Short-term changes in booking behaviors can significantly undermine naive forecasting methods in the travel and hospitality industry, especially during periods of global upheaval. Traditional metrics like average or median lead times capture only broad trends, often missing subtle yet impactful distributional shifts. In this study, we introduce a normalized L1 (Manhattan) distance to measure the full distributional divergence in Airbnb booking lead times from 2018 to 2022, with particular emphasis on the COVID-19 pandemic. Using data from four major U.S. cities, we find a two-phase pattern of disruption: a sharp initial change at the pandemic's onset, followed by partial recovery but persistent divergences from pre-2018 norms. Our approach reveals shifts in travelers' planning horizons that remain undetected by conventional summary statistics. These findings highlight the importance of examining the entire lead-time distribution when forecasting demand and setting pricing strategies. By capturing nuanced changes in booking behaviors, the normalized L1 metric enhances both demand forecasting and the broader strategic toolkit for tourism stakeholders, from revenue management and marketing to operational planning, amid continued market volatility.

We investigate a simple model for a galactic halo under the assumption that it is dominated by a dark matter component in the form of a Bose-Einstein condensate involving an ultra-light scalar particle. In particular we discuss the possibility if the dark matter is in superfluid state then a rotating galactic halo might contain quantised vortices which would be low-energy analogues of cosmic strings. Using known solutions for the density profiles of such vortices we compute the self-gravitational interactions in such halos and place bounds on the parameters describing such models, such as the mass of the particles involved.

We investigate the evolution of cosmic voids in the Schrodinger Poisson formalism, finding wave mechanical solutions for the dynamics in a standard cosmological background with appropriate boundary conditions. We compare the results in this model to those obtained using the Zel'dovich approximation. We discuss the advantages of studying voids in general and the advantages of the Schrodinger Poisson description over other approaches. In particular, emphasizing the utility of the free particle approximation. We also discuss a dimensionless number, similar to the Reynolds number, for this system which allows our void solutions to be scaled to systems of different physical dimensions.

Journal of Astronomical InstrumentationVol. 08, No. 03, 1980001 (2019) Book ReviewFree AccessBook Review: "Data Analysis for Scientists and Engineers by Edward L. Robinson (Princeton University Press, 2016)"Peter ColesPeter ColesNational University of Ireland, Maynooth, Irelandhttps://doi.org/10.1142/S2251171719800011Cited by:0 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Librarian ShareShare onFacebookTwitterLinked InRedditEmail In any discipline that relies on experiment and measurement, the proper analysis and interpretation of data is of paramount importance. Education in science and engineering disciplines has not always reflected that fact, and it is not too long ago that courses in probability and statistics were missing from the curriculum in some areas of physical science. It is good to see that this is changing.This book is a graduate-level introduction to data analysis aimed at scientists and engineers. It has many strengths, but also some weaknesses which I shall touch on below after first briefly summarizing the contents.As is the case with most texts on this topic, the book begins with an introduction to the basics probability theory after which some familiar probability distributions (e.g. Gaussian, Poisson, Binomial, etc.) are introduced. There is then a chapter about random number generators, which also serves to introduce the idea of Markov Chains and related matters such as Gibbs Sampling.The rest of the book is devoted to introductory statistics approached from the frequentist perspective in which probabilities are interpreted as proportions defined over some sort of ensemble, e.g. repeated tosses of a coin. There then follow discussions of least-squares estimation and goodness of fit (both linear and non-linear) before the alternative, Bayesian, approach to statistics is described. In the Bayesian approach, a probability is not interpreted as a proportion but as a generalization of the Boolean states of “0” (false) and “1” (true) to an intermediate state p in which there is insufficient information to be sure.The remaining three chapters of the book are devoted to the analysis of sequences of variables, e.g. Time Series (including spectral analysis, covariance and deconvolution).The strengths of this book are that it is well produced and well written, with good illustrations and numerous worked examples. I can find little fault with the way the material included is presented and described. The weaknesses of the book are to do with what is left out than what is included.Surprisingly, there is little to no discussion of hypothesis testing (of either frequentist or Bayesian variety) anywhere in the book, so there is no mention of significance levels, p-values, Type I and Type II errors, and so on. I would have thought one of the aims of a book of this kind would be to introduce the student to concepts much used in the literature, so it is to me a rather glaring omission. Likewise there is nothing in this book about Bayesian inference, model comparison, evidence or any of these very important topics.Also surprising for a modern textbook there is little discussion of the computational implementation of the methods discussed, and no examples of scripts illustrating how these ideas can be coded up. Data analysis in the age of “Big Data” is very much driven by computers, so this is also surprising. All the modern courses in data analysis in the various universities of which I am aware base their teaching around computational laboratory sessions, so this book would not really work very well as a companion to such a course. It is true that bits of code written in the either of the current industry standards (R or Python) may well have dated in a few years, just as the Matlab scripts of the recent past have now been superseded, but I still think it is useful to include some sample codes as these can easily be translated into other languages if necessary.The emphasis of the latter chapters of the book on the analysis of random sequences in the context of time-series data perhaps reflects the author’s research interests (in astronomy) which is quite reasonable for a graduate-level text, but the jacket states that there is an “extensive look at analysis techniques for time-series data and images” and there is actually very little on anything other than the one-dimensional case.The final criticism arises from my personal view that the Bayesian approach to inference offers a far more compelling and coherent way of treating all data analysis challenges than the collection of ad hoc methods generated by frequentist considerations. In accord with that view — which of course you are free to reject — I would like to have seen a far more extensive discussion of Bayesian methods.The author includes a little discussion at the end of Chapter 7 on Bayesian methods in which he reveals himself as a skeptic. For example, “It appears to your author that the concerns of frequentists about the meaning of probability in Bayesian statistics are legitimate.” It would be inappropriate to debate this issue at length in a book review, but I will say that Bayesian methods have long since been the mainstay of data analysis techniques in astronomy and astrophysics — for what I believe to be very good reasons.In summary, then, I think that what this book does, it does very well. I do however have serious concerns about the selection of topics, and the absence of material that I would consider essential were I to be teaching a course on this subject.I will also mention without further comment that the book is priced at £62.95. FiguresReferencesRelatedDetails Recommended Vol. 08, No. 03 Metrics History Received 16 May 2019 Published: June 6, 2019 PDF download

The modern era of cosmology began with the publication of Einstein's general theory of relativity in 1915. The first experimental test of this theory was Eddington's famous expedition to. measure the bending of light at a total solar eclipse in 1919. So famous is, this experiment, and so dramatic was the impact on Einstein himself, that history tends not to recognize the controversy that surrounded the results at the time. In this paper I discuss the experiment in its historical and sociological context and show that it provides valuable lessons for modern astronomy and cosmology.

The thought of a scientist trying to design a laboratory experiment in which to create a whole new universe probably sounds like it belongs in the plot of a science-fiction B-movie. But as author Zeeya Merali explains in her new book A Big Bang in a Little Room, there are more than a few eminent physicists who think that this is theoretically possible.

The position-dependent power spectrum has been recently proposed as a descriptor of gravitationally induced non-Gaussianity in galaxy clustering, as it is sensitive to the "soft limit" of the bispectrum (i.e. when one of the wave number tends to zero). We generalise this concept to higher order and clarify their relationship to other known statistics such as the skew-spectrum, the kurt-spectra and their real-space counterparts the cumulants correlators. Using the Hierarchical Ansatz (HA) as a toy model for the higher order correlation hierarchy, we show how in the soft limit, polyspectra at a given order can be identified with lower order polyspectra with the same geometrical dependence but with renormalised amplitudes expressed in terms of amplitudes of the original polyspectra. We extend the concept of position-dependent bispectrum to bispectrum of the divergence of the velocity field Θ and mixed multispectra involving δ and Θ in the 3D perturbative regime. To quantify the effects of transients in numerical simulations, we also present results for lowest order in Lagrangian perturbation theory (LPT) or the Zel'dovich approximation (ZA). Finally, we discuss how to extend the position-dependent spectrum concept to encompass cross-spectra. And finally study the application of this concept to two dimensions (2D), for projected galaxy maps, convergence κ maps from weak-lensing surveys or maps of CMB secondaries e.g. the frequency cleaned y-parameter maps of thermal Sunyaev-Zel'dovich (tSZ) effect from CMB surveys.

We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using appropriately defined parameters to describe the evolution of the scalar field energy in this situation, we find that there are two extra fixed points that are not present in the case without curvature. We also analyse the evolution of the effective equation-of-state parameter for different initial values of the curvature.

We propose a novel technique to separate the late-time, post-reionization component of the kinetic Sunyaev-Zeldovich (kSZ) effect from the contribution to it from a (poorly understood and probably patchy) reionization history. The kSZ effect is one of the most promising probe of the missing baryons in the Universe. We study the possibility of reconstructing it in three dimensions (3D), using future spectroscopic surveys such as the Euclid survey. By reconstructing a 3D template from galaxy density and peculiar velocity fields from spectroscopic surveys we cross-correlate the estimator against CMB maps. The resulting cross-correlation can help us to map out the kSZ contribution to CMB in 3D as a function of redshift thereby extending previous results which use tomographic reconstruction. This allows the separation of the late-time effect from the contribution owing to reionization. By construction, it avoids contamination from foregrounds, primary CMB, tSZ effect as well as from star-forming galaxies. Due to a high number density of galaxies the signal-to-noise ratio (S/N) for such cross-correlational studies is higher, compared to the studies involving CMB power-spectrum analysis. Using a spherical Bessel-Fourier (sFB) transform we introduce a pair of 3D power spectra: C-l(parallel to)(k) and C-l(perpendicular to)(k) that can be used for this purpose. We find that in a future spectroscopic survey with near all-sky coverage and a survey depth of z approximate to 1, reconstruction of C-l(perpendicular to) can be achieved in a few radial wave bands k approximate to (0.01-0.5 h(-1) Mpc) with a S/N ratio of up to O(10) for angular harmonics in the range l = (200-2000).

We study Modified Gravity (MG) theories by modelling the redshifted matter power spectrum in a spherical Fourier–Bessel basis. We use a fully non-linear description of the real-space matter power spectrum and include the lowest order redshift-space correction (Kaiser effect), taking into account some additional non-linear contributions. Ignoring relativistic corrections, which are not expected to play an important role for a shallow survey, we analyse two different MG scenarios, namely the generalized Dilaton scalar–tensor theories and the f (R) models in the large curvature regime. We compute the 3D power spectrum Csl(k1,k2) Cls(k1,k2) for various such MG theories with and without redshift-space distortions, assuming precise knowledge of background cosmological parameters. Using an all-sky spectroscopic survey with Gaussian selection function φ(r)∝exp(−r2/r20),r0=150h−1 φ(r)∝exp⁡(−r2/r02),r0=150h−1 Mpc, and number density of galaxies N¯=10−4Mpc−3 N¯=10−4Mpc−3 , we use a χ2 analysis, and find that the lower order (l ≤ 25) multipoles of Csl(k,k′) Cls(k,k′) (with radial modes restricted to k < 0.2 h Mpc−1) can constraint the parameter fR0 fR0 at a level of 2 × 10−5(3 × 10−5) with 3σ confidence for n = 1(2). Combining constraints from higher l > 25 modes can further reduce the error bars and thus in principle make cosmological gravity constraints competitive with Solar system tests. However this will require an accurate modelling of non-linear redshift-space distortions. Using a tomographic β(a)–m(a) parametrization we also derive constraints on specific parameters describing the Dilaton models of MG.

We use the cosmic shear data from the Canada-France-Hawaii Telescope Lensing Survey to place constraints on $f(R)$ and {\it Generalized Dilaton} models of modified gravity. This is highly complimentary to other probes since the constraints mainly come from the non-linear scales: maximal deviations with respects to the General-Relativity + $\Lambda$CDM scenario occurs at $k\sim1 h \mbox{Mpc}^{-1}$. At these scales, it becomes necessary to account for known degeneracies with baryon feedback and massive neutrinos, hence we place constraints jointly on these three physical effects. To achieve this, we formulate these modified gravity theories within a common tomographic parameterization, we compute their impact on the clustering properties relative to a GR universe, and propagate the observed modifications into the weak lensing $\xi_{\pm}$ quantity. Confronted against the cosmic shear data, we reject the $f(R)$ $\{ |f_{R_0}|=10^{-4}, n=1\}$ model with more than 99.9% confidence interval (CI) when assuming a $\Lambda$CDM dark matter only model. In the presence of baryonic feedback processes and massive neutrinos with total mass up to 0.2eV, the model is disfavoured with at least 94% CI in all different combinations studied. Constraints on the $\{ |f_{R_0}|=10^{-4}, n=2\}$ model are weaker, but nevertheless disfavoured with at least 89% CI. We identify several specific combinations of neutrino mass, baryon feedback and $f(R)$ or Dilaton gravity models that are excluded by the current cosmic shear data. Notably, universes with three massless neutrinos and no baryon feedback are strongly disfavoured in all modified gravity scenarios studied. These results indicate that competitive constraints may be achieved with future cosmic shear data.

The Planck mission has produced a map of the cosmic microwave background at higher resolution than ever before. Peter Coles explains its implications for our understanding of the universe.

We provide generic predictions for the lower order cumulants of weak lensing maps, and their correlators for tomographic bins as well as in three dimensions (3D). Using small-angle approximation, we derive the corresponding one- and two-point probability distribution function for the tomographic maps from different bins and for 3D convergence maps. The modelling of weak lensing statistics is obtained by adopting a detailed prescription for the underlying density contrast that involves hierarchal ansatz and lognormal distribution. We study the dependence of our results on cosmological parameters and source distributions corresponding to the realistic surveys such as LSST and DES. We briefly outline how photometric redshift information can be incorporated in our results. We also show how topological properties of convergence maps can be quantified using our results.

We show how cross-correlating a high-redshift external tracer field, such as the 21-cm neutral hydrogen distribution and product maps involving cosmic microwave background (CMB) temperature and polarization fields, that probe mixed bispectrum involving these fields, can help to determine the reionization history of the Universe, beyond what can be achieved from cross-spectrum analysis. Taking clues from recent studies for the detection of primordial non-Gaussianity, we develop a set of estimators that can study reionization using a power spectrum associated with the bispectrum (or skew-spectrum). We use the matched filtering inherent in this method to investigate different reionization histories. We check to what extent they can be used to rule out various models of reionization and study cross-contamination from different sources such as the lensing of the CMB. The estimators can be fine-tuned to optimize study of a specific reionization history. We consider three different types of tracers in our study, namely: proto-galaxies; 21-cm maps of neutral hydrogen; and quasars. We also consider four alternative models of reionization. We find that the cumulative signal-to-noise ratio (S/N) for detection at l(max) = 2000 can reach O(70) for cosmic variance limited all-sky experiments. Combining 100 GHz, 143 GHz and 217 GHz channels of the Planck experiment, we find that the S/N lies in the range O (5)-O(35). The S/N depends on the specific choice of a tracer field, and multiple tracers can be effectively used to map out the entire reionization history with reasonable S/N. Contamination from weak lensing is investigated and found to be negligible, and the effects of Thomson scattering from patchy reionization are also considered.

We present novel statistical tools to cross-correlate frequency cleaned thermal Sunyaev-Zel'dovich (tSZ) maps and tomographic weak lensing (wl) convergence maps. Moving beyond the lowest order cross-correlation, we introduce a hierarchy of mixed higher order statistics, the cumulants and cumulant correlators, to analyse non-Gaussianity in real space, as well as corresponding polyspectra in the harmonic domain. Using these moments, we derive analytical expressions for the joint two-point probability distribution function for smoothed tSZ (y) and convergence (kappa) maps. The presence of tomographic information allows us to study the evolution of higher order mixed tSZ-wl statistics with redshift. We express the joint PDFs p(kappa y)(kappa, y) in terms of individual one-point PDFs [p(kappa)(kappa), p(y)(y)] and the relevant bias functions [b(kappa)(kappa), b(y)(y)]. Analytical results for two different regimes are presented that correspond to the small and large angular smoothing scales. Results are also obtained for corresponding hotspots in the tSZ and convergence maps. In addition to results based on hierarchical techniques and perturbative methods, we present results of calculations based on the lognormal approximation. The analytical expressions derived here are generic and applicable to cross-correlation studies of arbitrary tracers of large-scale structure including, e.g., that of tSZ and soft X-ray background. We provide detailed comparison of our analytical results against state of the art Millennium Gas Simulations with and without non-gravitational effects such as pre-heating and cooling. Comparison of these results with gravity only simulations, shows reasonable agreement and can be used to isolate effect of non-gravitational physics from observational data.

On small angular scales, i.e. at high angular frequencies, beyond the damping tail of the primary power spectrum, the dominant contribution to the power spectrum of cosmic microwave background temperature fluctuations is the thermal Sunyaev–Zel'dovich (tSZ) effect. We investigate various important statistical properties of the Sunyaev–Zel'dovich maps, using well-motivated models for dark matter clustering to construct statistical descriptions of the tSZ effect to all orders enabling us to determine the entire probability distribution function (PDF). Any generic deterministic biasing scheme can be incorporated in our analysis and the effects of projection, biasing and the underlying density distribution can be analysed separately and transparently in this approach. We introduce the cumulant correlators as tools to analyse tSZ catalogues and relate them to corresponding statistical descriptors of the underlying density distribution. The statistics of hot spots in frequency-cleaned tSZ maps are also developed in a self-consistent way to an arbitrary order, to obtain results complementary to those found using the halo model. We also consider different beam sizes to check the extent to which the PDF can be extracted from various observational configurations. The formalism is presented with two specific models for underlying matter clustering, the hierarchical ansatz and the lognormal distribution. We find both models to be in very good agreement with the simulation results, though the extension of the hierarchical model has an edge over the lognormal model. In addition to testing against simulations made using semi-analytical techniques, we have also used the maps made using Millennium Gas Simulations to prove that the PDF and bias can indeed be predicted with very high accuracy using these models. The presence of significant non-gravitational effects such as preheating, however, cannot be modelled using an analytical approach which is based on the modelling of gravitational clustering alone. Our results indicate that the PDFs we construct are insensitive to the underlying cosmology and can thus provide a useful probe of non-gravitational processes, e.g. preheating or feedback.