Local dimension reduction of summary statistics for likelihood-free inference

Statistics and Computing - Approximate Bayesian computation (ABC) and other likelihood-free inference methods have gained popularity in the last decade, as they allow rigorous statistical inference...     

Optimal Viterbi Bayesian predictive classification for data from finite alphabets

A family of Viterbi Bayesian predictive classifiers has been recently popularized for speech recognition applications with continuous acoustic signals modeled by finite mixture densities embedded in a hidden Markov framework. Here we generalize such classifiers to sequentially observed data from multiple finite alphabets and derive the optimal predictive classifier under exchangeability of the emitted symbols. We demonstrate that the optimal predictive classifier which learns from unlabelled test items improves considerably upon marginal maximum a posteriori rule in the presence of sparse training data. It is shown that the learning process saturates when the amount of test data tends to infinity, such that no further gain in classification accuracy is possible upon arrival of new test items in the long run.     

Have I seen you before? Principles of Bayesian predictive classification revisited

A general inductive Bayesian classification framework is considered using a simultaneous predictive distribution for test items. We introduce a principle of generative supervised and semi-supervised classification based on marginalizing the joint posterior distribution of labels for all test items. The simultaneous and marginalized classifiers arise under different loss functions, while both acknowledge jointly all uncertainty about the labels of test items and the generating probability measures of the classes. We illustrate for data from multiple finite alphabets that such classifiers achieve higher correct classification rates than a standard marginal predictive classifier which labels all test items independently, when training data are sparse. In the supervised case for multiple finite alphabets the simultaneous and the marginal classifiers are proven to become equal under generalized exchangeability when the amount of training data increases. Hence, the marginal classifier can be interpreted as an asymptotic approximation to the simultaneous classifier for finite sets of training data. It is also shown that such convergence is not guaranteed in the semi-supervised setting, where the marginal classifier does not provide a consistent approximation.     

Stratified Gaussian graphical models

Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide certain forms of context-specific independence that are natural to consider from an applied perspective. Such independencies have been earlier introduced to generalize discrete graphical models and Bayesian networks into more flexible model families. Here, we adapt the idea of context-specific independence to Gaussian graphical models by introducing a stratification of the Euclidean space such that a conditional independence may hold in certain segments but be absent elsewhere. It is shown that the stratified models define a curved exponential family, which retains considerable tractability for parameter estimation and model selection.     

Categorical Representation of Facial Expressions in the Infant Brain

Categorical perception, demonstrated as reduced discrimination of within‐category relative to between‐category differences in stimuli, has been found in a variety of perceptual domains in adults. To examine the development of categorical perception in the domain of facial expression processing, we used behavioral and event‐related potential (ERP) methods to assess discrimination of within‐category (happy‐happy) and between‐category (happy‐sad) differences in facial expressions in 7‐month‐old infants. Data from a visual paired‐comparison test and recordings of attention‐sensitive ERPs showed no discrimination of facial expressions in the within‐category condition, whereas reliable discrimination was observed in the between‐category condition. The results also showed that face‐sensitive ERPs over occipital‐temporal scalp (P400) were attenuated in the within‐category condition relative to the between‐category condition, suggesting a potential neural basis for the reduced within‐category sensitivity. Together, these results suggest that the neural systems underlying categorical representation of facial expressions emerge during the early stages of postnatal development, before acquisition of language.     

Mixed estimation of old‐age mortality

The estimation of the mortality of the “oldest old”; is subject to considerable random error, but important prior information exists that can be used to make the estimates more robust. Mixed estimation is a method of incorporating auxiliary information into the statistical estimation of linear models. We extend the method to cover general maximum likelihood estimation, and show that the mixed estimator can be represented approximately as a weighted average of the purely data based estimator and the auxiliary estimator. The methods can be applied to the analysis of the old‐age mortality via logistic and Poisson regression. A major advantage of the mixed estimator is the simplicity with which it can incorporate partial prior information. Moreover, no special software is needed in the fitting. We show how the targeting methods of Coale and Kisker can be represented as mixed estimation in a natural way that is more flexible than the original proposal. We also derive empirical estimates of the target information based on pooled data from several countries with high quality data. We consider the mortality of Finland at ages 80 +, study the reliability of the evidence of mortality crossover, and derive estimates of life expectancy at age 100.     

Computing exact clustering posteriors with subset convolution

ABSTRACT

An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters and pairwise co-occurrence. The method is based on subset convolution and yields the posterior distribution for the number of clusters in O(n3ⁿ) operations or O(n³2ⁿ) using fast subset convolution. Pairwise co-occurrence probabilities are then obtained in O(n³2ⁿ) operations. This is considerably faster than exhaustive enumeration of all partitions.     

Pre-employment antecedents of health resources,job factors and health risk behaviour in men and women

Abstract

The role of individual factors in youth as predictors of adult health resources, job factors and health risk behaviour was studied in men and women. The studied health risk behaviours were smoking, use of alcohol and sedentary behaviour. Sense of coherence (SOC) was the used measure of adult health resources. The pre-employment data had been collected from a sample of 1084 subjects representative of Finnish youth at the mean age of 12 years. For this follow-up study, 345 women and 361 men, working in Finland, responded to a questionnaire at the mean age of 36 years. In the analyses of structural relationships, individual factors in youth were related to adult variables for both sexes, although only two consistent relationships were found for women: outgoing, social activities in youth predicted adult smoking and use of alcohol. Of the job factors, low job demands were related to smoking and lack of support at work was related to sedentary behaviour in women. The strong relationships of SOC with perceptions of social support and influence at work for both sexes characterized its role in health-promoting experiences at work, and supported its importance as a general health resource.     

A Modular Bayesian Salmonella Source Attribution Model for Sparse Data

Several statistical models for salmonella source attribution have been presented in the literature. However, these models have often been found to be sensitive to the model parameterization, as well as the specifics of the data set used. The Bayesian salmonella source attribution model presented here was developed to be generally applicable with small and sparse annual data sets obtained over several years. The full Bayesian model was modularized into three parts (an exposure model, a subtype distribution model, and an epidemiological model) in order to separately estimate unknown parameters in each module. The proposed model takes advantage of the consumption and overall salmonella prevalence of the studied sources, as well as bacteria typing results from adjacent years. The latter were used for a smoothed estimation of the annual relative proportions of different salmonella subtypes in each of the sources. The source‐specific effects and the salmonella subtype‐specific effects were included in the epidemiological model to describe the differences between sources and between subtypes in their ability to infect humans. The estimation of these parameters was based on data from multiple years. Finally, the model combines the total evidence from different modules to proportion human salmonellosis cases according to their sources. The model was applied to allocate reported human salmonellosis cases from the years 2008 to 2015 to eight food sources.