Twenty questions with noise: Bayes optimal policies for entropy loss

We consider the problem of twenty questions with noisy answers, in which we seek to find a target by repeatedly choosing a set, asking an oracle whether the target lies in this set, and obtaining an answer corrupted by noise. Starting with a prior distribution on the target's location, we seek to minimize the expected entropy of the posterior distribution. We formulate this problem as a dynamic program and show that any policy optimizing the one-step expected reduction in entropy is also optimal over the full horizon. Two such Bayes optimal policies are presented: one generalizes the probabilistic bisection policy due to Horstein and the other asks a deterministic set of questions. We study the structural properties of the latter, and illustrate its use in a computer vision application.

Natural and anthropogenic methane fluxes in Eurasia: a mesoscale quantification by generalized atmospheric inversion

Eight surface observation sites providing quasi-continuous measurements of atmospheric methane mixingratios have been operated since the mid-2000’s in Siberia. For the first time in a single work, we assimilate 1 year of these in situ observations in an atmospheric inversion. Our objective is to quantify methane surface fluxes from anthropogenic and wetland sources at the mesoscale in the Siberian lowlands for the year 2010. To do so, we first inquire about the way the inversion uses the observations and the way the fluxes are constrained by the observation sites. As atmospheric inver- sions at the mesoscale suffer from mis-quantified sources of uncertainties, we follow recent innovations in inversion techniques and use a new inversion approach which quantifies the uncertainties more objectively than the previous inversion systems. We find that, due to errors in the representation of the atmospheric transport and redundant pieces of information, only one observation every few days is found valuable by the inversion. The remaining high-resolution quasi-continuous signal is representative of very local emission patterns difficult to analyse with a mesoscale system. An analysis of the use of information by the inversion also reveals that the observation sites constrain methane emissions within a radius of 500 km. More observation sites than the ones currently in operation are then necessary to constrain the whole Siberian lowlands. Still, the fluxes within the constrained areas are quantified with objectified uncertainties. Finally, the tolerance intervals for posterior methane fluxes are of roughly 20 % (resp. 50 %) of the fluxes for anthropogenic (resp. wetland) sources. About 50–70 % of Siberian lowlands emissions are constrained by the inversion on average on an annual basis. Extrapolating the figures on the constrained areas to the whole Siberian lowlands, we find a regional methane budget of 5–28 TgCH4 for the year 2010, i.e. 1–5 % of the global methane emissions. As very few in situ observations are available in the region of interest, observations of methane total columns from the Greenhouse Gas Observing SATellite (GOSAT) are tentatively used for the evaluation of the inversion results, but they exhibit only a marginal signal from the fluxes within the region of interest.

A Single-blinded, Randomized Clinical Trial of How to Implement an Evidence-based Treatment for Generalized Anxiety Disorder [IMPLEMENT] — Effects of Three Different Strategies of Implementation

BACKGROUND: Despite long-standing calls to disseminate evidence-based treatments for generalized anxiety (GAD), modest progress has been made in the study of how such treatments should be implemented. The primary objective of this study was to test three competing strategies on how to implement a cognitive behavioral treatment (CBT) for out-patients with GAD (i.e., comparison of one compensation vs. two capitalization models). METHODS: For our three-arm, single-blinded, randomized controlled trial (implementation of CBT for GAD [IMPLEMENT]), we recruited adults with GAD using advertisements in high-circulation newspapers to participate in a 14-session cognitive behavioral treatment (Mastery of your Anxiety and Worry, MAW-packet). We randomly assigned eligible patients using a full randomization procedure (1:1:1) to three different conditions of implementation: adherence priming (compensation model), which had a systematized focus on patients' individual GAD symptoms and how to compensate for these symptoms within the MAW-packet, and resource priming and supportive resource priming (capitalization model), which had systematized focuses on patients' strengths and abilities and how these strengths can be capitalized within the same packet. In the intention-to-treat population an outcome composite of primary and secondary symptoms-related self-report questionnaires was analyzed based on a hierarchical linear growth model from intake to 6-month follow-up assessment. This trial is registered at ClinicalTrials.gov (identifier: NCT02039193) and is closed to new participants. FINDINGS: From June 2012 to Nov. 2014, from 411 participants that were screened, 57 eligible participants were recruited and randomly assigned to three conditions. Forty-nine patients (86%) provided outcome data at post-assessment (14% dropout rate). All three conditions showed a highly significant reduction of symptoms over time. However, compared with the adherence priming condition, both resource priming conditions indicated faster symptom reduction. The observer ratings of a sub-sample of recorded videos (n = 100) showed that the therapists in the resource priming conditions conducted more strength-oriented interventions in comparison with the adherence priming condition. No patients died or attempted suicide. INTERPRETATION: To our knowledge, this is the first trial that focuses on capitalization and compensation models during the implementation of one prescriptive treatment packet for GAD. We have shown that GAD related symptoms were significantly faster reduced by the resource priming conditions, although the limitations of our study included a well-educated population. If replicated, our results suggest that therapists who implement a mental health treatment for GAD might profit from a systematized focus on capitalization models. FUNDING: Swiss Science National Foundation (SNSF-Nr. PZ00P1_136937/1) awarded to CF. KEYWORDS: Cognitive behavioral therapy; Evidence-based treatment; Implementation strategies; Randomized controlled trial

Shadow Profit Maximization and a Generalized Measure of Inefficiency

Determining the profit maximizing input-output bundle of a firm requires data on prices. This paper shows how endogenously determined shadow prices can be used in place of actual prices to obtain the optimal input-output bundle where the firm.s shadow profit is maximized. This approach amounts to an application of the Weak Axiom of Profit Maximization (WAPM) formulated by Varian (1984) based on shadow prices rather than actual prices. At these prices the shadow profit of a firm is zero. Thus, the maximum profit that could have been attained at some other input-output bundle is a measure of the inefficiency of the firm. Because the benchmark input-output bundle is always an observed bundle from the data, it can be determined without having to solve any elaborate programming problem. An empirical application to U.S. airlines data illustrates the proposed methodology.

Input Price Variation Across Locations and a Generalized Measure of Cost Efficiency

We propose a nonparametric model for global cost minimization as a framework for optimal allocation of a firm's output target across multiple locations, taking account of differences in input prices and technologies across locations. This should be useful for firms planning production sites within a country and for foreign direct investment decisions by multi-national firms. Two illustrative examples are included. The first example considers the production location decision of a manufacturing firm across a number of adjacent states of the US. In the other example, we consider the optimal allocation of US and Canadian automobile manufacturers across the two countries.

Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

Detecting genetic and nutritional lung cancer risk factors related to folate metabolism using Bayesian generalized linear models

Complex diseases, such as cancer, are caused by various genetic and environmental factors, and their interactions. Joint analysis of these factors and their interactions would increase the power to detect risk factors but is statistically. Bayesian generalized linear models using student-t prior distributions on coefficients, is a novel method to simultaneously analyze genetic factors, environmental factors, and interactions. I performed simulation studies using three different disease models and demonstrated that the variable selection performance of Bayesian generalized linear models is comparable to that of Bayesian stochastic search variable selection, an improved method for variable selection when compared to standard methods. I further evaluated the variable selection performance of Bayesian generalized linear models using different numbers of candidate covariates and different sample sizes, and provided a guideline for required sample size to achieve a high power of variable selection using Bayesian generalize linear models, considering different scales of number of candidate covariates. ^ Polymorphisms in folate metabolism genes and nutritional factors have been previously associated with lung cancer risk. In this study, I simultaneously analyzed 115 tag SNPs in folate metabolism genes, 14 nutritional factors, and all possible genetic-nutritional interactions from 1239 lung cancer cases and 1692 controls using Bayesian generalized linear models stratified by never, former, and current smoking status. SNPs in MTRR were significantly associated with lung cancer risk across never, former, and current smokers. In never smokers, three SNPs in TYMS and three gene-nutrient interactions, including an interaction between SHMT1 and vitamin B12, an interaction between MTRR and total fat intake, and an interaction between MTR and alcohol use, were also identified as associated with lung cancer risk. These lung cancer risk factors are worthy of further investigation.^