Much research shows that the ratings that critics, judges, and consumers assign to wines are heteroscedastic. A rating observed is one draw from a latent distribution that is wine- and judge-specific. Estimating the shape of a rating’s distribution by minimizing a sum of cross entropies has been proposed and tested. This article proposes a method of improving the accuracy of that estimate by using information about the context of a wine competition or cross-section ratings data. Tests using the distributions implied by 90 blind triplicate ratings show that the sum of squared errors for the solution using context or cross-section information is 50% more accurate than not using such information and over 99% more accurate than ignoring the uncertainty about a rating.

Analyses and aggregations of the ratings that wine critics and judges assign to wines are made difficult by stochastic error and biases that remain even when wines are assessed blind to price, label, capsule, and closure. Stochastic error is due to the partially random nature of ratings. Cognitive and omitted-variable biases are due to anchoring, expectation, serial position, commercial, and other factors. Differences in decanting, filtering, aeration, and temperature can also affect ratings.

Much research shows that the ratings that judges assign to the same wine are uncertain. And while the ratings may be independent, research also shows that they are not identically distributed. Thus, an acute difficulty in ratings-related research and in calculating consensus among judges is that each rating is one observation drawn from a latent distribution that is wine- and judge-specific. What can be deduced about the shape of a latent distribution from one observation? A simple maximum entropy estimator is proposed to describe the distribution of a rating observed. The estimator can express the implications of zero, one, a few blind replicates, and many observations. Several tests of the estimator show that results are consistent with the results of experiments with blind replicates and that results are more accurate than results based on observed ratings alone.

The present study was undertaken to estimate the (co)variance components and genetic parameters of body weights recorded in Landlly piglets from birth to weaning at weekly intervals (w0 to w6). The data pertained to body weights of 2462 piglets, born to 91 sires and 159 dams across different generations during a 7-year period from 2014 to 2020. Five animal models (I–V), differentiated by inclusion or exclusion of maternal effects with or without covariance between maternal and direct genetic effects, were fitted on the data using the Bayesian algorithm. The analyses were implemented by Gibbs sampling in the BLUPF90 program and Markov chain Monte Carlo (MCMC) methodology was used to draw samples of posterior distribution pertaining to (co)variance components. Based on deviance information criteria (DIC), model V with inclusion of direct additive genetic, direct maternal genetic and permanent environmental effect of dam as random factors along with covariance between direct additive and maternal effects best fitted the data on pre-weaning traits (w0 to w5). Whereas, model I incorporating only the direct additive genetic effect best fitted the weaning weight (w6) data in Landlly piglets. The posterior mean estimates of direct heritability under the best models for W0 to W6 were 0.13, 0.19, 0.29, 0.13, 0.26, 0.32 and 0.46, respectively. Inclusion of the maternal component helped in better partitioning of variance for different body weights in Landlly piglets. The maternal heritability ranged from 0.06 to 0.14, while the litter heritability ranged from 0.11 to 0.15 for pre-weaning weights (W0 to W5) under the best-fit models. The influence of maternal environment was greater than maternal genetic effect from birth to 4th week of age. The results implied that variations in body weight of Landlly pigs were genetically controlled to moderate levels (especially w2 and w4) with contributions from direct additive and maternal genotype that can be exploited by designing efficient breeding programmes.

We study two models of an age-biased graph process: the $\delta$ -version of the preferential attachment graph model (PAM) and the uniform attachment graph model (UAM), with m attachments for each of the incoming vertices. We show that almost surely the scaled size of a breadth-first (descendant) tree rooted at a fixed vertex converges, for $m=1$ , to a limit whose distribution is a mixture of two beta distributions and a single beta distribution respectively, and that for $m>1$ the limit is 1. We also analyze the likely performance of two greedy (online) algorithms, for a large matching set and a large independent set, and determine – for each model and each greedy algorithm – both a limiting fraction of vertices involved and an almost sure convergence rate.

We compared systematic and random survey techniques to estimate breeding population sizes of burrow-nesting petrel species on Marion Island. White-chinned (Procellaria aequinoctialis) and blue (Halobaena caerulea) petrel population sizes were estimated in systematic surveys (which attempt to count every colony) in 2009 and 2012, respectively. In 2015, we counted burrows of white-chinned, blue and great-winged (Pterodroma macroptera) petrels within 52 randomized strip transects (25 m wide, total 144 km). Burrow densities were extrapolated by Geographic Information System-derived habitat attributes (geology, vegetation, slope, elevation, aspect) to generate island-wide burrow estimates. Great-winged petrel burrows were found singly or in small groups at low densities (2 burrows ha−1); white-chinned petrel burrows were in loose clusters at moderate densities (3 burrows ha−1); and blue petrel burrows were in tight clusters at high densities (13 burrows ha−1). The random survey estimated 58% more white-chinned petrels but 42% fewer blue petrels than the systematic surveys. The results suggest that random transects are best suited for species that are widely distributed at low densities, but become increasingly poor for estimating population sizes of species with clustered distributions. Repeated fixed transects provide a robust way to monitor changes in colony density and area, but might fail to detect the formation/disappearance of new colonies.

Judges confer various awards on wines entered in dozens of wine competitions each year. This article employs data on blind replicates to show that those awards are based on one instance of stochastic ratings assigned by wine judges; awards based on the expected values of those stochastic ratings would be different. This article recognizes the stochastic nature of ratings and builds on the work of many others to propose and test a conditional-probability model that yields maximum-likelihood estimates of judges’ latent consensus, idiosyncratic, and random assignments of scores to wines. The exact p-value for a likelihood test of the null hypothesis that the model's results are random is less than 0.001. Applying the notion of conditional probability may lead to better methods of assigning awards to entries in wine competitions and of assessing the capabilities of wine judges. (JEL Classifications: A10, C10, C00, C12, D12)

The inability of many wine judges to achieve perfect consistency by assigning the same rating to the same wine in a blind tasting is well established. Results for four wine tastings that include blind replicates are examined in this article. Although perfection is rare, the probability distributions of those results show that wine judges do tend to assign closer ratings to replicates than is likely due to chance alone. Approximately one-third of judges assign ratings that are within one rank of perfect consistency, and two-thirds assign ratings within two ranks of perfect consistency. This finding is sensitive to judges’ capabilities, the mechanics of the tasting protocol, and the extent to which the replicate is different from other wines in the tasting. Much wine-related research to date takes judges’ individual ratings as deterministic, yet these results show that those ratings are stochastic. These results yield a probability distribution that may guide future research concerning the uses and economic implications of wine ratings. (JEL Classifications: A10, C10, C00, C12, D12)

We study a bivariate stochastic process {X(t)} = Z(t))}, where {XE(t)} is a continuous-time Markov chain describing the environment and {Z(t)} is the process of interest. In the context which motivated this study, {Z(t)} models the gating behaviour of a single ion channel. It is assumed that given {XE(t)}, the channel process {Z(t)} is a continuous-time Markov chain with infinitesimal generator at time t dependent on XE(t), and that the environment process {XE{t)} is not dependent on {Z(t)}. We derive necessary and sufficient conditions for {X(t)} to be time reversible, showing that then its equilibrium distribution has a product form which reflects independence of the state of the environment and the state of the channel. In the special case when the environment controls the speed of the channel process, we derive transition probabilities and sojourn time distributions for {Z(t)} by exploiting connections with Markov reward processes. Some of these results are extended to a stationary environment. Applications to problems arising in modelling multiple ion channel systems are discussed. In particular, we present ways in which a multichannel model in a random environment does and does not exhibit behaviour identical to a corresponding model based on independent and identically distributed channels.