Correlation Function Analysis Research Articles

Intensity correlation functions of microwave maser sources

Abstract Astrophysical sources of microwave radiation with extremely high spectral brightness are interpreted as masers. But by itself, the information about high brightness of radiation does not make it possible to establish whether the radiation is thermal or maser. This can be determined only on the basis of the analysis of high-order correlation functions. A possible measurement procedure for the second-order autocorrelation function (the bunching parameter) for these sources is proposed.

Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis.

We theoretically investigate an electric-field-driven system of charged spheres as a primitive model of concentrated electrolytes under an applied electric field. First, we provide a unified formulation for the stochastic charge and density dynamics of the electric-field-driven primitive model using the stochastic density functional theory (DFT). The stochastic DFT integrates the four frameworks (the equilibrium and dynamic DFTs, the liquid state theory and the field-theoretic approach), which allows us to justify in a unified manner various modifications previously made for the Poisson-Nernst-Planck model. Next, we consider stationary density-density and charge-charge correlation functions of the primitive model with a static electric field. We predict an electric-field-induced synchronization between emergences of density and charge oscillations. We are mainly concerned with the emergence of stripe states formed by segregation bands transverse to the external field, thereby demonstrating the following: (i) the electric-field-induced crossover occurs prior to the conventional Kirkwood crossover without an applied electric field, and (ii) the ion concentration dependence of the decay lengths at the onset of oscillations bears a similarity to the underscreening behavior found by recent simulation and theoretical studies on equilibrium electrolytes. Also, the 2D inverse Fourier transform of the correlation function illustrates the existence of stripe states beyond the electric-field-induced Kirkwood crossover.

Pinwheel valence bond crystal ground state of the spin- 12 Heisenberg antiferromagnet on the shuriken lattice

We investigate the nature of the ground-state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice by complementary state-of-the-art numerical techniques, such as variational Monte Carlo (VMC) with versatile Gutzwiller-projected Jastrow wave functions, unconstrained multi-variable variational Monte Carlo (mVMC), and pseudo-fermion/Majorana functional renormalization group (PF/PM-FRG) methods. We establish the presence of a quantum paramagnetic ground state and investigate its nature, by classifying symmetric and chiral quantum spin liquids, and inspecting their instabilities towards competing valence-bond-crystal (VBC) orders. Our VMC analysis reveals that a VBC with a pinwheel structure emerges as the lowest-energy variational ground state, and it is obtained as an instability of the U(1) Dirac spin liquid. Analogous conclusions are drawn from mVMC calculations employing accurate BCS pairing states supplemented by symmetry projectors, which confirm the presence of pinwheel VBC order by a thorough analysis of dimer-dimer correlation functions. Our work highlights the nontrivial role of quantum fluctuations via the Gutzwiller projector in resolving the subtle interplay between competing orders.

Prolonged Association between Water Molecules under Hydrophobic Nanoconfinement.

We present an investigation of the dynamics of water confined among rigid carbon rods and between parallel graphene sheets with molecular dynamics simulations. Diffusion coefficients, activation energy of diffusion, and residence-time correlation functions as a function of confinement geometry reveal a retardation of water dynamics under hydrophobic confinement compared to bulk water. In fact, water under various confinements possesses longer associations with its neighbors and exhibits diffusion dynamics characteristic of a lower temperature. Analysis of the residence-time correlation functions reveals long and short residence times, which we relate to the diffusion coefficient and activation energy of diffusion, respectively. Additional investigations reveal how the level of confining surface hydrophobicity affects water dynamics, further broadening our understanding of water diffusion inside diverse media. Overall, this study sheds light on the physical origin of retarded water dynamics under hydrophobic confinement and the close relationship between residence times and diffusion behavior.

Time Series Analysis of Evaporation Duct Height over South China Sea: A Stochastic Modeling Approach

The evaporation duct could significantly affect the work status of maritime microwave communication systems in the South China Sea. Therefore, the exact forecasting of the evaporation duct is vital for the normal operation of the systems. This study presents a stochastic modeling approach to predict the future trends of the evaporation duct over the South China Sea. The autoregressive integrated moving average (ARIMA) model has been used for modeling the monthly evaporation duct height estimated from the Climate Forecast System Reanalysis dataset released by the National Centers for Environment Prediction. The long-term evaporation duct height data were collected for a period of 10 years from 2008 to 2017. The analysis of correlation function reveals the existence of seasonality in the time series. Therefore, a seasonal ARIMA model with the form as ARIMA (0,0,1) × (0,1,2)12 is proposed by fitting the monthly data optimally. The fitted model is further used to forecast the evaporation duct variation for the year 2018 at 95% level of confidence, and high-accuracy results are obtained. Our study demonstrates the feasibility of the proposed stochastic modeling technique to predict the future variations of the evaporation duct over South China Sea.

Spatiotemporal Characterization of VIIRS Night Light

The Visible Infrared Imaging Radiometer Suite (VIIRS) Day Night Band (DNB) on board the Suomi NPP satellite now provides almost a decade of daily observations of night light. The temporal frequency of sampling, without the degree of temporal averaging of annual composites, makes it necessary to consider the distinction between apparent temporal changes of night light related to the imaging process and actual changes in the underlying sources of the night light being imaged. The most common approach to night light change detection involves direct attribution of observed changes to the phenomenon of interest. Implicit in this approach is the assumption that other forms of actual and apparent change in the light source are negligible or non-existent. An alternative approach is to characterize the spatiotemporal variability prior to deductive attribution of causation so that the attribution can be made in the context of the full range of spatial and temporal variation. The primary objective of this study is to characterize night light variability over a range of spatial and temporal scales to provide a context for interpretation of night light changes observed on both subannual and interannual time scales. This analysis is based on a combination of temporal moments, spatial correlation and Empirical Orthogonal Function (EOF) analysis. A key result of this study is the pervasive heteroskedasticity of VIIRS monthly mean night light. Specifically, the monotonic decrease of variability with increasing mean brightness. Anthropogenic night light is remarkably stable on subannual time scales while background luminance varies considerably. The variance partition from the eigenvalues of the spatiotemporal covariance matrix are 88, 2 and 2% for spatial, seasonal and interannual variance (respectively) in the most diverse region on Earth (Eurasia). Heteroskedasticity is pervasive in the monthly composites; present in all areas for all months of the year, suggesting that much, if not most, of the month-to-month variability may be related to luminance of otherwise stable sources subjected to multiple aspects of the imaging process varying in time. Given the skewed distribution of all night light arising from radial peripheral dimming of bright sources subject to atmospheric scattering, even aggregate metrics using thresholds must be interpreted in light of the fact that much larger numbers of more variable low luminance pixels may statistically overwhelm smaller numbers of stable higher luminance pixels and cause apparent changes related to the imaging process to be interpreted as actual changes in the light sources.

Responsiveness of Dichrostachys cinerea to seasonal variations in temperature and rainfall in central Namibia

Woody plants provide natural archives of climatic variation which can be investigated by applying dendroclimatological methods. Such studies are limited in Southern Africa but have great potential of improving our understanding of past climates and plant functional adaptations in the region. This study therefore investigated the responsiveness of Dichrostachys cinerea to seasonal variations in temperature and rainfall at two sites in central Namibia, Waterberg and Kuzikus. Dichrostachys cinerea is one of the encroacher species thriving well in Namibia. A moving correlation and response function analysis were used to test its responsiveness to seasonal climatic variations over time. Dichrostachys cinerea growth rings showed relationships to late summer warming, lasting up to half of the rainy season. The results also revealed that past temperatures had been fluctuating and their influence on growth rings had been intensifying over the years, but to varying extents between the two sites. Temperature was a more important determinant of ring growth at the drier site (Kuzikus), while rainfall was more important at the wetter site (Waterberg). Growth ring responsiveness to rainfall was not immediate but showed a rather lagged pattern. We conclude that D. cinerea differentially responds to variations in rainfall and temperature across short climatic gradients. This study showed that the species, due to its somewhat wide ecological amplitude, has great potential for dendroclimatological studies in tropical regions.

Non‐palimpsested crowded Skolithos ichnofabrics in a Carboniferous tidal rhythmite: Disentangling ecological signatures from the spatio‐temporal bias of outcrop

AbstractA heterolithic tidalite succession yielding spring–neap bundles is newly reported from a mid‐Carboniferous (Serpukhovian) section of the Alston Formation of Northumberland, England. The rhythmite records deposition over an interval that can be confidently calibrated to at least 84 lunar days, and attests to a non‐negligible tidal range in parts of the Northwest European Seaway in the late Mississippian. The tidalite is notable for the presence of a striking crowded Skolithos ichnofabric on both bedding planes and in vertical section. Bedding plane expressions of the ichnofabric reveal true substrates of sand piles excavated during burrow construction, in addition to an apparently remarkable equal spacing between individual burrows that is shown to be genuine through pair correlation function analysis. These characteristics show that the burrowed horizons were registered by contemporaneous ichnocoenoses, with no palimpsesting of burrows. The irregular vertical distribution of burrow horizons, despite a near‐continuous semi‐diurnal record of sedimentation, is suggested to be an artefact of spatial patchiness of burrowing communities in the depositional environment; imperfectly registered in a vertical profile with high‐temporal, low‐spatial resolution. The succession proves that burrow palimpsesting is not an inevitable ichnological conclusion of sedimentary stasis, and attests to intermittent palaeoecological fidelity of the stratigraphic record at the small spatio‐temporal scales recorded at outcrop.

Prognostic implications of ferroptosis-associated gene signature in colon adenocarcinoma.

BACKGROUNDColon adenocarcinoma (COAD) is one of the most common and fatal malignant tumors, which increases the difficulty of prognostic predictions. Thus, new biomarkers for the diagnosis and prognosis of COAD should be explored. Ferroptosis is a recently identified programmed cell death process that has the characteristics of iron-dependent lipid peroxide accumulation. However, the predictive value of ferroptosis-related genes (FRGs) for COAD still needs to be further clarified. AIMTo identify some critical FRGs and construct a COAD patient prognostic signature for clinical utilization. METHODSThe Cancer Genome Atlas database (TCGA) and Gene Expression Omnibus databases were the data sources for mRNA expression and corresponding COAD patient clinical information. Differentially expressed FRGs were recognized using R and Perl software. We constructed a multi-FRG signature of the TCGA-COAD cohort by performing a univariate Cox regression and least absolute shrinkage and selection operator Cox regression analysis. COAD patients from the Gene Expression Omnibus cohort were utilized for verification. RESULTSOur research showed that most of the FRGs (85%) were differentially expressed between the corresponding adjacent normal tissues and cancer tissues in the TCGA-COAD cohort. Seven FRGs were related to overall survival (OS) in the univariate Cox analysis (all P < 0.05). A model with five FRGs (AKR1C1, AKR1C3, ALOX12, CRYAB, and FDFT1) was constructed to divide patients into high- and low-risk groups. The OS of patients in the high-risk group was significantly lower than that of the low-risk group (all P < 0.01 in the TCGA and Gene Expression Omnibus cohorts). The risk score was an independent prognosticator of OS in the multivariate Cox analysis (hazard ratio > 1, P < 0.01). The predictive capacity of the model was verified by a receiver operating characteristic curve analysis. In addition, a nomogram based on the expression of five hub FRGs and risk score can precisely predict the OS of individual COAD cancer patients. Immune correlation analysis and functional enrichment analysis results revealed that immunology-related pathways were abundant, and the immune states of the high-risk group and the low-risk group were different.CONCLUSIONIn conclusion, a novel five FRG model can be utilized for predicting prognosis in COAD. Targeting ferroptosis may be a treatment option for COAD.

C3: Cluster Clustering Cosmology. ii. First Detection of the Baryon Acoustic Oscillations Peak in the Three-point Correlation Function of Galaxy Clusters

Abstract Third-order statistics of the cosmic density field provides a powerful cosmological probe containing synergistic information to the more commonly explored second-order statistics. Here, we exploit a spectroscopic catalog of 72,563 clusters of galaxies extracted from the Sloan Digital Sky Survey (SDSS), providing the first detection of the baryon acoustic oscillations (BAO) peak in the three-point correlation function (3PCF) of galaxy clusters. We measure and analyze both the connected and the reduced 3PCF of SDSS clusters from intermediate (r ∼ 10 Mpc h−1) up to large (r ∼ 140 Mpc h−1) scales, exploring a variety of different configurations. From the analysis of reduced 3PCF at intermediate scales, in combination with the analysis of the two-point correlation function, we constrain both the cluster linear and nonlinear bias parameters, b 1 = 2.75 ± 0.03 and b 2 = 1.2 ± 0.5. We analyze the measurements of the 3PCF at larger scales, comparing them with theoretical models. The data show clear evidence of the BAO peak in different configurations, which appears more visible in the reduced 3PCF rather than in the connected one. From the comparison between theoretical models that do or do not consider the BAO peak, we obtain a quantitative estimate of this evidence, with a Δχ 2 between 2 and 94, depending on the considered configuration. Finally, we set up a generic framework to estimate the expected signal-to-noise ratio of the BAO peak in the 3PCF, exploring different possible definitions that can be used to forecast the most favorable configurations to be explored in future surveys, and applying it to the case of the Euclid mission.

Experimental evaluation of a sound diffuse field in a ordinary room

This paper presents a methodology based on analysis of spatial correlation functions for assessing diffusivity of a sound field in reverberant and ordinary reflective rooms. A set of sound field measurements using a microphone array is performed in a room excited by a broadband signal and for many positions of loudspeakers. Each recorded signal is then broken down with a filter bank and the spatial correlation of each obtained band-limited signal is computed. Theoretical predictions of the spatial correlation function and the measured ones show very good agreement when spatial averaging and frequency conditions are met for producing a diffuse field. Evolution of the spatial correlation functions versus frequency and number of spatial averaging, i.e., number of sources positions, are examined in a reflective room. Results show that the proposed technique allows to determine the minimum number of required source positions and the actual lower frequency bound for considering that the field is diffuse. The latter is analogous to the Schroeder frequency for reverberant room. Interest of the presented methodology is its ability to experimentally assess in any reflective ordinary room the actual frequency range over which the field can be considered as diffuse. [Work funded by the AMIDEX Foundation.]

Gaudin models and multipoint conformal blocks: general theory

The construction of conformal blocks for the analysis of multipoint correlation functions with N > 4 local field insertions is an important open problem in higher dimensional conformal field theory. This is the first in a series of papers in which we address this challenge, following and extending our short announcement in [1]. According to Dolan and Osborn, conformal blocks can be determined from the set of differential eigenvalue equations that they satisfy. We construct a complete set of commuting differential operators that characterize multipoint conformal blocks for any number N of points in any dimension and for any choice of OPE channel through the relation with Gaudin integrable models we uncovered in [1]. For 5-point conformal blocks, there exist five such operators which are worked out smoothly in the dimension d.

Strategy of multiple selection indices for discrimination of potential genotypes and associated traits for yield improvement in pearl millet [Pennisetum glaucum (L.) R.Br.

A study was conducted with 31 genotypes of pearl millet to identify the potential through correlation, path analysis and discriminant function analysis for yield and yield attributing traits at the Department of Millets, Tamil Nadu Agricultural University, Coimbatore during Kharif 2019. The top ranking genotypes for single plant yield was Cumbu 2, Kizikuppam local, PT6706, PT6582 and PT6581. High PCV and GCV were recorded for harvest index, single plant yield, biological yield, thousand grain weight, the number of productive tillers and total grains per panicle. The path coefficient analysis revealed that harvest index, biological yield, panicle length and flag leaf length showed a positive high direct effect on grain yield per plant, which can be utilized for the formulation of selection indices. The discriminant function analysis revealed that the maximum genetic gain for grain yield per plant can be obtained by selecting the traits like leaf sheath length, leaf length, flag leaf length, flag leaf width, the number of nodes, panicle length, the number of productive tillers, thousand grain weight, biological yield, harvest index and single plant yield in combination when path direct effect was used as economic weights. Selection criterion score values showed that the genotypes such as Cumbu 2, Kizikuppam local, Nattu Cumbu, PT6705, PT6580, PT6706, Cumbu 1 and PT6067 have outperformed others and can be utilized for further breeding programmes. Key words: Genetic variability, Path correlation, Discriminant function, Selection index, Pearl millet

Incipient Surge Analysis in Time and Frequency Domain for Centrifugal Compressors

Abstract The use of centrifugal compressors has been increasing tremendously in the last decade as they are a key component in the present energy scenario both in the modern internal combustion engine design and in advanced cycles and innovative plant layouts as fuel cell systems. Instability phenomena limit the operating range of the whole compressor system, especially during fast transients. The target is therefore to extend the minimum flow limit in order to improve the operability of each unit while avoiding compressor surge operation and guaranteeing safe operation. For this reason, it is necessary to develop a monitoring system capable of preventing surge and extending the operating range of these machines, their performance, and reliability to allow the integration with the other plant components. The experimental investigation carried out at the University of Genoa turbocharger test facility and presented in this work, consists of steady-state and transient measurements used to characterize and identify compressor behavior in correspondence of surge inception conditions to determine different techniques which could represent surge precursors. The data analysis concentrates on pressure and vibro-acoustic signals by applying different signal processing techniques in the time and frequency domain to classify compressor operation as stable or unstable. The cross correlation function and wavelet analysis have been identified as techniques to define a precursor able to detect incipient surge conditions. Through cross correlation function analysis, it has been possible to identify the presence of propagation phenomena in the system and to evaluate how these events become more significant near an unstable low-mass flow rate condition. At low mass flow rate condition, spikes of significant amplitude are well detectable in the cross correlation function indicating the rise of significant random content in the system responses associated with the rise of incipient surge condition. Additionally, the continuous wavelet transform has been applied to operational signals to show how their time-dependent spectral structure responses can highlight the rise of unstable phenomena, not easily identifiable with traditional signal processing techniques. Exploiting its features in terms of good frequency and time resolution allowed us to identify different contents in system responses regarding phenomena that take place close to surge line and were able to detect their nature in conditions very close to deep surge ones (e.g., rotating stall with its intermitting characteristic nature). Moreover, system response was studied in high frequency range and through a demodulation technique, it was found how blade passes frequency energy content change interacting with rotating stall inception, moving close to surge line. The obtained results provide an interesting diagnostic and predictive solution to detect compressor instabilities at low mass flow rate operating conditions and to prevent compressor fails.

Higher-order spin-hole correlations around a localized charge impurity

Analysis of higher-order correlation functions has become a powerful tool for investigating interacting many-body systems in quantum simulators, such as quantum gas microscopes. Experimental measurements of mixed spin-charge correlation functions in the 2D Hubbard have been used to study equilibrium properties of magnetic polarons and to identify coherent and incoherent regimes of their dynamics. In this paper we consider theoretically an extension of this technique to systems which use a pinning potential to reduce the mobility of a single dopant in the Mott insulating regime of the 2D Hubbard model. We find that localization of the dopant has a dramatic effect on its magnetic dressing. The connected third-order spin correlations are weakened in the case of a mobile hole but strengthened near an immobile hole. In the case of the fifth-order correlation function, we find that its bare value has opposite signs in cases of the mobile and of fully pinned dopant, whereas the connected part is similar for both cases. We study suppression of higher-order correlators by thermal fluctuations and demonstrate that they can be observed up to temperatures comparable to the spin-exchange energy $J$. We discuss implications of our results for understanding the interplay of spin and charge in doped Mott insulators.

Interannual variability of chlorophyll-a and impact of extreme climatic events in the South Eastern Arabian Sea

South Eastern Arabian Sea (SEAS) is an upwelling dominated region, where the distribution of chlorophyll-a (Chl-a) is mainly controlled by basin-scale to mesoscale processes associated with seasonal reversal of winds and currents. The analysis of long-term satellite-derived Chl-a data revealed interannual variability in association with extreme climatic events. Chl-a data were obtained from Ocean Colour Climate Change Initiative (OC-CCI) which provides high resolution cloud free data for the Arabian Sea during summer monsoon season (June to September). Satellite measurements of Sea Level Anomaly (SLA), Sea Surface Temperature (SST) and sea surface wind data were also compiled from various sources. The monthly data for the above environmental variables during 1998 to 2016 were analysed as representatives of the possible causative physical processes influencing the variability in Chl-a. The time series and Hovmöller analyses shows that the maximum variability occurred during summer monsoon. This study shows that the interannual variability in Chl-a was prominently influenced by the underlying processes involved in coastal upwelling. The relative variability in Chl-a and associated environmental variables with these events was remarkable during strong El Niño-Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) events. Cross Correlation Function (CCF) analysis points out that Chl-a content is negatively correlated with IOD to an extent of one month lag or less whereas, ENSO does not indicate such direct relations. Further, the variability associated with IOD was more conspicuous than ENSO. The study elucidates the interannual variability of Chl-a and the overall influence of associated extreme events in the SEAS.

Quantifying Nanoparticle Ordering Induced by Polymer Crystallization.

It has recently been established that polymer crystallization can preferentially place nanoparticles (NPs) into the amorphous domains of a lamellar semicrystalline morphology. The phenomenology of this process is clear: when the time for NP diffusion is shorter than the crystal growth time, then the NPs are rejected by the growing crystals and placed in the amorphous domains. However, since there is no quantitative characterization of this ordered NP state, we develop a correlation function analysis for small-angle X-ray scattering data, inspired by classical methods used for enunciating the local morphology of lamellar semicrystalline polymers. We show that when the spherulitic growth rate is slower than NP diffusion, then all the NPs are expelled from the crystals. As we increase the crystallization temperature, Tc, the long period characterizing the periodically repeating crystal-amorphous polymer structure, rcc, increases. This results in a smaller number of amorphous domains per unit volume-the number of NPs per amorphous domain thus increases. While the scattering contrast between the pure silica and the polymer is constant, these arguments predict that the apparent contrast between the NP-rich and the polymer-rich domains scale linearly with rcc, as we confirm from our experiments. These facts allow us to posit that the NPs become more efficiently packed in the interlamellar zone with increasing Tc until they form a fully filled monolayer. Above this temperature, NP multilayers form within each of the NP-rich domains. Our analysis approach, therefore, describes NP ordering that is achieved when driven by polymer crystallization.

Theoretical analysis of Hanbury Brown and Twiss interferometry at soft-x-ray free-electron lasers

In this work we provide theoretical background for the analysis of second-order correlation functions in experiments performed at the soft x-ray free-electron lasers (XFELs). Typically, soft x-ray beamlines at XFELs are equipped by the variable line spacing (VLS) monochromators. We perform examination of the beam propagation through such VLS monochromator taking specially into account the interplay between the finite monochromator resolution and the exit slits width. We then provide general analysis of the second-order correlation intensities in spectral and spatial domains. Finally, we connect these functions with the statistical properties of the beam incoming to the monochromator unit in the limit of Gaussian Schell-model pulses.

Climate Response in Tree-Rings of Sawara Cypress [Chamaecyparis pisifera (Siebold &amp; Zucc.) Endl.] in Poland

Sawara cypress [Chamaecyparis pisifera (Siebold &amp; Zucc.) Endl.] is originally from Japan. It was introduced to Europe in the latter half of the 19th century (in England and Holland in 1861, and in Poland in 1864). The aim of this study was to examine the influence of climatic conditions on tree-ring width among Sawara cypress populations growing in Poland. Additionally, other indicators determining the growth-climate relationship for the studied tree species were investigated such as false rings, missing rings, or frost rings. Five stands of Sawara cypress from northwestern and central Poland were selected for study. Samples were taken from 97 trees, using Pressler borers at breast-height. Tree-ring widths were measured down to 0.01 mm. Climatic data came from weather stations located the nearest to the study plots. Tree-ring width in the studied populations of Sawara cypress varies (from 1.94 to 4.47 mm). The oldest Sawara cypresses grow in Glinna Arboretum and are nearly 130 years old. The youngest ones grow in Rogów Arboretum (67 years old) and Wirty Arboretum (58 years old). Ten regional pointer years, including six negative and four positive ones, were determined for local chronologies. Negative pointer years were associated with the occurrence of cold winters and water shortages in summer. Positive pointer years are mostly periods with a warm winter season, early and warm spring, and with high precipitation totals during summer months. Correlation and response function analysis corroborates the results yielded by pointer year analysis. False rings carry an additional information on pluvial conditions in the summer period, and frost rings are an aid in dating dendrochronological series and indicate the occurrence of both very cold winters and persistent ground frost occurrences in the spring period. In comparison to native conifers, the Sawara cypress can be regarded as a fast-growing species. The knowledge of acclimatization, growth rate, and growth-climate relationship may be useful, especially in the time of a rapidly changing climate, increasing human impact, and highly intensified invasion of insect and fungal species attacking native forest-forming taxa.

On the accuracy and precision of correlation functions and field-level inference in cosmology

ABSTRACT We present a comparative study of the accuracy and precision of correlation function methods and full-field inference in cosmological data analysis. To do so, we examine a Bayesian hierarchical model that predicts lognormal (LN) fields and their two-point correlation function. Although a simplified analytic model, the LN model produces fields that share many of the essential characteristics of the present-day non-Gaussian cosmological density fields. We use three different statistical techniques: (i) a standard likelihood-based analysis of the two-point correlation function; (ii) a likelihood-free (simulation-based) analysis of the two-point correlation function; (iii) a field-level analysis, made possible by the more sophisticated data assimilation technique. We find that (a) standard assumptions made to write down a likelihood for correlation functions can cause significant biases, a problem that is alleviated with simulation-based inference; and (b) analysing the entire field offers considerable advantages over correlation functions, through higher accuracy, higher precision, or both. The gains depend on the degree of non-Gaussianity, but in all cases, including for weak non-Gaussianity, the advantage of analysing the full field is substantial.