Additional Nuisance Parameters Research Articles

Cosmological Constraints from the BOSS DR12 Void Size Function

We present the first cosmological constraints derived from the analysis of the void size function. This work relies on the final Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) data set, a large spectroscopic galaxy catalog, ideal for the identification of cosmic voids. We extract a sample of voids from the distribution of galaxies, and we apply a cleaning procedure aimed at reaching high levels of purity and completeness. We model the void size function by means of an extension of the popular volume-conserving model, based on two additional nuisance parameters. Relying on mock catalogs specifically designed to reproduce the BOSS DR12 galaxy sample, we calibrate the extended size function model parameters and validate the methodology. We then apply a Bayesian analysis to constrain the Lambda cold dark matter (ΛCDM) model and one of its simplest extensions, featuring a constant dark energy equation of state parameter, w. Following a conservative approach, we put constraints on the total matter density parameter and the amplitude of density fluctuations, finding Ωm = 0.29 ± 0.06 and . Testing the alternative scenario, we derive w = −1.1 ± 0.2, in agreement with the ΛCDM model. These results are independent and complementary to those derived from standard cosmological probes, opening up new ways to identify the origin of potential tensions in the current cosmological paradigm.

Neutrino mass constraints beyond linear order: cosmology dependence and systematic biases

We demonstrate the impact on forecasted neutrino mass constraints of improving galaxy clustering and CMB lensing predictions from linear to next-to-leading-order power spectra. The redshift-space 1-loop power spectrum model we adopt requires an additional four free bias parameters, a velocity bias parameter and two new stochastic parameters. These additional nuisance parameters appreciably weaken the constraints on M ν . CMB lensing plays a significant role in helping to alleviate these degeneracies and tighten the final constraints. The constraint on the optical depth to reionisation τ has a strong effect on the constraint on M ν , but only when CMB lensing is included in the analysis to keep the degeneracies with the nuisance parameters under control. We also extract constraints when 1) using the BAO signature only as a distance probe, and 2) isolating the scale-dependence of the power spectrum, which, as shown in previous work, provides a cosmology-independent probe of M ν . All constraints except the latter remain strongly sensitive to the assumption of a flat ΛCDM universe. We perform an analysis of the magnitude of the shift introduced in the inferred M ν value when neglecting nonlinear corrections, and show that, for a Euclid-like survey, this shift becomes roughly equal to the 1σ constraint itself even with a conservative cut-off scale of k max = 0.1 h Mpc-1. We also perform a calculation of the approximate expected bias in neutrino mass caused by not including the next, 2-loop order and expect a shift of only about 20% of the 1σ error for k max = 0.2 h Mpc-1 in a Euclid-like survey.

Assessing non-linear models for galaxy clustering – II. Model validation and forecasts for Stage IV surveys

ABSTRACT Accurate modelling of non-linear scales in galaxy clustering will be crucial for data analysis of Stage IV galaxy surveys. A selection of competing non-linear models must be made based on validation studies. We provide a comprehensive set of forecasts of two different models for the halo redshift space power spectrum, namely the commonly applied TNS model and an effective field theory of large-scale structure (EFTofLSS) inspired model. Using simulation data and a least-χ2 analysis, we determine ranges of validity for the models. We then conduct an exploratory Fisher analysis using the full anisotropic power spectrum to investigate parameter degeneracies. We proceed to perform an MCMC analysis utilizing the monopole, quadrupole, and hexadecapole spectra, with a restricted range of scales for the latter in order to avoid biasing our growth rate, f, constraint. We find that the TNS model with a Lorentzian damping and standard Eulerian perturbative modelling outperforms other variants of the TNS model. Our MCMC analysis finds that the EFTofLSS-based model may provide tighter marginalized constraints on f at z = 0.5 and z = 1 than the TNS model, despite having additional nuisance parameters. However this depends on the range of scales used as well as the fiducial values and priors on the EFT nuisance parameters. Finally, we extend previous work to provide a consistent comparison between the Fisher matrix and MCMC forecasts using the multipole expansion formalism, and find good agreement between them.

Nuisance hardened data compression for fast likelihood-free inference

ABSTRACT We show how nuisance parameter marginalized posteriors can be inferred directly from simulations in a likelihood-free setting, without having to jointly infer the higher dimensional interesting and nuisance parameter posterior first and marginalize a posteriori. The result is that for an inference task with a given number of interesting parameters, the number of simulations required to perform likelihood-free inference can be kept (roughly) the same irrespective of the number of additional nuisances to be marginalized over. To achieve this, we introduce two extensions to the standard likelihood-free inference set-up. First, we show how nuisance parameters can be recast as latent variables and hence automatically marginalized over in the likelihood-free framework. Secondly, we derive an asymptotically optimal compression from N data to n summaries – one per interesting parameter - such that the Fisher information is (asymptotically) preserved, but the summaries are insensitive to the nuisance parameters. This means that the nuisance marginalized inference task involves learning n interesting parameters from n ‘nuisance hardened’ data summaries, regardless of the presence or number of additional nuisance parameters to be marginalized over. We validate our approach on two examples from cosmology: supernovae and weak-lensing data analyses with nuisance parametrized systematics. For the supernova problem, high-fidelity posterior inference of Ωm and w0 (marginalized over systematics) can be obtained from just a few hundred data simulations. For the weak-lensing problem, six cosmological parameters can be inferred from just $\mathcal {O}(10^3)$ simulations, irrespective of whether 10 additional nuisance parameters are included in the problem or not.

ROBUST INFERENCE IN STRUCTURAL VECTOR AUTOREGRESSIONS WITH LONG-RUN RESTRICTIONS

Long-run restrictions are a very popular method for identifying structural vector autoregressions, but they suffer from weak identification when the data is very persistent, i.e., when the highest autoregressive roots are near unity. Near unit roots introduce additional nuisance parameters and make standard weak-instrument-robust methods of inference inapplicable. We develop a method of inference that is robust to both weak identification and strong persistence. The method is based on a combination of the Anderson-Rubin test with instruments derived by filtering potentially nonstationary variables to make them near stationary using the IVX instrumentation method of Magdalinos and Phillips (2009). We apply our method to obtain robust confidence bands on impulse responses in two leading applications in the literature.

Milk protein fractions strongly affect the patterns of coagulation, curd firming, and syneresis

The aim of this study was to assess the role of milk protein fractions in the coagulation, curd firming, and syneresis of bovine milk. Analyses were performed on 1,271 individual milk samples from Brown Swiss cows reared in 85 herds classified into 4 types of farming systems, from the very traditional (tied cows, feed manually distributed, summer highland pasture) to the most modern (loose cows, use of total mixed rations with or without silage). Fractions αS1-casein (CN), αS2-CN, β-CN, κ-CN, β-lactoglobulin (LG), and α-lactalbumin (LA) and genotypes at CSN2, CSN3, and BLG were obtained by reversed-phase HPLC. The following milk coagulation properties were measured with a lactodynamograph, with the testing time extended to 60 min: rennet coagulation time (RCT, min), curd firming time (min), and curd firmness at 30 and 45 min (mm). All the curd firmness measures recorded over time (total of 240 observations/sample) were used in a 4-parameter nonlinear model to obtain parameters of coagulation, curd firming, and syneresis: RCT estimated from the equation (min), asymptotic potential curd firmness (mm), the curd firming and syneresis instant rate constants (%/min), and the maximum curd firmness value (CFmax, mm) and the time taken to reach it (min). All the aforementioned traits were analyzed with 2 linear mixed models, which tested the effects of the protein fractions expressed in different ways: in the first, quantitative model, each protein fraction was expressed as content in milk; in the second, qualitative model, each protein fraction was expressed as a percentage of total casein content. Besides proteins, additional nuisance parameters were herd (included as a random effect), daily milk production (only for the quantitative model), casein content (only for the qualitative model), dairy system, parity, days in milk, the pendulum of the lactodynamograph, and the CSN2, CSN3, and BLG genotypes. Both αS1-CN and β-CN showed a clear and favorable effect on CFmax, where the former effect was almost double the latter. Milk coagulation ability was favorably affected by κ-CN, which reduced both the RCT and RCT estimated from the equation, increased the curd firming and syneresis instant rate constants, and allowed a higher CFmax to be reached. In contrast, αS2-CN delayed gelation time and β-LG worsened curd firming, both resulting in a low CFmax. The results of this study suggest that modification of the relative contents of specific protein fractions can have an enormous effect on the technological behavior of bovine milk.

Evaluating accuracy of diagnostic tests without conditional independence assumption.

Evaluating the accuracy (ie, estimating the sensitivity and specificity) of new diagnostic tests without the presence of a gold standard is of practical meaning and has been the subject of intensive study for several decades. Existing methods use 2 or more diagnostic tests under several basic assumptions and then estimate the accuracy parameters via the maximum likelihood estimation. One of the basic assumptions is the conditional independence of the tests given the disease status. This assumption is impractical in many real applications in veterinary research. Several methods have been proposed with various dependence models to relax this assumption. However, these methods impose subjective dependence structures, which may not be practical and may introduce additional nuisance parameters. In this article, we propose a simple method for addressing this problem without the conditional independence assumption, using an empirical conditioning approach. The proposed method reduces to the popular Hui-Walter model in the case of conditional independence. Also, our likelihood function is of order-2 polynomial in parameters, while that of Hui-Walter is of order-3. The reduced model complexity increases the stability in estimation. Simulation studies are conducted to evaluate the performance of the proposed method, which shows overall smaller biases in estimation and is more stable than the existing method, especially when tests are conditionally dependent. Two real data examples are used to illustrate the proposed method.

Exploring light mediators with low-threshold direct detection experiments

We explore the potential of future cryogenic direct detection experiments to determine the properties of the mediator that communicates the interactions between dark matter and nuclei. Due to their low thresholds and large exposures, experiments like CRESST-III, SuperCDMS SNOLAB and EDELWEISS-III will have excellent capability to reconstruct mediator masses in the MeV range for a large class of models. Combining the information from several experiments further improves the parameter reconstruction, even when taking into account additional nuisance parameters related to background uncertainties and the dark matter velocity distribution. These observations may offer the intriguing possibility of studying dark matter self-interactions with direct detection experiments.

Robust Inference in Structural Vars with Long-Run Restrictions

Long-run restrictions are a very popular method for identifying structural vector autoregressions, but they suffer from weak identification when the data is very persistent, i.e., when the highest autoregressive roots are near unity. Near unit roots introduce additional nuisance parameters and make standard weak-instrument-robust methods of inference inapplicable. We develop a method of inference that is robust to both weak identification and strong persistence. The method is based on a combination of the Anderson-Rubin test with instruments derived by filtering potentially non-stationary variables to make them near stationary. We apply our method to obtain robust confidence bands on impulse responses in two leading applications in the literature.

Accurate weak lensing of standard candles. II. Measuringσ8with supernovae

Soon the number of type Ia supernova (SN) measurements should exceed 100,000. Understanding the effect of weak lensing by matter structures on the supernova brightness will then be more important than ever. Although SN lensing is usually seen as a source of systematic noise, we will show that it can be in fact turned into signal. More precisely, the non-Gaussianity introduced by lensing in the SN Hubble diagram dispersion depends rather sensitively on the amplitude sigma8 of the matter power spectrum. By exploiting this relation, we are able to predict constraints on sigma8 of 7% (3%) for a catalog of 100,000 (500,000) SNe of average magnitude error 0.12 without having to assume that such intrinsic dispersion is known a priori. The intrinsic dispersion has been assumed to be Gaussian; possible intrinsic non-Gaussianities in the dataset (due to the SN themselves and/or to other transients) could be potentially dealt with by means of additional nuisance parameters describing higher moments of the intrinsic dispersion distribution function. This method is independent of and complementary to the standard methods based on CMB, cosmic shear or cluster abundance observables.

Optimal designs under a multivariate linear model with additional nuisance parameters

The purpose of this paper is to characterize optimal designs under a multivariate linear model with additional nuisance parameters. We give relationships between optimality of designs in univariate models and in their multivariate extensions with known and partially known dispersion matrices.

Overparameterized Least-Squares Adjustment with Linear Models for Geodetic and Surveying Applications

Least-squares (LS) estimation is a standard tool for the optimal processing of geodetic and surveying observations. In many applications, additional nuisance parameters are frequently included within the LS adjustment process in order to account for unknown instrumental biases and other external disturbances that have affected the input data. Moreover, in view of the availability of more precise instruments and data sensors, the enhancement of the mathematical models with additional parameters is justified on the basis of detecting new higher-order systematic effects from the optimal inversion of progressively more accurate data sets. The objective of this paper is to expose an important trade off in the LS adjustment with linear models which are augmented with additional parameters in the presence of unknown systematic effects in the input data. In particular, a condition is derived that quantifies the necessary reduction in the data noise level which ensures the improvement in the estimation accuracy for the original model parameters, when a linear(-ized) model enhancement takes place.

Limits and confidence intervals in the presence of nuisance parameters

We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible parameter values for important classes of problems, in particular whenever there are additional nuisance parameters with statistical or systematic errors. Programs are available for calculating these intervals.

A note on a partial empirical likelihood

A partial profile empirical likelihood for a semiparametric mixture model (Zou et al., 2002) is shown to originate in a conditional likelihood involving additional nuisance parameters. The partial likelihood is the conditional likelihood with the nuisance parameters replaced by their estimators from the full likelihood. The conditional likelihood suggests alternative estimators. We demonstrate that the partial likelihood estimator is more efficient than an estimator for which the nuisance parameters are known. The practical implications of this counter-intuitive result are discussed.

Efficiency Gain from Auxiliary Data Requiring Additional Nuisance Parameters

In a mark-recapture study of an animal population, live-recapture information may be supplemented by resightings from marked animals obtained throughout the period of the study and the two types of data analyzed simultaneously. The resighting data can only contribute to estimates of survival probability if they are jointly modeled with the live-recapture data and require the inclusion of additional nuisance parameters. We show that, under quite general conditions, estimates of the original parameters are estimated with the same, or improved, precision despite the inclusion of the nuisance parameters. Banding data from female goldeneye ducks (Bucephala clangula) are used as an illustration.

On the effect of nuisance parameters on the threshold SNR value of the Barankin bound

The performance of nonlinear estimators of signal parameters in noise appears to exhibit a threshold phenomenon. Below a critical value of signal-to-noise ratio (SNR), the performance of these estimators deviates significantly from the Cramer-Rao bound. In a large-error (ambiguity-prone) SNR region, the Barankin bound has been proved to be an advantageous tool to assess the attainable performance and the threshold value. Obviously, when the estimation problem involves additional unknown nuisance parameters, the mean square error (MSE) of the estimator does not decrease. However, the impact of these nuisance parameters on the threshold value is not clear. In this correspondence, we discuss the influence of unknown nuisance parameters on the threshold value. The analysis is done for the common problem concerning estimating parameters of a Gaussian process. We confine our scope to a simplified problem concerning only two estimated parameters. However, we explain how this simplified analysis can be used to handle a more complicated problem comprising multiple nuisance parameters. We derive a sufficient condition applied to the structure of the data covariance matrix. When the condition is satisfied, then the need to estimate additional nuisance parameters does not change the threshold value. Using the proposed condition, we prove that the threshold SNR in passive source localization does not increase when the spectral parameters of the source are unknown, whereas the presence of another source at an unknown bearing may change the threshold SNR.

Association within twin pairs for a dichotomous trait.

We propose an odds-ratio measure of twin association for a dichotomous trait. This odds ratio can be estimated without arbitrarily specifying an index twin and without estimating additional nuisance parameters. Tests of association and confidence intervals may be computed easily, in contrast to those proposed previously [Donner et al. (1995) Genet Epidemiol 12:267-277] for a correlation measure of association. For testing homogeneity of association in two samples of twins, monozygotic and dizygotic, we propose a large-sample test and an exact test, both based on the odds-ratio parameterization. Large-sample tests of homogeneity are slightly anticonservative when some cell counts are small, and the exact test may be preferred in these situations. We also propose a long-linear parameterization useful for modeling more complex data sets.

Trends and random walks in macroeconomic time series: Further evidence from a new approach

This paper presents a summary of recent work on a new methodology to test for the presence of a unit root in univariate time series models. The stochastic framework is quite general. While the Dickey-Fuller approach accounts for the autocorrelation of the first-differences of a series in a parametric fashion by estimating additional nuisance parameters, this new approach deals with this phenomenon in a nonparametric way. We apply these new tests to reassess recent findings on the behavior of common macroeconomic time series, including the various series studied by Nelson and Plosser (1982).