Awareness Growth and Belief Revision

The problem of awareness growth, also known as the problem of new hypotheses, is a persistent challenge to Bayesian theories of rational belief and decision making. Cases of awareness growth include coming to consider a completely new possibility (called expansion), or coming to consider finer distinctions through the introduction of a new partition (called refinement). Recent work has centred on Reverse Bayesianism, a proposal for rational awareness growth due to Karni and Vierø. This essay develops a "Reserve Bayesian" position and defends it against two challenges. The first, due to Anna Mahtani, says that Reverse Bayesian approaches yield the wrong result in cases where the growth of awareness constitutes an expansion relative to one partition, but a refinement relative to a different partition. The second, due to Steele and Stefánsson, says that Reverse Bayesian approaches cannot deal with new propositions that are evidentially relevant to old propositions. I argue that these challenges confuse questions of belief revision with questions of awareness change. Mahtani’s cases reveal that the change of awareness itself requires a model which specifies how propositions in the agent’s old algebra are identified with propositions in the new algebra. I introduce a lattice-theoretic model for this purpose, which resolves Mahtani’s problem cases and some of Steele and Stefánsson’s cases. Applying my model of awareness change, then Reverse Bayesianism, and then a generalised belief revision procedure, resolves Steele and Stefánsson’s remaining cases. In demonstrating this, I introduce a simple and general model of belief revision in the face of new information about previously unknown propositions.

Bayesian Processing of Data on Bursts of Pressure Vessels

Two alternative Bayesian approaches are proposed for the prediction of fragmentation of pressure vessels triggered off by accidental explosions (bursts) of these containment structures. It is shown how to carry out this prediction with post-mortem data on fragment numbers counted after past explosion accidents. Results of the prediction are estimates of probabilities of individual fragment numbers. These estimates are expressed by means of Bayesian prior or posterior distributions. It is demonstrated how to elicit the prior distributions from relatively scarce post-mortem data on vessel fragmentations. Specifically, it is suggested to develop priors with two Bayesian models known as compound Poisson-gamma and multinomial-Dirichlet probability distributions. The available data is used to specify non-informative prior for Poisson parameter that is subsequently transformed into priors of individual fragment number probabilities. Alternatively, the data is applied to a specification of Dirichlet concentration parameters. The latter priors directly express epistemic uncertainty in the fragment number probabilities. Example calculations presented in the study demonstrate that the suggested non-informative prior distributions are responsive to updates with scarce data on vessel explosions. It is shown that priors specified with Poisson-gamma and multinomial-Dirichlet models differ tangibly; however, this difference decreases with increasing amount of new data. For the sake of brevity and concreteness, the study was limited to fire induced vessel bursts known as boiling liquid expanding vapour explosions (BLEVEs).

Simple and Two-Level Hierarchical Bayesian Approaches for Parameter Estimation with One- and Two-Layer Evapotranspiration Models of Crop Fields

The two-layer Shuttleworth–Wallace (SW) evapotranspiration (ET) model has been widely used for predicting ET with good results. Since the SW model has a large number of specific parameters, these parameters have been estimated using a simple non-hierarchical Bayesian (SB) approach. To further improve the performance of the SW model, we aimed to assess parameter estimation using a two-level hierarchical Bayesian (HB) approach that takes into account the variation in observed conditions through the comparison with a traditional one-layer Penman–Monteith (PM) model. The difference between the SB and HB approaches were evaluated using a field-based ET dataset collected from five agricultural fields over three seasons in Myanmar. For a calibration period with large variation in environmental factors, the models with parameters calibrated by the HB approach showed better fitting to observed ET than that with parameters estimated using the SB approach, indicating the potential importance of accounting for seasonal fluctuations and variation in crop growth stages. The validation of parameter estimation showed that the ET estimation of the SW model with calibrated parameters was superior to that of the PM model, and the SW model provided acceptable estimations of ET, with little difference between the SB and HB approaches.

A Polyphasic Characterisation of Tetradesmus almeriensis sp. nov. (Chlorophyta: Scenedesmaceae)

The microalga Tetradesmus almeriensis, previously known as Scenedesmus almeriensis, has been isolated and cultivated as a highly productive, fast-growing strain known as a natural source of different products of commercial interest, including bioactive compounds such as lutein. This strain produces up to 40 g·m−2·day−1 of lutein under optimal conditions and is highly recommendable for outdoor production in temperate and warm climates, showing maximal performance at temperatures up to 35 °C with no photo-inhibition taking place with irradiances greater than 1000 μE·m−2·s−1. Morphological and molecular data allow its assignment to the Chlorophycean genus Tetradesmus. The new species can be distinguished from similar Tetradesmus taxa due to its unique combination of features that are seen under light microscopy. We present herein a robust and comprehensive phylogenetic analysis of T. almeriensis, together with several additional Scenedesmaceae species, using a combination of maximum likelihood and Bayesian approaches. Our results confirm T. almeriensis as a distinct species consistently clustering with other Scenedesmaceae.

Bayesian Approaches for Poisson Distribution Parameter Estimation

The Bayesian approach, a non-classical estimation technique, is very widely used in statistical inference for real world situations. The parameter is considered to be a random variable, and knowledge of the prior distribution is used to update the parameter estimation. Herein, two Bayesian approaches for Poisson parameter estimation by deriving the posterior distribution under the squared error loss or quadratic loss functions are proposed. Their performances were compared with frequentist (maximum likelihood estimator) and Empirical Bayes approaches through Monte Carlo simulations. The mean square error was used as the test criterion for comparing the methods for point estimation; the smallest value indicates the best performing method with the estimated parameter value closest to the true parameter value. Coverage Probabilities (CPs) and average lengths (ALs) were obtained to evaluate the performances of the methods for constructing confidence intervals. The results reveal that the Bayesian approaches were excellent for point estimation when the true parameter value was small (0.5, 1 and 2). In the credible interval comparison, these methods obtained CP values close to the nominal 0.95 confidence level and the smallest ALs for large sample sizes (50 and 100), when the true parameter value was small (0.5, 1 and 2). Doi: 10.28991/esj-2021-01310 Full Text: PDF