Airbnb\u27s Effect on the Hospitality Industry

I examined the effect that Airbnb’s entrance into and disruption of the hospitality market in 2011 had on hotel room rates across the world by 2017. Hotel room rates were taken from published data tables rather than my own analysis because of an unavailability of raw hotel pricing data. Price comparisons between current Airbnb and hotel room rates were researched to see if one method of accommodation would be better than the other. Twenty-seven cities’ hotel rate averages and Airbnb entire-home prices were averaged and compared. There was a significant difference in hotel room rates between 2011 and 2017, during which prices rose, potentially as a factor of the willingness for consumers to spend more. No significant difference in 2017 Airbnb entire-home and 2017 hotel room prices was found. Mediation of Airbnb’s entry into the market was not tested it cannot be stated whether this itself had a significant effect

Simulation from endpoint-conditioned, continuous-time Markov chains on a finite state space, with applications to molecular evolution

Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging from computational finance to human genetics and genomics. A common theme among these diverse applications is the need to simulate sample paths of a CTMC conditional on realized data that is discretely observed. Here we present a general solution to this sampling problem when the CTMC is defined on a discrete and finite state space. Specifically, we consider the generation of sample paths, including intermediate states and times of transition, from a CTMC whose beginning and ending states are known across a time interval of length $T$. We first unify the literature through a discussion of the three predominant approaches: (1) modified rejection sampling, (2) direct sampling, and (3) uniformization. We then give analytical results for the complexity and efficiency of each method in terms of the instantaneous transition rate matrix $Q$ of the CTMC, its beginning and ending states, and the length of sampling time $T$. In doing so, we show that no method dominates the others across all model specifications, and we give explicit proof of which method prevails for any given $Q,T,$ and endpoints. Finally, we introduce and compare three applications of CTMCs to demonstrate the pitfalls of choosing an inefficient sampler.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS247 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org