Filtering returns for unspecified biases in priors when testing asset pricing theory

Procedures are presented that allow the empiricist to estimate and test asset pricing models on limited-liability securities without the assumption that the historical payoff distribution provides a consistent estimate of the market's prior beliefs. The procedures effectively filter return data for unspecified historical biases in the market's priors. They do not involve explicit estimation of the market's priors, and hence, economize on parameters. The procedures derive from a new but simple property of Bayesian learning, namely: if the correct likelihood is used, the inverse posterior at the true parameter value forms a martingale process relative to the learner's information filtration augmented with the true parameter value. Application of this central result to tests of asset pricing models requires a deliberate selection bias. Hence, as a by-product, the article establishes that biased samples contain information with which to falsify an asset pricing model or estimate its parameters. These include samples subject to, e.g. survivorship bias or Peso problems

Modelling Dependency Structures Produced by the Introduction of a Flipped Classroom

Teaching processes have been changing in the lasts few decades from a traditional lecture-example-homework format to more active strategies to engage the students in the learning process. One of the most popular methodologies is the flipped classroom, where traditional structure of the course is turned over by moving out of the classroom, most basic knowledge acquisition. However, due to the workload involved in this kind of methodology, an objective analysis of the results should be carried out to assess whether the lecturer’s workload is worth the effort or not. In this paper, we compare the results obtained from two different methodologies: traditional lecturing and flipped classroom methodology, in terms of some performance indicators and an attitudinal survey, in an introductory statistics course for engineering students. Finally, we analysed the changes in the relationships among variables of interest when the traditional teaching was moved to a flipped classroom by using Bayesian networks

Conditionally externally Bayesian pooling operators in chain graphs

We address the multivariate version of French’s group decision problem where the m members of a group, who are jointly responsible for the decisions they should make, wish to combine their beliefs about the possible values of n random variables into the group consensus probability distribution. We shall assume the group has agreed on the structure of associations of variables in a problem, as might be represented by a commonly agreed partially complete chain graph (PCG) we define in the paper. However, the members diverge about the actual conditional probability distributions for the variables in the common PCG. The combination algorithm we suggest they adopt is one which demands, at least on learning information which is common to the members and which preserves the originally agreed PCG structure, that the pools of conditional distributions associated with the PCG are externally Bayesian (EB). We propose a characterization for such conditionally EB (CEB) poolings which is more general and flexible than the characterization proposed by Genest, McConway and Schervish. In particular, such a generalization allows the weights attributed to the joint probability assessments of different individuals in the pool to differ across the distinct components of each joint density. We show that the group’s commitment to being CEB on chain elements can be accomplished by the group being EB on the whole PCG when the group also agrees to perform the conditional poolings in an ordering compatible with evidence propagation in the graph

Inferential stability in systems biology

The modern biological sciences are fraught with statistical difficulties. Biomolecular stochasticity, experimental noise, and the “large p, small n” problem all contribute to the challenge of data analysis. Nevertheless, we routinely seek to draw robust, meaningful conclusions from observations. In this thesis, we explore methods for assessing the effects of data variability upon downstream inference, in an attempt to quantify and promote the stability of the inferences we make. We start with a review of existing methods for addressing this problem, focusing upon the bootstrap and similar methods. The key requirement for all such approaches is a statistical model that approximates the data generating process. We move on to consider biomarker discovery problems. We present a novel algorithm for proposing putative biomarkers on the strength of both their predictive ability and the stability with which they are selected. In a simulation study, we find our approach to perform favourably in comparison to strategies that select on the basis of predictive performance alone. We then consider the real problem of identifying protein peak biomarkers for HAM/TSP, an inflammatory condition of the central nervous system caused by HTLV-1 infection. We apply our algorithm to a set of SELDI mass spectral data, and identify a number of putative biomarkers. Additional experimental work, together with known results from the literature, provides corroborating evidence for the validity of these putative biomarkers. Having focused on static observations, we then make the natural progression to time course data sets. We propose a (Bayesian) bootstrap approach for such data, and then apply our method in the context of gene network inference and the estimation of parameters in ordinary differential equation models. We find that the inferred gene networks are relatively unstable, and demonstrate the importance of finding distributions of ODE parameter estimates, rather than single point estimates

Returns to Compulsory Schooling in Britain: Evidence from a Bayesian Fuzzy Regression Discontinuity Analysis

In this paper we reevaluate the returns to education based on the increase in the compulsory schooling age from 14 to 15 in the UK in 1947. We provide a Bayesian fuzzy regression discontinuity approach to infer the effect on earnings for a subset of subjects who turned 14 in a narrow window around the policy change and whose schooling was affected by the policy change. Our approach and our results are quite different from previous work that has focused on large sets of cohorts and 2SLS based approaches and has reported positive earnings and wage effects of 5% and above. Our empirical analysis, using data from the UK General Household Surveys, yields considerably lower earnings and wage effects for the additional year of compulsory schooling than previous work. These findings are consistent with the implementation of the policy change that affected students at the lower end of the schooling distribution and did not lead students to acquire additional qualifications. The results add further evidence to a number of recent studies that have found no effect from this policy change on socio-economic outcomes correlated with earnings.Bayesian inference, causal effects, imperfect compliance, natural experiment, principal stratification, regression discontinuity, returns to schooling

Genetic and phenotypic divergence in an island bird: isolation by distance, by colonization or by adaptation?

Discerning the relative roles of adaptive and nonadaptive processes in generating differences among populations and species, as well as how these processes interact, is a fundamental aim in biology. Both genetic and phenotypic divergence across populations can be the product of limited dispersal and gradual genetic drift across populations (isolation by distance), of colonization history and founder effects (isolation by colonization) or of adaptation to different environments preventing migration between populations (isolation by adaptation). Here, we attempt to differentiate between these processes using island populations of Berthelot's pipit (Anthus berthelotii), a passerine bird endemic to three Atlantic archipelagos. Using microsatellite markers and approximate Bayesian computation, we reveal that the northward colonization of this species ca. 8500years ago resulted in genetic bottlenecks in the colonized archipelagos. We then show that high levels of genetic structure exist across archipelagos and that these are consistent with a pattern of isolation by colonization, but not with isolation by distance or adaptation. Finally, we show that substantial morphological divergence also exists and that this is strongly concordant with patterns of genetic structure and bottleneck history, but not with environmental differences or geographic distance. Overall, our data suggest that founder effects are responsible for both genetic and phenotypic changes across archipelagos. Our findings provide a rare example of how founder effects can persist over evolutionary timescales and suggest that they may play an important role in the early stages of speciation