26,449 research outputs found
Bayesian Inference of Online Social Network Statistics via Lightweight Random Walk Crawls
Online social networks (OSN) contain extensive amount of information about
the underlying society that is yet to be explored. One of the most feasible
technique to fetch information from OSN, crawling through Application
Programming Interface (API) requests, poses serious concerns over the the
guarantees of the estimates. In this work, we focus on making reliable
statistical inference with limited API crawls. Based on regenerative properties
of the random walks, we propose an unbiased estimator for the aggregated sum of
functions over edges and proved the connection between variance of the
estimator and spectral gap. In order to facilitate Bayesian inference on the
true value of the estimator, we derive the approximate posterior distribution
of the estimate. Later the proposed ideas are validated with numerical
experiments on inference problems in real-world networks
Comparative Statics, Informativeness, and the Interval Dominance Order
We identify a natural way of ordering functions, which we call the interval dominance order and develop a theory of monotone comparative statics based on this order. This way of ordering functions is weaker then the standard one based on the single crossing property (Milgrom and Shannon, 1994) and so our results apply in some settings where the single crossing property does not hold. For example, they are useful when examining the comparative statics of optimal stopping time problems. We also show that certain basic results in statistical decision theory which are important in economics – specifically, the complete class theorem of Karlin and Rubin (1956) and the results connected with Lehmann’s (1988) concept of informativeness – generalize to payoff functions obeying the interval dominance order.single crossing property, interval dominance order, supermodularity, comparative statics, optimal stopping time, complete class theorem, statistical decision theory, informativeness
Discounting and Patience in Optimal Stopping and Control Problems
This paper establishes that the optimal stopping time of virtually any optimal stopping problem is increasing in "patience," understood as a particular partial order on discount rate functions. With Markov dynamics, the result holds in a continuation- domain sense even if stopping is combined with an optimal control problem. Under intuitive additional assumptions, we obtain comparative statics on both the optimal control and optimal stopping time for one-dimensional diusions. We provide a simple example where, without these assumptions, increased patience can precipitate stopping. We also show that, with optimal stopping and control, a project's expected value is decreasing in the interest rate, generalizing analogous results in a deterministic context. All our results are robust to the presence of a salvage value. As an application we show that the internal rate of return of any endogenously-interrupted project is essentially unique, even if the project also involves a management problem until its interruption. We also apply our results to the theory of optimal growth and capital deepening and to optimal bankruptcy decisions.capital growth, comparative statics, discounting, internal rate of return, optimal control, optimal stopping, patience, present value, project valuation
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