A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

Evaluation of liquid Bacillus thuringiensis var. israelensis products for control of Australian Aedes arbovirus vectors

Laboratory bioassay studies were conducted in southeast Queensland, Australia,: on the efficacy of Teknar (R), VectoBac (R) 12AS, and Cybate (R) (active ingredient: 1,200 international toxic units Bacillus thuringiensis var, israelensis [Bti]) against 3rd instars of the arbovirus vectors Aedes aegypti. Ae. notoscriptus, Ae. vigilax, and Ae. camptorhynchus. Probit analyses were then used to determine LD,, (median lethal dose), LD95, and lethal dose ratios (LDR). Aedes aegypti and Ae. notoscriptus, both container-habitat species, tolerated the highest Bti concentrations compared with saltmarsh Ae. vigilax and Ae. camptorhynchus. For example, the LDR for Ae. vigilax versus Ae. notoscriptus exposed to Cybate was 0.14 (95% confidence limit [CL] 0.03-0.61). Similarly, the Cybate LDR for Ae. camptorhynchus versus Ae. notoscriptus was 0.22 (95% CL 0.07-0.70). Teknar produced similar results with an LDR of 0.21 (95% CL 0.04-1.10) for Aedes vigilax versus Aedes notoscriptus. Differences in product efficacy were found when tested against the 2 container-breeding species. Cybate was less effective than Teknar with LDRs of 1.55 (95% CL 0.65-3.67) and 1.87 (95% CL 0.68-5.15) for Aedes aegypti and Ae. notoscriptus, respectively. The significant differences in susceptibility between mosquito species and varying efficacy between products highlight the importance of evaluating concentration-response data prior to contracting with distributors of mosquito control products. This information is crucial to resistance management strategies.

Bayesian feedback versus Markovian feedback in a two-level atom

We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty and Jacobs [Phys. Rev. A 60, 2700 (1999)]. Here we choose to call it, for brevity, Bayesian feedback. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtained without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However, it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections.

Fitting genetic models to twin data with binary and ordered categorical responses: A comparison of structural equation modelling and Bayesian hierarchical models

We compare Bayesian methodology utilizing free-ware BUGS (Bayesian Inference Using Gibbs Sampling) with the traditional structural equation modelling approach based on another free-ware package, Mx. Dichotomous and ordinal (three category) twin data were simulated according to different additive genetic and common environment models for phenotypic variation. Practical issues are discussed in using Gibbs sampling as implemented by BUGS to fit subject-specific Bayesian generalized linear models, where the components of variation may be estimated directly. The simulation study (based on 2000 twin pairs) indicated that there is a consistent advantage in using the Bayesian method to detect a correct model under certain specifications of additive genetics and common environmental effects. For binary data, both methods had difficulty in detecting the correct model when the additive genetic effect was low (between 10 and 20%) or of moderate range (between 20 and 40%). Furthermore, neither method could adequately detect a correct model that included a modest common environmental effect (20%) even when the additive genetic effect was large (50%). Power was significantly improved with ordinal data for most scenarios, except for the case of low heritability under a true ACE model. We illustrate and compare both methods using data from 1239 twin pairs over the age of 50 years, who were registered with the Australian National Health and Medical Research Council Twin Registry (ATR) and presented symptoms associated with osteoarthritis occurring in joints of the hand.

Presumed unconstrained dispersal of Aedes aegypti in the city of Rio de Janeiro, Brazil

OBJECTIVE: To evaluate dispersal of Aedes aegypti females in an area with no container manipulation and no geographic barriers to constrain mosquito flight. METHODS: A mark-release-recapture experiment was conducted in December 2006, in the dengue endemic urban district of Olaria in Rio de Janeiro, Southeastern Brazil, where there is no evident obstacle to the dispersal of Ae. aegypti females. Mosquito traps were installed in 192 houses (96 Adultraps and 96 MosquiTRAPs). RESULTS: A total of 725 dust-marked gravid females were released and recapture rate was 6.3%. Ae. aegypti females traveled a mean distance of 288.12 m and their maximum displacement was 690 m; 50% and 90% of females flew up to 350 m and 500.2 m, respectively. CONCLUSIONS: Dispersal of Ae. aegypti females in Olaria was higher than in areas with physical and geographical barriers. There was no evidence of a preferred direction during mosquito flight, which was considered random or uniform from the release point.

Reinforcement Learning Based on the Bayesian Theorem for Electricity Markets Decision Support

This paper presents the applicability of a reinforcement learning algorithm based on the application of the Bayesian theorem of probability. The proposed reinforcement learning algorithm is an advantageous and indispensable tool for ALBidS (Adaptive Learning strategic Bidding System), a multi-agent system that has the purpose of providing decision support to electricity market negotiating players. ALBidS uses a set of different strategies for providing decision support to market players. These strategies are used accordingly to their probability of success for each different context. The approach proposed in this paper uses a Bayesian network for deciding the most probably successful action at each time, depending on past events. The performance of the proposed methodology is tested using electricity market simulations in MASCEM (Multi-Agent Simulator of Competitive Electricity Markets). MASCEM provides the means for simulating a real electricity market environment, based on real data from real electricity market operators.

Separating sequential equilibrium in a Bayesian international duopoly

We consider two Cournot firms, one located in the home country and the other in the foreign country, producing substitute goods for consumption in a third country. We suppose that neither the home government nor the foreign firm know the costs of the home firm, while the foreign firm cost is common knowledge. We determine the separating sequential equilibrium outputs.

Spatio-temporal patterns of tuberculosis incidence in Ribeirão Preto, State of São Paulo, southeast Brazil, and their relationship with social vulnerability: a Bayesian analysis

INTRODUCTION: The purpose of this ecological study was to evaluate the urban spatial and temporal distribution of tuberculosis (TB) in Ribeirão Preto, State of São Paulo, southeast Brazil, between 2006 and 2009 and to evaluate its relationship with factors of social vulnerability such as income and education level. METHODS: We evaluated data from TBWeb, an electronic notification system for TB cases. Measures of social vulnerability were obtained from the SEADE Foundation, and information about the number of inhabitants, education and income of the households were obtained from Brazilian Institute of Geography and Statistics. Statistical analyses were conducted by a Bayesian regression model assuming a Poisson distribution for the observed new cases of TB in each area. A conditional autoregressive structure was used for the spatial covariance structure. RESULTS: The Bayesian model confirmed the spatial heterogeneity of TB distribution in Ribeirão Preto, identifying areas with elevated risk and the effects of social vulnerability on the disease. We demonstrated that the rate of TB was correlated with the measures of income, education and social vulnerability. However, we observed areas with low vulnerability and high education and income, but with high estimated TB rates. CONCLUSIONS: The study identified areas with different risks for TB, given that the public health system deals with the characteristics of each region individually and prioritizes those that present a higher propensity to risk of TB. Complex relationships may exist between TB incidence and a wide range of environmental and intrinsic factors, which need to be studied in future research.