Distributionally robust optimization is a paradigm for decision making under uncertainty where the uncertain problem data are governed by a probability distribution that is itself subject to ...uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker’s prior information. In this paper, we propose a unifying framework for modeling and solving distributionally robust optimization problems. We introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold. These ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases. They also allow us to characterize distributional families in terms of several classical and/or robust statistical indicators that have not yet been studied in the context of robust optimization. We determine conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable. We also provide tractable conservative approximations for problems that violate these conditions.
In recent years, wind speed forecasting is a challenging task required for the prediction of wind energy resources. As a highly varying data source, wind speed time series requires highly nonlinear ...temporal features for the prediction tasks. However, most forecasting approaches apply shallow supervised features extracted using architectures with few nonlinear hidden layers. Moreover, the exact features captured in such methodologies cannot decrease the wind data uncertainties. In this paper, an interval probability distribution learning (IPDL) model is proposed based on restricted Boltzmann machines and rough set theory to capture unsupervised temporal features from wind speed data. The proposed model contains a set of interval latent variables tuned to capture the probability distribution of wind speed time series data using contrastive divergence with Gibbs sampling. A real-valued interval deep belief network (IDBN) is further designed employing a stack of IPDLs with a fuzzy type II inference system (FT2IS) for the supervised regression of future wind speed values. In order to automatically learn meaningful unsupervised features from the underlying wind speed data, real-valued input units are designed inside IDBN to better approximate the wind speed probability distribution function compared to classic deep belief networks. The high generalization capability of our unsupervised feature learning model incorporated with the robustness of IPDLs and FT2IS leads to accurate predictions. Simulation results on the Western Wind Dataset reveal significant performance improvement in 1-h up to 24-h ahead predictions compared to single-model approaches including both shallow and deep architectures, as well as recently proposed hybrid methodologies.
Abstract
We report the discovery of a candidate galaxy with a photo-
z
of
z
∼ 12 in the first epoch of the James Webb Space Telescope (JWST) Cosmic Evolution Early Release Science Survey. Following ...conservative selection criteria, we identify a source with a robust
z
phot
=
11.8
−
0.2
+
0.3
(1
σ
uncertainty) with
m
F200W
= 27.3 and ≳7
σ
detections in five filters. The source is not detected at
λ
< 1.4
μ
m in deep imaging from both Hubble Space Telescope (HST) and JWST and has faint ∼3
σ
detections in JWST F150W and HST F160W, which signal a Ly
α
break near the red edge of both filters, implying
z
∼ 12. This object (Maisie’s Galaxy) exhibits F115W − F200W > 1.9 mag (2
σ
lower limit) with a blue continuum slope, resulting in 99.6% of the photo-
z
probability distribution function favoring
z
> 11. All data-quality images show no artifacts at the candidate’s position, and independent analyses consistently find a strong preference for
z
> 11. Its colors are inconsistent with Galactic stars, and it is resolved (
r
h
= 340 ± 14 pc). Maisie’s Galaxy has log
M
*
/
M
⊙
∼ 8.5 and is highly star-forming (log sSFR ∼ −8.2 yr
−1
), with a blue rest-UV color (
β
∼ −2.5) indicating little dust, though not extremely low metallicity. While the presence of this source is in tension with most predictions, it agrees with empirical extrapolations assuming UV luminosity functions that smoothly decline with increasing redshift. Should follow-up spectroscopy validate this redshift, our universe was already aglow with galaxies less than 400 Myr after the Big Bang.
We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the ...example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated with these states. We establish the connection with the properties and structure of entangled probability distributions.
The last decade has seen the development of a range of new statistical and computational techniques for analysing large collections of radiocarbon (14C) dates, often but not exclusively to make ...inferences about human population change in the past. Here we introduce rcarbon, an open-source software package for the R statistical computing language which implements many of these techniques and looks to foster transparent future study of their strengths and weaknesses. In this paper, we review the key assumptions, limitations and potentials behind statistical analyses of summed probability distribution of 14C dates, including Monte-Carlo simulation-based tests, permutation tests, and spatial analyses. Supplementary material provides a fully reproducible analysis with further details not covered in the main paper.
Ingredients for 21 cm Intensity Mapping Villaescusa-Navarro, Francisco; Genel, Shy; Castorina, Emanuele ...
The Astrophysical journal,
10/2018, Letnik:
866, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Current and upcoming radio telescopes will map the spatial distribution of cosmic neutral hydrogen (H i) through its 21 cm emission. In order to extract the maximum information from these surveys, ...accurate theoretical predictions are needed. We study the abundance and clustering properties of H i at redshifts z ≤ 5 using TNG100, a large state-of-the-art magnetohydrodynamic simulation of a 75 h−1 Mpc box size, which is part of the IllustrisTNG Project. We show that most of the H i lies within dark matter halos, and we provide fits for the halo H i mass function, i.e., the mean H i mass hosted by a halo of mass M at redshift z. We find that only halos with circular velocities larger than 30 km s−1 contain H i. While the density profiles of H i exhibit a large halo-to-halo scatter, the mean profiles are universal across mass and redshift. The H i in low-mass halos is mostly located in the central galaxy, while in massive halos the H i is concentrated in the satellites. Our simulation reproduces the bias value of damped Ly systems from observations. We show that the H i and matter density probability distribution functions differ significantly. Our results point out that for small halos, the H i bulk velocity goes in the same direction and has the same magnitude as the halo peculiar velocity, while in large halos, differences show up. We find that halo H i velocity dispersion follows a power law with halo mass. We find a complicated H i bias, with H i already becoming nonlinear at k = 0.3 h Mpc−1 at z 3. The clustering of H i can, however, be accurately reproduced by perturbative methods. We find a new secondary bias by showing that the clustering of halos depends not only on mass but also on H i content. We compute the amplitude of the H i shot noise and find that it is small at all redshifts, verifying the robustness of BAO measurements with 21 cm intensity mapping. We study the clustering of H i in redshift space and show that linear theory can explain the ratio between the monopoles in redshift and real space down to 0.3, 0.5, and 1 h Mpc−1 at redshifts 3, 4, and 5, respectively. We find that the amplitude of the Fingers-of-God effect is larger for H i than for matter, since H i is found only in halos above a certain mass. We point out that 21 cm maps can be created from N-body simulations rather than full hydrodynamic simulations. Modeling the one-halo term is crucial for achieving percent accuracy with respect to a full hydrodynamic treatment. Although our results are not converged against resolution, they are, however, very useful as we work at the resolution where the model parameters have been calibrated to reproduce galaxy properties.
A simulation study investigated how ceiling and floor effect (CFE) affect the performance of Welch's t-test, F-test, Mann-Whitney test, Kruskal-Wallis test, Scheirer-Ray-Hare-test, trimmed t-test, ...Bayesian t-test, and the "two one-sided tests" equivalence testing procedure. The effect of CFE on the estimate of group difference and on its confidence interval, and on Cohen's d and on its confidence interval was also evaluated. In addition, the parametric methods were applied to data transformed with log or logit function and the performance was evaluated. The notion of essential maximum from abstract measurement theory is used to formally define CFE and the principle of maximum entropy was used to derive probability distributions with essential maximum/minimum. These distributions allow the manipulation of the magnitude of CFE through a parameter. Beta, Gamma, Beta prime and Beta-binomial distributions were obtained in this way with the CFE parameter corresponding to the logarithm of the geometric mean. Wald distribution and ordered logistic regression were also included in the study due to their measure-theoretic connection to CFE, even though these models lack essential minimum/maximum. Performance in two-group, three-group and 2 × 2 factor design scenarios was investigated by fixing the group differences in terms of CFE parameter and by adjusting the base level of CFE.
In general, bias and uncertainty increased with CFE. Most problematic were occasional instances of biased inference which became more certain and more biased as the magnitude of CFE increased. The bias affected the estimate of group difference, the estimate of Cohen's d and the decisions of the equivalence testing methods. Statistical methods worked best with transformed data, albeit this depended on the match between the choice of transformation and the type of CFE. Log transform worked well with Gamma and Beta prime distribution while logit transform worked well with Beta distribution. Rank-based tests showed best performance with discrete data, but it was demonstrated that even there a model derived with measurement-theoretic principles may show superior performance. Trimmed t-test showed poor performance. In the factor design, CFE prevented the detection of main effects as well as the detection of interaction. Irrespective of CFE, F-test misidentified main effects and interactions on multiple occasions. Five different constellations of main effect and interactions were investigated for each probability distribution, and weaknesses of each statistical method were identified and reported. As part of the discussion, the use of generalized linear models based on abstract measurement theory is recommended to counter CFE. Furthermore, the necessity of measure validation/calibration studies to obtain the necessary knowledge of CFE to design and select an appropriate statistical tool, is stressed.
We developed a deep convolutional neural network (CNN), used as a classifier, to estimate photometric redshifts and associated probability distribution functions (PDF) for galaxies in the Main Galaxy ...Sample of the Sloan Digital Sky Survey at z < 0.4. Our method exploits all the information present in the images without any feature extraction. The input data consist of 64 × 64 pixel ugriz images centered on the spectroscopic targets, plus the galactic reddening value on the line-of-sight. For training sets of 100k objects or more (≥20% of the database), we reach a dispersion σMAD < 0.01, significantly lower than the current best one obtained from another machine learning technique on the same sample. The bias is lower than 10−4, independent of photometric redshift. The PDFs are shown to have very good predictive power. We also find that the CNN redshifts are unbiased with respect to galaxy inclination, and that σMAD decreases with the signal-to-noise ratio (S/N), achieving values below 0.007 for S/N > 100, as in the deep stacked region of Stripe 82. We argue that for most galaxies the precision is limited by the S/N of SDSS images rather than by the method. The success of this experiment at low redshift opens promising perspectives for upcoming surveys.
We present a measurement of the Hubble constant H0 using the gravitational wave (GW) event GW190814, which resulted from the coalescence of a 23 M black hole with a 2.6 M compact object, as a ...standard siren. No compelling electromagnetic counterpart has been identified for this event; thus our analysis accounts for thousands of potential host galaxies within a statistical framework. The redshift information is obtained from the photometric redshift (photo-z) catalog from the Dark Energy Survey. The luminosity distance is provided by the LIGO/Virgo gravitational wave sky map. Since this GW event has the second-smallest localization volume after GW170817, GW190814 is likely to provide the best constraint on cosmology from a single standard siren without identifying an electromagnetic counterpart. Our analysis uses photo-z probability distribution functions and corrects for photo-z biases. We also reanalyze the binary black hole GW170814 within this updated framework. We explore how our findings impact the H0 constraints from GW170817, the only GW merger associated with a unique host galaxy. From a combination of GW190814, GW170814, and GW170817, our analysis yields (68% highest-density interval, HDI) for a prior in H0 uniform between . The addition of GW190814 and GW170814 to GW170817 improves the 68% HDI from GW170817 alone by ∼18%, showing how well-localized mergers without counterparts can provide a significant contribution to standard siren measurements, provided that a complete galaxy catalog is available at the location of the event.
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