Common Learning with Intertemporal Dependence

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. Will the agents commonly learn the value of the parameter, i.e., will the true value of the parameter become approximate common-knowledge? If the signals are independent and identically distributed across time (but not necessarily across agents), the answer is yes (Cripps, Ely, Mailath, and Samuelson, 2008). This paper explores the implications of allowing the signals to be dependent over time. We present a counterexample showing that even extremely simple time dependence can preclude common learning, and present sufficient conditions for common learning.Common learning, common belief, private signals, private beliefs

Common Learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that that when each agent's signal space is finite, the agents will commonly learn its value, i.e., that the true value of the parameter will become approximate common-knowledge. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.Common learning, Common belief, Private signals, Private beliefs

Common Learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that that when each agent's signal space is finite, the agents will commonly learn its value, i.e., that the true value of the parameter will become approximate common-knowledge. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.Common learning, common belief, private signals, private beliefs

Some recent radio talks.

Wastage in weaners - By L. C. SNOOK, D.Sc, Animal Nutrition Officer Ever since I can remember, the breeders of Merino sheep have been plagued with what is known as the weaner problem. During the dry summer months, unthriftiness becomes apparent, the affected animals lose condition, and unless green feed becomes available a number will die. The losses on any one property are rarely devastating but over the years the collective wastage of young sheep has been, in some cases, considerable. A puzzling feature is that weaners will be lost on pasture which appears to be adequate for the grown sheep. Also the unthriftiness is often restricted to 10% or so of the weaners in any one flock. It is not uncommon to hear sheep men complain that while the bulk of their young sheep are thriving, there is a tail which looks dreadful. The importance of weed control in the vegetable garden - By W. KOOYMAN, Vegetable Instructor I suppose every vegetable grower realises that to obtain satisfactory yields of high quality produce, control of weeds is of considerable importance. There are many reasons why weed control is important, however, as each crop has special problems and characteristics, time would be too short to give a detailed account of all aspects. An endeavour will be made in this talk to touch on some of the more important aspects of weed control. Strawberry growing - By J. CRIPPS, Horticultural Adviser Strawberries are not grown on a large scale commercially in this State, but many private growers cultivate them and indeed they are an ideal backyard fruit crop since they can be grown in a small area and are not subject to attacks by fruit fly

Debiasing Welch's Method for Spectral Density Estimation

Welch's method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite length time series, while the variance of the estimator decreases as the number of segments increase, the magnitude of the estimator's bias increases: a bias-variance trade-off ensues when setting the segment number. We address this issue by providing a novel method for debiasing Welch's method which maintains the computational complexity and asymptotic consistency, and leads to improved finite-sample performance. Theoretical results are given for fourth-order stationary processes with finite fourth-order moments and absolutely convergent fourth-order cumulant function. The significant bias reduction is demonstrated with numerical simulation and an application to real-world data. Our estimator also permits irregular spacing over frequency and we demonstrate how this may be employed for signal compression and further variance reduction. Code accompanying this work is available in R and python.Comment: Resubmitted to Biometrik

A 1.8-3.2 GHz Doherty Power Amplifier in quasi-MMIC Technology

This letter presents the design and characterization of a quasi-integrated Doherty power amplifier for base-station applications. The prototype is based on GaN on SiC 0.25-μm 50-V transistors, whereas the passive matching networks are realized on a GaAs substrate. The design, based on a dual-input Doherty architecture, achieves a continuous-wave (CW) output power higher than 42 dBm and a backoff efficiency higher than 38% over the 1.8-3.2-GHz frequency band. By using an off-chip coupler, a single-input operation is also possible with a slight reduction in performance, i.e., CW output power and backoff efficiency higher than 41.4 dBm and 36%, respectively, on the 1.8-3.2-GHz band. System-level characterization shows higher peak power achievable than in CW condition as well as the linearizability of the amplifier under modulated signal conditions

Monitoring the CMS strip tracker readout system

The CMS Silicon Strip Tracker at the LHC comprises a sensitive area of approximately 200 m2 and 10 million readout channels. Its data acquisition system is based around a custom analogue front-end chip. Both the control and the readout of the front-end electronics are performed by off-detector VME boards in the counting room, which digitise the raw event data and perform zero-suppression and formatting. The data acquisition system uses the CMS online software framework to configure, control and monitor the hardware components and steer the data acquisition. The first data analysis is performed online within the official CMS reconstruction framework, which provides many services, such as distributed analysis, access to geometry and conditions data, and a Data Quality Monitoring tool based on the online physics reconstruction. The data acquisition monitoring of the Strip Tracker uses both the data acquisition and the reconstruction software frameworks in order to provide real-time feedback to shifters on the operational state of the detector, archiving for later analysis and possibly trigger automatic recovery actions in case of errors. Here we review the proposed architecture of the monitoring system and we describe its software components, which are already in place, the various monitoring streams available, and our experiences of operating and monitoring a large-scale system

Towards a modeling of the time dependence of contact area between solid bodies

I present a simple model of the time dependence of the contact area between solid bodies, assuming either a totally uncorrelated surface topography, or a self affine surface roughness. The existence of relaxation effects (that I incorporate using a recently proposed model) produces the time increase of the contact area $A(t)$ towards an asymptotic value that can be much smaller than the nominal contact area. For an uncorrelated surface topography, the time evolution of $A(t)$ is numerically found to be well fitted by expressions of the form [$A(\infty)-A(t)]\sim (t+t_0)^{-q}$, where the exponent $q$ depends on the normal load $F_N$ as $q\sim F_N^{\beta}$, with $\beta$ close to 0.5. In particular, when the contact area is much lower than the nominal area I obtain $A(t)/A(0) \sim 1+C\ln(t/t_0+1)$, i.e., a logarithmic time increase of the contact area, in accordance with experimental observations. The logarithmic increase for low loads is also obtained analytically in this case. For the more realistic case of self affine surfaces, the results are qualitatively similar.Comment: 18 pages, 9 figure