Variational Bayes with Intractable Likelihood

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many interesting situations such as in state space models and in approximate Bayesian computation (ABC), where application of VB methods was previously impossible. This paper extends the scope of application of VB to cases where the likelihood is intractable, but can be estimated unbiasedly. The proposed VB method therefore makes it possible to carry out Bayesian inference in many statistical applications, including state space models and ABC. The method is generic in the sense that it can be applied to almost all statistical models without requiring too much model-based derivation, which is a drawback of many existing VB algorithms. We also show how the proposed method can be used to obtain highly accurate VB approximations of marginal posterior distributions.Comment: 40 pages, 6 figure

Fuzzy control system for a remote focusing microscope

Space Station Crew Health Care System procedures require the use of an on-board microscope whose slide images will be transmitted for analysis by ground-based microbiologists. Focusing of microscope slides is low on the list of crew priorities, so NASA is investigating the option of telerobotic focusing controlled by the microbiologist on the ground, using continuous video feedback. However, even at Space Station distances, the transmission time lag may disrupt the focusing process, severely limiting the number of slides that can be analyzed within a given bandwidth allocation. Substantial time could be saved if on-board automation could pre-focus each slide before transmission. The authors demonstrate the feasibility of on-board automatic focusing using a fuzzy logic ruled-based system to bring the slide image into focus. The original prototype system was produced in under two months and at low cost. Slide images are captured by a video camera, then digitized by gray-scale value. A software function calculates an index of 'sharpness' based on gray-scale contrasts. The fuzzy logic rule-based system uses feedback to set the microscope's focusing control in an attempt to maximize sharpness. The systems as currently implemented performs satisfactorily in focusing a variety of slide types at magnification levels ranging from 10 to 1000x. Although feasibility has been demonstrated, the system's performance and usability could be improved substantially in four ways: by upgrading the quality and resolution of the video imaging system (including the use of full color); by empirically defining and calibrating the index of image sharpness; by letting the overall focusing strategy vary depending on user-specified parameters; and by fine-tuning the fuzzy rules, set definitions, and procedures used

The Behavior of Savings and Asset Prices When Preferences and Beliefs Are Heterogeneous

Movements in asset prices are a major risk confronting individuals. This paper establishes new asset pricing results when agents differ in risk preference, time preference and/or expectations. It shows that risk tolerance is a critical concept driving savings decisions, consumption allocations, prices and return volatilities. Surprisingly, due to the equilibrium risk sharing, the precautionary savings motive in the aggregate can vastly exceed that of even the most prudent actual agent in the economy. Consequently, a low real interest rate, resulting from large aggregate savings, can prevail with reasonable risk aversions for all agents. One downside of a large aggregate savings motive is that savings rates become extremely sensitive to output fluctuation. Thus, the same mechanism that produces realistically low interest rates tends to make them unrealistically volatile. A powerful isomorphism allows differences in time preference and expectations to be swept away in the analysis, yielding an equivalent economy whose agents differ merely in risk aversion. These results hold great potential to simplify the analysis of heterogeneous-agent economies, as we demonstrate in quantifying how asset prices move and bounding their volatilities. All results are obtained in closed form for any number of agents possessing additively separable preferences in an endowment economy.

Ultrasonography of a Helical Left Common Carotid Artery

Case Presentation: An 83-year-old woman was admitted to the intensive care unit for septic shock at which point an internal jugular central venous line was placed. The patient’s common carotid artery was visualized in an atypical location, lateral to the internal jugular vein. Further inspection revealed the common carotid artery travelling in a rotational trajectory around the internal jugular vein.Discussion: For at least two decades, point-of-care ultrasound has become the standard of care for placing central venous lines. This surprising anatomical orientation is rare and cautions physicians to fully explore a patient’s anatomy prior to placing central lines