer process. Inferences of process are often based on ad hoc comparisons using a single spatial predictor. Here, we present an alternative approach that uses mixed-spatial models to measure the predictive potential of combinations of hypotheses. Biodiversity patterns are estimated from 8,362 occurrence records from 745 species of Malagasy amphibians and reptiles. By incorporating 18 spatially explicit predictions of 12 major biogeographic hypotheses, we show that mixed models greatly improve our ability to explain the observed biodiversity patterns. We conclude that patterns are influenced by a combination of diversification processes rather than by a single predominant mechanism. A ‘one-size-fits-all’ model does not exist. By developing a novel method for examining and synthesizing spatial parameters such as species richness, endemism and community similarity, we demonstrate the potential of these analyses for understanding the diversification history of Madagascar’s biota.

Toward Characterization Of The Type IIP Supernova Progenitor Population: A Statistical Sample Of Light Curves From Pan-STARRS1

In recent years, wide-field sky surveys providing deep multi-band imaging have presented a new path for indirectly characterizing the progenitor populations of core-collapse supernovae (SN): systematic light curve studies. We assemble a set of 76 grizy-band Type IIP SN light curves from Pan-STARRS1, obtained over a constant survey program of 4 years and classified using both spectroscopy and machine learning-based photometric techniques. We develop and apply a new Bayesian model for the full multi-band evolution of each light curve in the sample. We find no evidence of a sub-population of fast-declining explosions (historically referred to as "Type IIL" SNe). However, we identify a highly significant relation between the plateau phase decay rate and peak luminosity among our SNe IIP. These results argue in favor of a single parameter, likely determined by initial stellar mass, predominantly controlling the explosions of red supergiants. This relation could also be applied for supernova cosmology, offering a standardizable candle good to an intrinsic scatter of 0.2 mag. We compare each light curve to physical models from hydrodynamic simulations to estimate progenitor initial masses and other properties of the Pan-STARRS1 Type IIP SN sample. We show that correction of systematic discrepancies between modeled and observed SN IIP light curve properties and an expanded grid of progenitor properties, are needed to enable robust progenitor inferences from multi-band light curve samples of this kind. This work will serve as a pathfinder for photometric studies of core-collapse SNe to be conducted through future wide field transient searches.

Probabilistic Inference in Credal Networks: New Complexity Results

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove an analogous result for inference in Naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and Naive Bayes networks are used in real applications of imprecise probability.

Approximate credal network updating by linear programming with applications to decision making

Credal nets are probabilistic graphical models which extend Bayesian nets to cope with sets of distributions. An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to accurate inferences. A transformation is also derived to reduce decision making in credal networks based on the maximality criterion to updating. The decision task is proved to have the same complexity of standard inference, being NPPP-complete for general credal nets and NP-complete for polytrees. Similar results are derived for the E-admissibility criterion. Numerical experiments confirm a good performance of the method.

On the Complexity of Strong and Epistemic Credal Networks

Credal networks are graph-based statistical models whose parameters take values on a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The result of inferences with such models depends on the irrelevance/independence concept adopted. In this paper, we study the computational complexity of inferences under the concepts of epistemic irrelevance and strong independence. We strengthen complexity results by showing that inferences with strong independence are NP-hard even in credal trees with ternary variables, which indicates that tractable algorithms, including the existing one for epistemic trees, cannot be used for strong independence. We prove that the polynomial time of inferences in credal trees under epistemic irrelevance is not likely to extend to more general models, because the problem becomes NP-hard even in simple polytrees. These results draw a definite line between networks with efficient inferences and those where inferences are hard, and close several open questions regarding the computational complexity of such models.

IDS: A Divide-and-Conquer Algorithm for Inference in Polytree-Shaped Credal Networks

A credal network is a graph-theoretic model that represents imprecision in joint probability distributions. An inference in a credal net aims at computing an interval for the probability of an event of interest. Algorithms for inference in credal networks can be divided into exact and approximate. The selection of an algorithm is based on a trade off that ponders how much time someone wants to spend in a particular calculation against the quality of the computed values. This paper presents an algorithm, called IDS, that combines exact and approximate methods for computing inferences in polytree-shaped credal networks. The algorithm provides an approach to trade time and precision when making inferences in credal nets

Updating Credal Networks is Approximable in Polynomial Time

Credal networks relax the precise probability requirement of Bayesian networks, enabling a richer representation of uncertainty in the form of closed convex sets of probability measures. The increase in expressiveness comes at the expense of higher computational costs. In this paper, we present a new variable elimination algorithm for exactly computing posterior inferences in extensively specified credal networks, which is empirically shown to outperform a state-of-the-art algorithm. The algorithm is then turned into a provably good approximation scheme, that is, a procedure that for any input is guaranteed to return a solution not worse than the optimum by a given factor. Remarkably, we show that when the networks have bounded treewidth and bounded number of states per variable the approximation algorithm runs in time polynomial in the input size and in the inverse of the error factor, thus being the first known fully polynomial-time approximation scheme for inference in credal networks.

Generalized loopy 2U: A new algorithm for approximate inference in credal networks

Credal networks generalize Bayesian networks by relaxing the requirement of precision of probabilities. Credal networks are considerably more expressive than Bayesian networks, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal networks. The algorithm is based on an important representation result we prove for general credal networks: that any credal network can be equivalently reformulated as a credal network with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal network is then updated by L2U, a loopy approximate algorithm for binary credal networks. Overall, we generalize L2U to non-binary credal networks, obtaining a scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences with respect to other state-of-the-art algorithms is evaluated by extensive numerical tests.

Integração de evidências em redes credais e a regra de Jeffrey

Credal networks provide a scheme for dealing with imprecise probabilistic models. The inference algorithms often used in credal networks compute the interval of the posterior probability of an event of interest given evidence of the specific kind -- evidence that describe the current state of a set of variables. These algorithms do not perform evidential reasoning in case of the evidence must be processed according to the conditioning rule proposed by RC Jeffrey. This paper describes a procedure to integrate evidence with Jeffrey's rule when performing inferences with credal nets.

Algorithms for Hidden Markov Models With Imprecisely Specified Parameters

Hidden Markov models (HMMs) are widely used models for sequential data. As with other probabilistic graphical models, they require the specification of precise probability values, which can be too restrictive for some domains, especially when data are scarce or costly to acquire. We present a generalized version of HMMs, whose quantification can be done by sets of, instead of single, probability distributions. Our models have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. Efficient inference algorithms are developed to address standard HMM usage such as the computation of likelihoods and most probable explanations. Experiments with real data show that the use of imprecise probabilities leads to more reliable inferences without compromising efficiency.

Generalized Loopy 2U: A New Algorithm for Approximate Inference in Credal Networks

Credal nets generalize Bayesian nets by relaxing the requirement of precision of probabilities. Credal nets are considerably more expressive than Bayesian nets, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal nets. The algorithm is based on an important representation result we prove for general credal nets: that any credal net can be equivalently reformulated as a credal net with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal net is updated by L2U, a loopy approximate algorithm for binary credal nets. Thus, we generalize L2U to non-binary credal nets, obtaining an accurate and scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences is evaluated by empirical tests.

Improving parameter learning of Bayesian nets from incomplete data

This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood estimate. We argue that choosing the maximum log-likelihood estimate (as well as the maximum penalized log-likelihood and the maximum a posteriori estimate) has severe drawbacks, being affected both by overfitting and model uncertainty. Two ideas are discussed to overcome these issues: a maximum entropy approach and a Bayesian model averaging approach. Both ideas can be easily applied on top of EM, while the entropy idea can be also implemented in a more sophisticated way, through a dedicated non-linear solver. A vast set of experiments shows that these ideas produce significantly better estimates and inferences than the traditional and widely used maximum (penalized) log-likelihood and maximum a posteriori estimates. In particular, if EM is adopted as optimization engine, the model averaging approach is the best performing one; its performance is matched by the entropy approach when implemented using the non-linear solver. The results suggest that the applicability of these ideas is immediate (they are easy to implement and to integrate in currently available inference engines) and that they constitute a better way to learn Bayesian network parameters.

Belief Updating and Learning in Semi-Qualitative Probabilistic Networks

This paper explores semi-qualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NPPP-Complete. We then show that existing qualitative relations in SQPNs (plus probabilistic logic and imprecise assessments) can be dealt effectively through multilinear programming. We then discuss learning: we consider a maximum likelihood method that generates point estimates given a SQPN and empirical data, and we describe a Bayesian-minded method that employs the Imprecise Dirichlet Model to generate set-valued estimates.

Children's use of interventions to learn causal structure

Children aged between 5 and 8 years freely intervened on a three-variable causal system, with their task being to discover whether it was a common-cause structure or one of two causal chains. From 6-7 years, children were able to use information from their interventions to correctly disambiguate the structure of a causal chain. We used a Bayesian model to examine children’s interventions on the system; this showed that with development children became more efficient in producing the interventions needed to disambiguate the causal structure and that the quality of interventions, as measured by their informativeness, improved developmentally. The latter measure was a significant predictor of children’s correct inferences about the causal structure. A second experiment showed that levels of performance were not reduced in a task in which children did not select and carry out interventions themselves, indicating no advantage for self-directed learning. However, children’s performance was not related to intervention quality in these circumstances, suggesting that children learn in a different way when they carry out interventions themselves.