Excess Variance Research Articles

Variance reduction in Monte Carlo for Integrals

Abstract. Nowadays, the extensive use of Monte Carlo methods in various fields has promoted the scientific decision-making, improved the efficiency of social operation, and enabled better management of many uncertain factors in daily life. However, in some cases, traditional Monte Carlo methods doesn't work so well because of the excessive variance. This paper aims to explore a new numerical integration method called splitting method to minimize intrinsic variance in Monte Carlo simulations. Through this innovative method, we found that the variance was reduced significantly. Despite some oscillating functions which are still difficult to estimate because they have too many turning points, this study provides new insights into variance reduction in Monte Carlo for integrals to optimize calculations in various fields when the modelling functions are not monotonic.

X-ray reverberation as an explanation for UV/optical variability in nearby Seyferts

Context. Active galactic nuclei (AGNs) are known to be variable across all wavelengths. Significant observational efforts have been invested in the last decade in studying their ultraviolet (UV) and optical variability. Long and densely sampled, multi-wavelength monitoring campaigns of numerous Seyfert galaxies have been conducted with the aim of determining the X-ray/UV/optical continuum time lags. Time-lag studies can be used to constrain theoretical models. The observed time lags can be explained by thermal reprocessing of the X-rays illuminating the accretion disc (known as the X-ray reverberation model). However, the observed light curves contain more information that can be used to further constrain physical models. Aims. Our primary objective is to investigate whether, in addition to time lags, the X-ray reverberation model can also explain the UV/optical variability amplitude of nearby Seyferts. Methods. We measured the excess variance of four sources (namely Mrk 509, NGC 4151, NGC 2617, and Mrk 142) as a function of wavelength using data from archival long, multi-wavelength campaigns with Swift, and ground-based telescopes. We also computed the model excess variance in the case of the X-ray reverberation model by determining the disc’s transfer function and assuming a bending power law for the X-ray power spectrum. We tested the validity of the model by comparing the measured and model variances for a range of accretion rates and X-ray source heights. Results. Our main result is that the X-ray thermal reverberation model can fit both the continuum, UV/optical time lags, as well as the variance (i.e. the variability amplitude) in these AGNs, for the same physical parameters. Our results suggest that the accretion disc is constant and that all the observed UV/optical variations, on timescales of days and up to a few weeks, can be fully explained by the variable X-rays as they illuminate the accretion disc.

Metrics of Astrometric Variability in the International Celestial Reference Frame. I. Statistical Analysis and Selection of the Most Variable Sources

Using very long baseline interferometry data for the sources that comprise the third International Celestial Reference Frame (ICRF3), we examine the quality of the formal source-position uncertainties of ICRF3 by determining the excess astrometric variability (unexplained variance) for each source as a function of time. We also quantify multiple qualitatively distinct aspects of astrometric variability seen in the data, using a variety of metrics. Average position offsets, statistical dispersion measures, and coherent trends over time as explored by smoothing the data are combined to characterize the most and least positionally stable ICRF3 sources. We find a notable dependence of the excess variance and statistical variability measures on decl., as is expected for unmodeled ionospheric delay errors and the Northern Hemisphere–dominated network geometries of most astrometric and geodetic observing campaigns.

Optical Variability Properties of Southern TESS Blazars

We present a study of high-cadence, high-precision optical light curves from the TESS satellite of 67 blazars in the southern sky. We provide descriptive flux statistics, power spectral density (PSD) model parameters, and characteristic variability timescales. We find that only 15 BL Lacertae objects (BLLs) and 18 flat spectrum radio quasars (FSRQs) from the initial 26 and 41, respectively, exhibit statistically significant variability. We employ an adapted power spectral response method to test the goodness of fit for the PSD function to three power-law variant models. From our best-fitting description of the PSD, we extract the high-frequency power-spectral slopes, and if present, determine the significant bend or break in the model to identify characteristic timescales. We find no significant difference in the excess variance or rms scatter between blazar subpopulations. We identify a linear rms–flux relation in ∼69% of our sample, in which ∼20% show a strong correlation. We find that both subpopulations of blazars show power spectral slopes of α ∼ 2 in which a broken power-law best fits five BLLs and six FSRQs and a bending power-law best fits one BLL and five FSRQs. The shortest timescales of variability in each light-curve range widely from minutes to weeks. Additionally, these objects’ characteristic timescales range from ∼0.8 to 8 days, consistent with optical variability originating in the jet.

Exponentially weighted moving average chart using zero-inflated negative binomial distribution

Zero-inflated models are frequently used to deal with data having many zeros. A commonly used model for over-dispersed data containing zeros is known as the zero-inflated Poisson model. However, to account for the heterogeneity of counts that leads to excess variance besides inflation of zeros in the data using a more flexible model than the zero-inflated Poisson model, a zero-inflated negative binomial (ZINB) is suggested. In the present study, Shewhart and exponentially weighted moving average (EWMA) control charts are suggested to monitor the ZINB data. The charts are compared using the average run length and standard deviation of run length by using extensive Monte Carlo simulations. Besides a comprehensive simulation study assuming different settings of parameters of ZINB, a real data set is used to show the practicality of the proposed charts. The results indicate that the EWMA chart is better than the Shewhart chart.

Bias and excess variance in election polling: a not-so-hidden Markov model

Abstract With historic misses in the 2016 and 2020 US Presidential elections, interest in measuring polling errors has increased. The most common method for measuring directional errors and non-sampling excess variability during a postmortem for an election is by assessing the difference between the poll result and election result for polls conducted within a few days of the day of the election. Analysing such polling error data is notoriously difficult with typical models being extremely sensitive to the time between the poll and the election. We leverage hidden Markov models traditionally used for election forecasting to flexibly capture time-varying preferences and treat the election result as a peek at the typically hidden Markovian process. Our results are much less sensitive to the choice of time window, avoid conflating shifting preferences with polling error, and are more interpretable despite a highly flexible model. We demonstrate these results with data on polls from the 2004 through 2020 US Presidential elections and 1992 through 2020 US Senate elections, concluding that previously reported estimates of bias in Presidential elections were too extreme by 10%, estimated bias in Senatorial elections was too extreme by 25%, and excess variability estimates were also too large.

XMM–Newton Ultra Narrow Deep Field survey – II. X-ray spectral analysis of the brightest AGN population

ABSTRACT In this work, we present the results of a detailed X-ray spectral analysis of the brightest active galactic nuclei (AGNs) detected in the XMM–Newton 1.75 Ms Ultra Narrow Deep Field. We analysed 23 AGNs that have a luminosity range of $\sim 10^{42} {\!-\!} 10^{46}\, \rm {erg}\, \rm {s}^{-1}$ in the $2 {\!-\!} 10\, \rm {keV}$ energy band, redshifts up to 2.66, and $\sim 10\,000$ X-ray photon counts in the $0.3{ \!-\! }10\, \rm {keV}$ energy band. Our analysis confirms the ‘Iwasawa–Taniguchi effect,’ an anticorrelation between the X-ray luminosity ($L_x$) and the Fe–k$\alpha$ equivalent width (${\rm EW}_{\rm Fe}$) possibly associated with the decreasing of the torus covering factor as the AGN luminosity increases. We investigated the relationship among black hole mass ($M_{\rm BH}$), $L_x$, and X-ray variability, quantified by the Normalized Excess Variance ($\sigma ^2_{\rm rms}$). Our analysis suggest an anticorrelation in both $M_{\rm BH} - \sigma ^2_{\rm rms}$ and $L_x- \sigma ^2_{\rm rms}$ relations. The first is described as $\sigma ^2_{\rm rms} \propto M^{-0.26 \pm 0.05}_{\rm BH}$, while the second presents a similar trend with $\sigma ^2_{\rm rms} \propto L_{x}^{-0.31 \pm 0.04}$. These results support the idea that the luminosity–variability anticorrelation is a byproduct of an intrinsic relationship between the BH mass and the X-ray variability, through the size of the emitting region. Finally, we found a strong correlation among the Eddington ratio ($\lambda _{\rm Edd}$), the hard X-ray photon index ($\Gamma$), and the illumination factor $\log (A)$, which is related to the ratio between the number of Compton scattered photons and the number of seed photons. The $\log (\lambda _{\rm Edd})-\Gamma -\log (A)$ plane could arise naturally from the connection between the accretion flow and the hot corona.

The X-ray variability of active galactic nuclei: Power spectrum and variance analysis of the Swift/BAT light curves

Aims. We study the X-ray power spectrum of active galactic nuclei (AGN) in order to investigate whether Seyfert I and II power spectra are similar or not and whether AGN variability depends on the mass and accretion rate of black holes as well as to compare the power spectra of AGN with the power spectra of Galactic X-ray black hole binaries. Method. We used 14–195 keV band light curves from the 157-month Swift/BAT hard X-ray survey, and we computed the mean power spectrum and excess variance of AGN in narrow black hole mass and AGN luminosity bins. We fitted a power-law model to the AGN power spectra, and we investigated whether the power spectrum parameters and the excess variance depend on the black hole mass, luminosity, and accretion rate of AGN. Results. We found the Seyfert I and Seyfert II power spectra to be identical, in agreement with AGN unification models. The mean AGN X-ray power spectrum has the same power-law like shape, with a slope of −1 in all AGN irrespective of their luminosity and black hole mass. We did not detect any flattening to a slope of zero at frequencies as low as 10−9 Hz. We detected an anti-correlation between the power spectral density function (PSD) amplitude and the accretion rate, similar to what has been seen in the past in the 2–10 keV band. This implies that the variability amplitude in AGN decreases with an increasing accretion rate. The universal AGN power spectrum is consistent with the mean 2–9 keV band Cyg X-1 power spectrum in its soft state. We detected a small difference in amplitude, but this is probably due to the difference in energy. Conclusions. The mean low-frequency AGN X-ray power spectrum is consistent with the extension of the mean 0.01–25 Hz Cyg X-1 power spectrum in its soft state to lower frequencies. We cannot prove that the mean AGN PSD is analogous to the mean Cyg X-1 PSD in its soft state, as we do not know the location of the high-frequency break in the hard X-ray AGN PSDs. However, if this is the case, then the accretion disc in AGN probably extends to the radius of the innermost circular stable orbit (as is probably the case with the black hole binaries in their soft state). The X-ray corona will then be located on top, illuminating the disc and producing the X-ray reflection and disc reverberation phenomena commonly observed in these objects. Furthermore, the agreement between the PSD amplitude in AGN and the Cyg X-1 (either in the soft or the hard state) over many decades in frequency indicates that the X-ray variability process is probably the same in all accreting objects, irrespective of the mass of the compact object. We plan to investigate this issue further in the near future.

An effective screening of COVID‐19 pneumonia by employing chest X‐ray segmentation and attention‐based ensembled classification

AbstractQuick and accurate diagnosis of COVID‐19 is crucial in preventing its transmission. Chest X‐ray (CXR) imaging is often used for diagnosis, however, even experienced radiologists may misinterpret the results, necessitating computer‐aided diagnosis. Deep learning has yielded favourable results previously, but overfitting, excessive variance, and generalization errors may occur due to noise and limited datasets. Ensemble learning can improve predictions by using robust techniques. Therefore, this study, proposes two‐fold strategy that combines advanced and robust algorithms, including DenseNet201, EfficientNetB7, and Xception, to achieve faster and more accurate COVID‐19 detection. Segmented lung images were generated from CXR images using the residual U‐Net model, and two attention‐based ensemble neural networks were used for classification. The COVID‐19 radiography dataset was used to evaluate the proposed approach, which achieved an accuracy of 98.21%, 93.4%, and 89.06% for two, three, and four classes respectively which outperformed previous studies by a significant margin considering COVID, viral pneumonia, and lung opacity simultaneously. Despite the similarity in CXR images of COVID, pneumonia, and lung opacity, the proposed approach achieved 89.06% accuracy, demonstrating its ability to recognize distinguishable features. The developed algorithm is expected to have applications in clinics for diagnosing different diseases using X‐ray images.

Characterising X-ray variability in light curves with complex sampling patterns: Application to the eROSITA south ecliptic pole survey

Aims : During its all-sky survey phase, the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) X-ray telescope on board the Spectrum-Roentgen-Gamma (SRG) spacecraft scans through the ecliptic poles every 4 hours. This extensive data set of long-duration, frequent, and consistent observations of thousands of X-ray sources is ideal for a detailed long-term X-ray-variability analysis. However, individual observations are short, are separated by long but consistent gaps, and have varying exposure times. Therefore, the identification of variable sources and the characterisation and quantification of their variability requires a unique methodology. We aim to develop and evaluate variability analysis methods for eROSITA observations, focusing on sources close to the survey poles. We also aim to detect intrinsically variable sources at any count rate and quantify the variability of low-count-rate sources. Methods : We simulate eROSITA-like light curves to evaluate and quantify the effect of survey mode observations on the measured periodogram and normalised excess variance. We introduce a new method for estimating the normalised intrinsic variance of a source based on the Bayesian excess variance (bexvar) method. Results : We determine thresholds for identifying likely variable sources while minimising the false-positive rate, as a function of the number of bins, and the average count rate in the light curve. The bexvar normalised intrinsic variance estimate is significantly more accurate than the normalised excess variance method in the Poisson regime. At high count rates, the two methods are comparable. We quantify the scatter in the intrinsic variance of a stationary pink-noise process, and investigate how to reduce it. Finally, we determine a description of the excess noise in a periodogram caused by varying exposure times throughout a light curve. Although most of these methods were developed specifically for analysing variable active galactic nuclei in the eROSITA all-sky survey, they can also be used for the variability analysis of other datasets from other telescopes, with slight modifications.

Constraints on the Evolution of the Ionizing Background and Ionizing Photon Mean Free Path at the End of Reionization

The variations in Lyα forest opacity observed at z > 5.3 between lines of sight to different background quasars are too strong to be caused by fluctuations in the density field alone. The leading hypothesis for the cause of this excess variance is a late, ongoing reionization process at redshifts below six. Another model proposes strong ionizing background fluctuations coupled to a short, spatially varying mean free path of ionizing photons, without explicitly invoking incomplete reionization. With recent observations suggesting a short mean free path at z ∼ 6, and a dramatic improvement in z > 5 Lyα forest data quality, we revisit this latter possibility. Here, we apply the likelihood-free inference technique of approximate Bayesian computation (ABC) to jointly constrain the hydrogen photoionization rate ΓHI and the mean free path of ionizing photons λ mfp from the effective optical depth distributions at z = 5.0–6.1 from XQR-30. We find that the observations are well-described by fluctuating mean free path models with average mean free paths that are consistent with the steep trend implied by independent measurements at z ∼ 5–6, with a concomitant rapid evolution of the photoionization rate.

A Detection of Cosmological 21 cm Emission from CHIME in Cross-correlation with eBOSS Measurements of the Lyα Forest

We report the detection of 21 cm emission at an average redshift z¯=2.3 in the cross-correlation of data from the Canadian Hydrogen Intensity Mapping Experiment (CHIME) with measurements of the Lyα forest from eBOSS. Data collected by CHIME over 88 days in the 400–500 MHz frequency band (1.8 < z < 2.5) are formed into maps of the sky and high-pass delay filtered to suppress the foreground power, corresponding to removing cosmological scales with k ∥ ≲ 0.13 Mpc−1 at the average redshift. Line-of-sight spectra to the eBOSS background quasar locations are extracted from the CHIME maps and combined with the Lyα forest flux transmission spectra to estimate the 21 cm–Lyα cross-correlation function. Fitting a simulation-derived template function to this measurement results in a 9σ detection significance. The coherent accumulation of the signal through cross-correlation is sufficient to enable a detection despite excess variance from foreground residuals ∼6–10 times brighter than the expected thermal noise level in the correlation function. These results are the highest-redshift measurement of 21 cm emission to date, and they set the stage for future 21 cm intensity mapping analyses at z > 1.8.

Comparing indirect methods for black hole masses in AGN: the good, the bad, and the ugly

ABSTRACT The black hole mass MBH is crucial in constraining the growth of supermassive black holes within their host galaxies. Since direct measurements of MBH with dynamical methods are restricted to a limited number of nearly quiescent nearby galaxies and a small minority of active galactic nuclei (AGN), we must rely on indirect methods. In this work, we utilize an unbiased, volume-limited, hard X-ray selected sample of AGN to compare the reliability of some commonly used indirect methods, emphasizing those that can be applied to obscured AGN. Based on a subsample of AGN with MBH determined via dynamical methods, our study suggests that X-ray-based techniques, such as the scaling method and the one based on the variability measured through the excess variance, are in good agreement with the dynamical methods. On the other hand, the M–σ⋆ correlation based on inactive galaxies tends to systematically overestimate MBH, regardless of the level of obscuration. We provide a correcting factor that produces an acceptable agreement with dynamical values and can be used to quickly correct the MBH computed with this method. We also derive an alternative M–σ⋆ correlation based on this unbiased sample of AGN with a slope considerably shallower than the ones obtained using inactive galaxies, suggesting that the latter may not be appropriate to compute the MBH in AGN. Finally, we find that no quick fix can be applied to correct the MBH obtained from the fundamental plane of black hole activity, casting doubts on the reliability of this method.

Rapid Optical Flares in the Blazar OJ 287 on Intraday Timescales with TESS

We have analyzed the optical light curves of the blazar OJ 287 obtained with the Transiting Exoplanet Survey Satellite over about 80 days from 2021 October 13 to December 31, with an unprecedented sampling of 2 minutes. Although significant variability has been found during the entire period, we have detected two exceptional flares with flux nearly doubling and then nearly tripling over 2 days in the middle of 2021 November. We went through the light-curve analysis using the excess variance, generalized Lomb–Scargle periodogram, and continuous autoregressive moving average methods and estimated the flux halving/doubling timescales. The most probable shortest variability timescale was found to be 0.38 days in the rising phase of the first flare. We briefly discuss some emission models for the variability in radio-loud active galactic nuclei that could be capable of producing such fast flares.

Stellar-wind variability in Cygnus X-1 from high-resolution excess variance spectroscopy with Chandra

Context. Stellar winds of massive stars are known to be driven by line absorption of UV photons, a mechanism that is prone to instabilities, causing the wind to be clumpy. The clumpy structure hampers wind mass-loss estimates, limiting our understanding of massive star evolution. The wind structure also impacts accretion in high-mass X-ray binary (HMXB) systems. Aims. We aim to analyse the wavelength-dependent variability of X-ray absorption in the wind to study its structure. Such an approach is possible in HMXBs, where the compact object serves as an X-ray backlight. We probe different parts of the wind by analysing data taken at superior and inferior conjunctions. Methods. We applied excess variance spectroscopy to study the wavelength-dependent soft (2–14 Å) X-ray variability of the HMXB Cygnus X-1 in the hard spectral state. Excess variance spectroscopy quantifies the variability of an object above the statistical noise as a function of wavelength, which allows us to study the variability of individual spectral lines. This technique was applied to high-resolution gratings spectra provided by Chandra, accounting for various systematic effects. The frequency dependence is investigated by changing the time binning. Results. The strong orbital phase dependence we observe in the excess variance is consistent with column-density variations predicted by a simple model for a clumpy wind. We identify spikes of increased variability with spectral features found by previous spectroscopic analyses of the same data set, most notably from silicon in over-dense clumps in the wind. In the silicon line region, the variability power is redistributed towards lower frequencies, hinting at increased line variability in large clumps. In prospect of the microcalorimetry missions that are scheduled to launch within the next decade, excess variance spectra present a promising approach to constraining the wind structure, especially if accompanied by models that consider changing ionisation.

BASS-XL: X-ray variability properties of unobscured active galactic nuclei

ABSTRACT We investigate the X-ray variability properties of Seyfert 1 Galaxies belonging to the BAT AGN Spectroscopic Survey (BASS). The sample includes 151 unobscured (NH &amp;lt; 1022 cm−2) AGNs observed with XMM–Newton for a total exposure time of ∼27 ms, representing the deepest variability study done so far with high signal-to-noise XMM–Newton observations, almost doubling the number of observations analysed in previous works. We constrain the relation between the normalized excess variance and the 2–10 keV AGN luminosities, black hole masses, and Eddington ratios. We find a highly significant correlation between $\sigma _{\rm NXS}^2$ and MBH , with a scatter of ∼0.85 dex. For sources with high L2–10 this correlation has a lower normalization, confirming that more luminous (higher mass) AGNs show less variability. We explored the $\sigma _{\rm NXS}^2$ versus MBH relation for the sub-sample of sources with MBH estimated via the ‘reverberation mapping’ technique, finding a tighter anticorrelation, with a scatter of ∼0.65 dex. We examine how the $\sigma _{\rm NXS}^2$ changes with energy by studying the relation between the variability in the hard (3–10 keV) and the soft (0.2–1 keV)/medium (1–3 keV) energy bands, finding that the spectral components dominating the hard energy band are more variable than the spectral components dominating in softer energy bands, on time-scales shorter than 10 ks.

Modelling of Dengue Hemorrhagic Fever Disease in Semarang City Using Generalized Poisson Regression Model

Dengue Hemorrhagic Fever (DHF) is an infectious disease that can be life- threatening within a relatively short period of time and can be fatal if not promptly treated. DHF in Indonesia ranks second as a dangerous seasonal disease. DHF remains a serious issue in the Central Java Province, particularly in Semarang City. The cases of DHF can be modeled using a Poisson regression model due to the characteristics of DHF cases, which involve count data with small occurrence probabilities. The Poisson regression model assumes equality between the mean and variance (equidispersion). However, the application of the Poisson regression model often encounters violations of the assumption of excessive variance (overdispersion), which necessitates addressing the violation, and one possible approach is to use the Generalized Poisson Regression model. Based on the analysis results, the Generalized Poisson Regression model could handle the overdispersion because the ratio of Pearson Chi-Square by degrees of freedom was 0.976, approaching a value of 1. It has also been proven to be more suitable for evaluating factors influencing the number of DHF cases, as it has a lower AIC value compared to Poisson models, with a value of 123.64. The variables that were found to have an impact on DHF cases in Semarang City based on the Generalized Poisson Regression model are the number of larval habitats (X1), the number of hospitals (X2), population density (X3), and the number of healthcare workers (X4).

Unified Workflow for the Rapid and In-Depth Characterization of Bacterial Proteomes

Bacteria are the most abundant and diverse organisms among the kingdoms of life. Due to this excessive variance, finding a unified, comprehensive, and safe workflow for quantitative bacterial proteomics is challenging. In this study, we have systematically evaluated and optimized sample preparation, mass spectrometric data acquisition, and data analysis strategies in bacterial proteomics. We investigated workflow performances on six representative species with highly different physiologic properties to mimic bacterial diversity. The best sample preparation strategy was a cell lysis protocol in 100% trifluoroacetic acid followed by an in-solution digest. Peptides were separated on a 30-min linear microflow liquid chromatography gradient and analyzed in data-independent acquisition mode. Data analysis was performed with DIA-NN using a predicted spectral library. Performance was evaluated according to the number of identified proteins, quantitative precision, throughput, costs, and biological safety. With this rapid workflow, over 40% of all encoded genes were detected per bacterial species. We demonstrated the general applicability of our workflow on a set of 23 taxonomically and physiologically diverse bacterial species. We could confidently identify over 45,000 proteins in the combined dataset, of which 30,000 have not been experimentally validated before. Our work thereby provides a valuable resource for the microbial scientific community. Finally, we grew Escherichia coli and Bacillus cereus in replicates under 12 different cultivation conditions to demonstrate the high-throughput suitability of the workflow. The proteomic workflow we present in this manuscript does not require any specialized equipment or commercial software and can be easily applied by other laboratories to support and accelerate the proteomic exploration of the bacterial kingdom.

Data weighting: An iterative process linking surveys, data synthesis, and population models to evaluate mis-specification

Integrated stock assessments specify a distribution for multiple data types, and these distributions control the relative leverage assigned to each datum. A decade of research has demonstrated that (1) proper data weighting is necessary to avoid bias resulting from overweighting noisy age- and length-composition data; (2) sampling data can be pre-processed to estimate the likely sampling variance for composition data; and (3) using random effects to estimate time-varying parameters can improve the fit to data while also changing statistical leverage, and thereby serve a similar role to reweighting data. However, there are also unresolved questions including: (A) Is it more appropriate to model age and length data as proportions-at-age and as an index for the total, or as a series of indices-at-age? (B) Are correlated residuals appropriately addressed via data weighting or do they require additional model changes (i.e., time-varying parameters)? (C) How to efficiently communicate information about sampling imprecision and model errors between sampling and stock-assessment teams? (D) How does model-based expansion of sampling data affect data weighting? and (E) How to address alternative hypotheses about factors driving poor fit to data? Here, we argue that stock assessment errors can be classified using four categories: sampling bias (e.g., changes in survey coverage), sampling imprecision (e.g., finite sample sizes), assessment model bias (e.g., incorrect demographic assumptions) and assessment model imprecision (e.g., random effects). This categorization has several implications with resulting practical recommendations. For example, we define Percent Excess Variance (PEV) from the ratio of input sample size (the measured variance of sampling imprecision) and effective sample sizes (the variance of assessment-model residuals). We propose calculating PEV as standardized diagnostic measuring the net effect of survey bias and assessment model bias and imprecision. We demonstrate PEV in a simulation experiment fitted using the Woods Hole Assessment Model (WHAM) conditioned upon Gulf of Alaska walleye pollock, where unacknowledged variation in fishery selectivity results in a PEV of 77 % and this is eliminated when correctly specifying a time-varying estimation model. We also argue that model-based expansion of data inputs using auxiliary information can mitigate sampling bias, while also measuring sampling imprecision for spatially unrepresentative surveys. Similarly, including random effects can mitigate model bias while increasing model imprecision when the demographic model has little explanatory power. Finally, we observe that down-weighting compositional data for a given fleet fails to propagate information about model residuals when interpreting abundance indices or reference points for that same fleet. When PEV is large for important fleets, we therefore encourage focused research to explain the sources of these errors rather than simply downweighting without propagating information about residuals. However, we acknowledge a continuing role for automated data weighting for less important fleets, although we recommend explicit hypotheses about potential sources of errors in those cases.

The Long-term Monitoring Results of Insight-HXMT in the First 4 yr Galactic Plane Scanning Survey

The first X-ray source catalog of the Insight-HXMT Galactic Plane (∣b∣ < 10°) Scanning Survey (GPSS) is presented based on the data accumulated from 2017 June to 2021 August. The 4 yr limit sensitivities at main energy bands can reach 8.2 × 10−12 erg s−1 cm2 (2−6 keV), 4.21 × 10−11 erg s−1 cm2 (7−40 keV), and 2.78 × 10−11 erg s−1 cm2 (25−100 keV). More than 1300 sources have been monitored at a wide band (1−100 keV), of which 223 sources have a signal-to-noise ratio greater than 5. We combined the GPSS data of Insight-HXMT and MAXI and found it feasible to obtain more complete long-term light curves from their scanning results. The flux variabilities at different energy bands of the 223 bright sources are analyzed based on the excess variances. It is found that the fluxes of X-ray binaries are more active than those of supernova remnants and isolated pulsars. Different types of binaries, e.g., low-mass X-ray binaries (LMXBs), high-mass X-ray binaries (HMXBs), neutron star binaries, and black hole binaries, also distinctively show different regularities. In addition, the relations between the hardness ratio (HR) and excess variances, and HR and source types are analyzed. It is obvious that the HRs of HMXBs tend to be harder than those of LMXBs and HMXBs tend to be more active than those of LMXBs.