Estimating Subjective Probabilities

Subjective probabilities play a role in many economic decisions. There is a large theoretical literature on the elicitation of subjective probabilities, and an equally large empirical literature. However, there is a gulf between the two. The theoretical literature proposes a range of procedures that can be used to recover subjective probabilities, but stresses the need to make strong auxiliary assumptions or "calibrating adjustments" to elicited reports in order to recover the latent probability. With some notable exceptions, the empirical literature seems intent on either making those strong assumptions or ignoring the need for calibration. We illustrate how the joint estimation of risk attitudes and subjective probabilities using structural maximum likelihood methods can provide the calibration adjustments that theory calls for. This allows the observer to make inferences about the latent subjective probability, calibrating for virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with experiments in which we elicit subjective probabilities. We calibrate the estimates of subjective beliefs assuming that choices are made consistently with expected utility theory or rank-dependent utility theory. Inferred subjective probabilities are significantly different when calibrated according to either theory, thus showing the importance of undertaking such exercises. Our findings also have implications for the interpretation of probabilities inferred from prediction markets.

Inferring Beliefs as Subjectively Uncertain Probabilities

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task, and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other, and then a series of betting choices in which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance.

Estimating Subjective Probabilities

Subjective probabilities play a central role in many economic decisions, and act as an immediate confound of inferences about behavior, unless controlled for. Several procedures to recover subjective probabilities have been proposed, but in order to recover the correct latent probability one must either construct elicitation mechanisms that control for risk aversion, or construct elicitation mechanisms which undertake “calibrating adjustments” to elicited reports. We illustrate how the joint estimation of risk attitudes and subjective probabilities can provide the calibration adjustments that theory calls for. We illustrate this approach using data from a controlled experiment with real monetary consequences to the subjects. This allows the observer to make inferences about the latent subjective probability, under virtually any well-specified model of choice under subjective risk, while still employing relatively simple elicitation mechanisms

Estimating Aversion to Uncertainty

It is intuitive that decision-makers might have attitudes towards uncertainty just as they might have attitudes towards risk. However, it is only recently that this intuitive notion has been formalized and axiomatically characterized. We estimate the extent of uncertainty aversion in a manner that is parsimonious and consistent with theory. We demonstrate that one can jointly estimate attitudes towards uncertainty, attitudes towards risk, and subjective probabilities in a rigorous manner. Our structural econometric model constructively demonstrates the theoretical claims that it is possible to define uncertainty aversion in an empirically tractable manner. Our results show that attitudes towards risk and uncertainty can be different, qualitatively and quantitatively, and that allowing for these differences can have significant effects on inferences about subjective probabilities

Theory and Experiments

Subjective beliefs play a role in many economic decisions. There is a large theoretical literature on the elicitation of beliefs, and an equally large empirical literature. However, there is a gulf between the two. The theoretical literature proposes a range of procedures that can be used to recover beliefs, but stresses the need to make strong auxiliary assumptions or “calibrating adjustments” to elicited reports in order to recover the latent belief. With some notable exceptions, the empirical literature seems intent on either making those strong assumptions or ignoring the need for calibration. We make three contributions to bridge this gulf. First, we offer a general theoretical framework in which the belief elicitation task can be viewed as an exchange of state-dependent commodities between two traders. Second, we provide a specific elicitation procedure which has clear counterparts in field betting environments, and that is directly motivated by our theoretical framework. Finally, we illustrate how one can jointly estimate risk attitudes and subjective beliefs using structural maximum likelihood methods. This allows the observer to make inferences about the latent subjective belief, calibrating for virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with an experiment in which we elicit subjective probabilities over three future events and one fact

Estimating Subjective Probabilities

Subjective probabilities play a role in many economic decisions. There is a large theoretical literature on the elicitation of subjective probabilities, and an equally large empirical literature. However, there is a gulf between the two. The theoretical literature proposes a range of procedures that can be used to recover subjective probabilities, but stresses the need to make strong auxiliary assumptions or “calibrating adjustments” to elicited reports in order to recover the latent probability. With some notable exceptions, the empirical literature seems intent on either making those strong assumptions or ignoring the need for calibration. We illustrate how one can jointly estimate risk attitudes and subjective probabilities using structural maximum likelihood methods. This allows the observer to make inferences about the latent subjective probability, calibrating for virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with experiments in which we elicit subjective probabilities. We calibrate the estimates of subjective beliefs assuming that choices are made consistently with expected utility theory or rank-dependent utility theory. Inferred subjective probabilities are significantly different when calibrated according to either theory

ALICE: The Ultraviolet Imaging Spectrograph aboard the New Horizons Pluto-Kuiper Belt Mission

The New Horizons ALICE instrument is a lightweight (4.4 kg), low-power (4.4 Watt) imaging spectrograph aboard the New Horizons mission to Pluto/Charon and the Kuiper Belt. Its primary job is to determine the relative abundances of various species in Pluto's atmosphere. ALICE will also be used to search for an atmosphere around Pluto's moon, Charon, as well as the Kuiper Belt Objects (KBOs) that New Horizons hopes to fly by after Pluto-Charon, and it will make UV surface reflectivity measurements of all of these bodies as well. The instrument incorporates an off-axis telescope feeding a Rowland-circle spectrograph with a 520-1870 angstroms spectral passband, a spectral point spread function of 3-6 angstroms FWHM, and an instantaneous spatial field-of-view that is 6 degrees long. Different input apertures that feed the telescope allow for both airglow and solar occultation observations during the mission. The focal plane detector is an imaging microchannel plate (MCP) double delay-line detector with dual solar-blind opaque photocathodes (KBr and CsI) and a focal surface that matches the instrument's 15-cm diameter Rowland-circle. In what follows, we describe the instrument in greater detail, including descriptions of its ground calibration and initial in flight performance.Comment: 24 pages, 29 figures, 2 tables; To appear in a special volume of Space Science Reviews on the New Horizons missio

The disappearing cryosphere : impacts and ecosystem responses to rapid cryosphere loss

Author Posting. © American Institute of Biological Sciences, 2012. This article is posted here by permission of American Institute of Biological Sciences for personal use, not for redistribution. The definitive version was published in BioScience 62 (2012): 405-415, doi:10.1525/bio.2012.62.4.11.The cryosphere—the portion of the Earth's surface where water is in solid form for at least one month of the year—has been shrinking in response to climate warming. The extents of sea ice, snow, and glaciers, for example, have been decreasing. In response, the ecosystems within the cryosphere and those that depend on the cryosphere have been changing. We identify two principal aspects of ecosystem-level responses to cryosphere loss: (1) trophodynamic alterations resulting from the loss of habitat and species loss or replacement and (2) changes in the rates and mechanisms of biogeochemical storage and cycling of carbon and nutrients, caused by changes in physical forcings or ecological community functioning. These changes affect biota in positive or negative ways, depending on how they interact with the cryosphere. The important outcome, however, is the change and the response the human social system (infrastructure, food, water, recreation) will have to that change.The authors wish to thank the funding provided by the National Science Foundation’s (NSF) Long Term Ecological Research (LTER) Network for supporting our long-term studies, in which we track the ecosystem response to the disappearing cryosphere. NSF LTER Site Grants OPP 0823101, OPP 1115245, DEB 1114804, DEB-1026415, DEB-0620579, and DEB-1027341 supported the authors during the preparation of this article.2012-10-0

Coherent Plasmon-Exciton Coupling in Silver Platelet-J-aggregate Nanocomposites

Hybrid nanostructures that couple plasmon and exciton resonances generate hybridized energy states, called plexcitons, which may result in unusual light-matter interactions. We report the formation of a transparency dip in the visible spectra of colloidal suspensions containing silver nanoplatelets and a cyanine dye, 1,1′-diethyl-2,2′-cyanine iodide (PIC). PIC was electrostatically adsorbed onto the surface of silver nanoplatelet core particles, forming an outer J-aggregate shell. This core–shell architecture provided a framework for coupling the plasmon resonance of the silver nanoplatelet core with the exciton resonance of the J-aggregate shell. The sizes and aspect ratios of the silver nanoplatelets were controlled to ensure the overlap of the plasmon and exciton resonances. As a measure of the plasmon-exciton coupling strength in the system, the experimentally observed transparency dips correspond to a Rabi splitting energy of 207 meV, among the highest reported for colloidal nanoparticles. The optical properties of the silver platelet-J-aggregate nanocomposites were supported numerically and analytically by the boundary-element method and temporal coupled-mode theory, respectively. Our theoretical predictions and experimental results confirm the presence of a transparency dip for the silver nanoplatelet core J-aggregate shell structures. Additionally, the numerical and analytical calculations indicate that the observed transparencies are dominated by the coupling of absorptive resonances, as opposed to the coupling of scattering resonances. Hence, we describe the suppressed extinction in this study as an induced transparency rather than a Fano resonance.United States. Army (Basic Research Program)United States. Army Edgewood Chemical Biological CenterUnited States. Army Research Office. Institute for Soldier Nanotechnologies (Contract No. W911NF-13-D-0001

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes