Kepler Presearch Data Conditioning I - Architecture and Algorithms for Error Correction in Kepler Light Curves

Kepler provides light curves of 156,000 stars with unprecedented precision. However, the raw data as they come from the spacecraft contain significant systematic and stochastic errors. These errors, which include discontinuities, systematic trends, and outliers, obscure the astrophysical signals in the light curves. To correct these errors is the task of the Presearch Data Conditioning (PDC) module of the Kepler data analysis pipeline. The original version of PDC in Kepler did not meet the extremely high performance requirements for the detection of miniscule planet transits or highly accurate analysis of stellar activity and rotation. One particular deficiency was that astrophysical features were often removed as a side-effect to removal of errors. In this paper we introduce the completely new and significantly improved version of PDC which was implemented in Kepler SOC 8.0. This new PDC version, which utilizes a Bayesian approach for removal of systematics, reliably corrects errors in the light curves while at the same time preserving planet transits and other astrophysically interesting signals. We describe the architecture and the algorithms of this new PDC module, show typical errors encountered in Kepler data, and illustrate the corrections using real light curve examples.Comment: Submitted to PASP. Also see companion paper "Kepler Presearch Data Conditioning II - A Bayesian Approach to Systematic Error Correction" by Jeff C. Smith et a

Personal probabilities of probabilities

By definition, the subjective probability distribution of a random event is revealed by the (‘rational’) subject's choice between bets — a view expressed by F. Ramsey, B. De Finetti, L. J. Savage and traceable to E. Borel and, it can be argued, to T. Bayes. Since hypotheses are not observable events, no bet can be made, and paid off, on a hypothesis. The subjective probability distribution of hypotheses (or of a parameter, as in the current ‘Bayesian’ statistical literature) is therefore a figure of speech, an ‘as if’, justifiable in the limit. Given a long sequence of previous observations, the subjective posterior probabilities of events still to be observed are derived by using a mathematical expression that would approximate the subjective probability distribution of hypotheses, if these could be bet on. This position was taken by most, but not all, respondents to a ‘Round Robin’ initiated by J. Marschak after M. H. De-Groot's talk on Stopping Rules presented at the UCLA Interdisciplinary Colloquium on Mathematics in Behavioral Sciences. Other participants: K. Borch, H. Chernoif, R. Dorfman, W. Edwards, T. S. Ferguson, G. Graves, K. Miyasawa, P. Randolph, L. J. Savage, R. Schlaifer, R. L. Winkler. Attention is also drawn to K. Borch's article in this issue.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43847/1/11238_2004_Article_BF00169102.pd

Entrepreneurial Orientation Rhetoric in Franchise Organizations: The Impact of National Culture

This study examines the role of national culture on the entrepreneurial orientation (EO) rhetoric contained within franchisee recruitment promotional materials, where EO rhetoric is defined as the strategic use of words in organizational narratives to convey the risk taking, innovativeness, proactiveness, autonomy, and competitive aggressiveness of the firm. The sample comprised 378 franchise organizations, in five different countries (Australia, France, India, South Africa, and the UK). The results indicate that franchise systems operating in high uncertainty avoidance and feminine cultures use less entrepreneurially oriented rhetoric, suggesting that EO rhetoric in franchise organizations varies according to different national cultural contexts

Improving predictive distributions

Consider a sequence of decision problems S1, S2, ... and suppose that in problem Si the statistician must specify his predictive distribution Fi for some random variable Xi and make a decision based on that distribution. For example, Xi might be the return on some particular investment and the statistician must decide whether or not to make that investment. The random variables X1, X2, ... are assumed to be independent and completely unrelated. It is also assumed that each predictive distribution Fi assigned by the statistician is a subjective distribution based on his information and beliefs about Xi. In this context, the standard Bayesian approach provides no basis for evaluating whether the statistician's subjective predictive distribution for Xi is good or bad, and does not even recognize this question as being meaningful. In this paper we describe models in which the statistician can study his process for specifying predictive distributions, identify bad habits, and improve his predictions and decisions by gradually breaking these habits

Optimal Linear Opinion Pools

Consider a decision problem involving a group of m Bayesians in which each member reports his/her posterior distribution for some random variable \theta . The individuals all share a common prior distribution for \theta and a common loss function, but form their posterior distributions based on different data sets. A single distribution of \theta must be chosen by combining the individual posterior distributions in some type of opinion pool. In this paper, the optimal pool is presented when the data observed by the different members of the group are conditionally independent given \theta . When the data are not conditionally independent, the optimal weights to be used in a linear opinion pool are determined for problems involving quadratic loss functions and arbitrary distributions for \theta and the data. Properties of the optimal procedure are developed and some examples are discussed.Bayesian decision theory, combining probability distributions, linear opinion pools, multiple decision makers, restricted communications, scoring rules, teams, weights