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Michael Stein

Publications and source records attributed to Michael Stein.

At least 19 recordsLinked to original sources

User Involvement in Robotic Wheelchair Development: A Decade of Limited Progress

Robotic wheelchairs (RWs) offer significant potential to enhance autonomy and participation for people with mobility impairments, yet many systems have failed to achieve sustained real-world adoption. This narrative literature review examined the extent and quality of end-user involvement in RW design, development, and evaluation over the past decade (2015--2025), assessed against core principles shared by major user-involvement approaches (e.g., user-/human-centered design, participatory/co-design, and inclusive design). The findings indicate that user involvement remains limited and is predominantly concentrated in late-stage evaluation rather than in early requirements definition or iterative co-design. Of the 399 records screened, only 23 studies (about 6%) met the inclusion criteria of verifiable end-user involvement, and many relied on small samples, often around ten participants, with limited justification for sample size selection, proxy users, laboratory-based validation, and non-standardized feedback methods. Research teams were largely engineering-dominated (about 89%) and geographically concentrated in high-income countries. Despite strong evidence that sustained user engagement improves usability and adoption in assistive technology, its systematic implementation in RW research remains rare. Advancing the field requires embedding participatory methodologies throughout the design lifecycle and addressing systemic barriers that constrain meaningful user involvement.

cs.HC

CHANG-ES. XXXVIII. A Thin Radio Halo Shaped by Slow Cosmic-Ray Transport in the Quiescent Galaxy NGC 4565

We present the VLA C-array S-band (2--4 GHz) radio continuum observations of the nearby edge-on spiral galaxy NGC 4565, a target from the Continuum Halos in Nearby Galaxies - an EVLA (CHANG-ES) Survey. We conduct rotation measure synthesis to probe the magnetic field structure and analyze the vertical radio continuum intensity profiles using the 1-D cosmic ray transportation models. The radio continuum emission of NGC 4565 is vertically compact, with a vertical-to-radial extent ratio of $\sim 1/6$. Its vertical profile is optimally described by a two-component Gaussian distribution, yielding a mean Gaussian halo scale height of $\sim 3.0$ kpc. The magnetic field is weak, predominantly disk-parallel, with an equipartition strength of $\lesssim 5\ \mu$G and a rotation measure profile indicative of an axisymmetric spiral structure. Nevertheless, we identify a localized, faint vertical magnetic field component in the northeastern region, hinting at an X-shaped structure that spatially coincides with extraplanar structures detected in H I and soft X-ray emission. The CR transport modeling favors a flux-tube advection scenario, with a slow initial velocity of $v_0 \approx 60$ km s$^{-1}$, consistent with a limited energy input from star formation. Therefore, the absence of an extended radio halo can be explained by the low star formation rate, the weak magnetic field, and the inefficient CR transport. The localized X-shaped field may trace a weak, magnetically guided outflow or a tidal perturbation induced by the nearby companion. NGC 4565 is thus a key quiescent benchmark for understanding the physical conditions required to drive large-scale outflows and generate extended radio halos.

astro-ph.GA

MEDUSA I. Tracing magnetic field structures in tidal arms of the dwarf-dwarf merger NGC 1487

Dwarf galaxies are important laboratories for studying cosmic magnetism because they can maintain strong magnetic fields via the action of turbulent dynamo despite their low mass and weak gravitational potential. The Magnetic-field Evolution in Dwarf galaxies from Ultra-deep SKA Analysis (MEDUSA) survey is the first SKA-pathfinder programme designed to obtain deep continuum, polarisation, and HI data for dwarf galaxies, enabling a comprehensive study of their radio spectra, magnetic fields, and gas kinematics across a representative population. By analysing the radio continuum spectra and polarisation of the dwarf-dwarf galaxy merger NGC 1487 from the MEDUSA sample, we aim to determine its magnetic field strength and to characterise the large-scale and turbulent components of its magnetic field. We utilise highly sensitive multi-band radio continuum data from MeerKAT L-band (1.28 GHz) and Australia Telescope Compact Array (ATCA) L/S (2.1 GHz), C (5.5 GHz), and X-bands (9 GHz). We analysed the magnetic field configuration using polarisation and rotation measure (RM) synthesis. The integrated spectral energy distribution has a non-thermal spectral index of $\alpha_{\rm nth} = -0.678\pm0.085$. Synchrotron and inverse Compton losses cause a spectral break at $\nu_{\rm b} = 6.2\pm1.3$ GHz. In star-forming regions, the magnetic field exhibits strong small-scale fluctuations in RM, suggesting the action of a small-scale dynamo. Conversely, the field becomes more ordered, aligning with the tidal arms toward the galaxy's outskirts, showing a large-scale magnetic field over $\approx3$ kpc. Observations of the dwarf-dwarf merger NGC 1487 show that even low-mass galaxy mergers, likely the building blocks of larger galaxies in the early Universe, can rapidly amplify and produce coherent large-scale magnetic field structures, highlighting their key contribution in the early magnetisation of galaxies.

astro-ph.GA

CHILLING: Continuum Halos in LVHIS Local Irregular Nearby Galaxies - Radio continuum spectral behavior of dwarf galaxies

Dwarf galaxies, due to their shallow gravitational potentials, provide critical environments for studying feedback mechanisms from star formation and its impacts on dwarf galaxy evolution. In particular, radio continuum (RC) observations offer valuable insights into cosmic ray dynamics, which play a significant role in shaping these processes. This study investigates the detectability and spectral characteristics of RC emission in a sample of 15 dwarf galaxies (11 gas-rich, star forming dwarfs and 4 blue compact dwarfs) spanning a broad range of stellar masses and star formation histories. Using multi-band RC data (L/S-, C-, and X-band) from the Australia Telescope Compact Array, we analyse the physical conditions responsible for RC emission and explore the dominant emission mechanisms within these systems. RC emission is detected in 11 out of the 15 galaxies. Our results indicate that RC emission correlates strongly with star formation rate, far-infrared, and stellar mass, while dynamic parameters such as HI and rotational velocity exhibit no significant correlation with RC detectability. Spectral analysis reveals that the RC spectral energy distribution in these galaxies frequently deviate from a simple power-law behavior, instead displaying curvature that suggests more complex underlying physical processes. Statistical model comparison confirms that a single power-law model is inadequate to capture the observed spectral shapes, emphasising the necessity of more sophisticated approaches. Additionally, the observed radio-far-infrared correlation indicates that cosmic ray electrons in lower-mass dwarf galaxies cool more rapidly than they can escape (e.g. via galactic winds), resulting in a measurable RC deficit.

astro-ph.GA

Stellar tidal streams around nearby spiral galaxies with deep imaging from amateur telescopes

Tidal interactions between massive galaxies and their satellites are fundamental processes in a Universe with L-Cold Dark Matter cosmology, redistributing material into faint features that preserve records of past galactic interactions. While stellar streams in the Local Group impressively demonstrate satellite disruption, they do not constitute a statistically significant sample. Constructing a substantial catalog of stellar streams beyond the Local Group remains challenging due to the difficulties in obtaining deep, wide-field images of galaxies. Despite their potential to illuminate dark matter distribution and galaxy formation processes, stellar streams remain underutilized as cosmological probes. The Stellar Tidal Stream Survey (STSS) addresses this observational gap by leveraging amateur telescopes to obtain deep, scientific-grade images of galactic outskirts, capable of building a more statistically meaningful sample of stellar streams. Over the last decade, the STSS has acquired deep (up to surface brightness limit 28.3 mag/arcsec^2 in the r-band), wide-field images of 15 nearby Milky Way analog galaxies using a network of robotic amateur telescopes, avoiding the issues associated with "mosaicing" smaller images taken with a professional telescope. Our survey has revealed a diverse range of previously unreported faint features related to dwarf satellite accretion - including stellar streams, shells, and umbrella-like structures. We discover an ultra-diffuse galaxy (NGC150-UDG1), which shows hints of tidal tails. The STSS demonstrates the suitability of modern amateur telescopes to detect and study faint, diffuse structures in large fields around nearby spiral galaxies. Their economic and accessibility advantages enable larger samples with deep imaging, essential for testing galaxy formation models and constraining the properties of minor merger events in the local Universe.

astro-ph.GA

Exploring magnetised galactic outflows in starburst dwarf galaxies NGC 3125 and IC 4662

The study of radio emission in starburst dwarf galaxies provides a unique opportunity to investigate the mechanisms responsible for the amplification and transport of magnetic fields. Local dwarfs are often considered proxies for early-Universe galaxies, so this study may provide insights into the role of non-thermal components in the formation and evolution of larger galaxies. By investigating the radio continuum spectra and maps of the starburst dwarf galaxies, we aim to draw conclusions on their magnetic field strengths and configurations, as well as the dynamics of cosmic ray (CR) transport. We perform a radio continuum polarimetry study of two of the brightest starburst IRAS Revised Bright Galaxy Sample (RBGS) dwarf galaxies, NGC 3125 and IC 4662. By combining data of the Australian Telescope Compact Array (2.1 GHz) and MeerKAT (1.28 GHz), we analyse the underlying emission mechanism and the CR transport in these systems. We find flat spectra in those dwarf galaxies over the entire investigated frequency range, which sharply contrasts with observations of massive spiral galaxies. Because the expected cooling time of CR electrons is much shorter than their escape time, we would expect a steepened steady-state CR electron spectrum. The flat observed spectra suggest a substantial contribution from free-free emission at high frequencies and absorption at low frequencies, which may solve this puzzle. For NGC 3125, we measure a degree of polarisation between 0.75% and 2.6%, implying a turbulent field and supporting the picture of a comparably large thermal emission component that could be sourced by stellar radiation feedback and supernovae.

astro-ph.GA

CHANG-ES XXXV: Cosmic Ray Transport and Magnetic Field Structure of NGC 3556 at 3 GHz

Radio halos of edge-on galaxies are crucial for investigating cosmic ray propagation and magnetic field structures in galactic environments. We present VLA C-configuration S-band (2--4 GHz) observations of the spiral galaxy NGC 3556, a target from the Continuum Halos in Nearby Galaxies - an EVLA Survey (CHANG-ES). We estimate the thermal contribution to the radio emission from a combination of the H$\alpha$ and mid-IR data, and employ Rotation Measure Synthesis to reveal the magnetic field structures. In our data, NGC 3556 exhibits a box-like radio halo extending nearly 7 kpc from the galactic plane. The scale height of the total S-band intensity in the halo is $1.68\pm 0.29$ kpc, while that of the non-thermal intensity is $1.93\pm 0.28$ kpc. Fitting the data to a 1-D cosmic-ray transport model, we find advection to describe the cosmic-ray propagation within the halo better than diffusion, with advection speeds of $245 \pm 15$ km s$^{-1}$ and $205 \pm 25$ km s$^{-1}$ above and below the disk, respectively. The magnetic field is detected patchily across the galaxy, displaying a toroidal configuration in the rotation measure map. The mean equipartition magnetic field strength is approximately $8.3\ \mu$G in the disk and $4.5\ \mu$G in the halo. In addition, a bubble-like structure extends nearly 3~kpc into the southern halo, aligned with the polarized intensity and H$\alpha$ image, suggestive of superwinds generated by recent star formation feedback in the nuclear region.

astro-ph.GA

DeepMIDE: A Multi-Output Spatio-Temporal Method for Ultra-Scale Offshore Wind Energy Forecasting

To unlock access to stronger winds, the offshore wind industry is advancing towards significantly larger and taller wind turbines. This massive upscaling motivates a departure from wind forecasting methods that traditionally focused on a single representative height. To fill this gap, we propose DeepMIDE--a statistical deep learning method which jointly models the offshore wind speeds across space, time, and height. DeepMIDE is formulated as a multi-output integro-difference equation model with a multivariate nonstationary kernel characterized by a set of advection vectors that encode the physics of wind field formation and propagation. Embedded within DeepMIDE, an advanced deep learning architecture learns these advection vectors from high-dimensional streams of exogenous weather information, which, along with other parameters, are plugged back into the statistical model for probabilistic multi-height space-time forecasting. Tested on real-world data from offshore wind energy areas in the Northeastern United States, the wind speed and power forecasts from DeepMIDE are shown to outperform those from prevalent time series, spatio-temporal, and deep learning methods.

cs.LG

CHANG-ES XXXII: Spatially Resolved Thermal/Nonthermal Separation from Radio Data Alone -- New Probes into NGC 3044 and NGC 5775

We have carried out spatially resolved thermal/nonthermal separation on two edge-on galaxies, NGC~3044 and NGC~5775, using only radio data. Narrow-band imaging within a frequency band that is almost contiguous from 1.25 to 7.02 GHz (L-band, S-band and C-band) has allowed us to fit spectra and construct thermal, nonthermal, and nonthermal spectral index maps. This method does not require any ancillary H$\alpha$ and infrared data, or reliance on dust corrections that are challenging in edge-on galaxies. For NGC~3044, at 15 arcsec resolution, we find a median thermal fraction of $\sim\, 13$\% with an estimated uncertainty in this fraction of $\sim\, 50$\% at 4.13 GHz. This compares well with the H$\alpha$ mixture method results. We uncovered evidence for a vertical outflow feature reaching at least $z\,\sim\,3.5$ kpc in projection above the plane, reminiscent of M82's starburst wind. For the higher SFR galaxy, NGC~5775 at 12 arcsec resolution, we find a median thermal fraction of 44\% at 4.13 GHz with an estimated error on this fraction of 17\%. Both galaxies show a change of slope (flattening) in L-band. These results suggest that a radio-only method for separating thermal from nonthermal emission is not only feasible, but able to reveal new features that might otherwise be obscured in edge-on disks.

astro-ph.GA

Tracing satellite planes in the Sculptor group: II. Discovery of five faint dwarf galaxies in the DESI Legacy Survey

Although substantial progress has been made in reconciling LCDM simulations with the observed abundance and distribution of satellite galaxies, important tensions persist. Studying satellite systems around spiral galaxies thus remains key in addressing these tensions. In this series of papers we report the first results of an on-going systematic survey of faint dwarf spheroidal galaxies in the vicinity of the bright late-type spiral NGC 253 galaxy, the brightest member of the Sculptor filament located at a distance of 3.7 Mpc. We performed a new NGC 253 satellite search by means of visual inspection using co-added image cutouts reprocessed in the DESI Legacy image surveys, reaching a very low surface brightness regime (28.0--29.0 mag arcsec-2). Five new dwarf galaxy candidates have been discovered in the vicinity of NGC 253, that we named them Do V, Do VI, Do VII, Do VIII and Do IX. Assuming they are associated to NGC 253, their total absolute V-magnitudes fall in the -7 to -9 mag range, which is typical for dwarf satellites in the local Universe. The central surface brightness tend to be extremely low for all the discovered dwarfs and fall roughly in the range of 25--26 mag arcsec-2 in g-band. We present a new list of galaxies located around the giant spiral NGC 253. With the inclusion of these additional satellite candidates, the overall spatial distribution of the system becomes less flattened and is now broadly consistent with analogs drawn from Lambda-CDM expectations. Interestingly, the distribution appears to be rather lopsided. Yet, firm conclusions on the presence of absence of a correlated satellite structure are hampered since distance information is lacking, the census of observed dwarfs in the system remains far from complete, and spectroscopic velocities are not even available for most known satellites.

astro-ph.GA

Tracking before detection using partial orders and optimization

This article addresses the problem of multi-object tracking by using a non-deterministic model of target behaviors with hard constraints. To capture the evolution of target features as well as their locations, we permit objects to lie in a general topological target configuration space, rather than a Euclidean space. We obtain tracker performance bounds based on sample rates, and derive a flexible, agnostic tracking algorithm. We demonstrate our algorithm on two scenarios involving laboratory and field data.

math.DS

Stellar Population Properties in the Stellar Streams Around SPRC047

We have investigated the properties (e.g., age, metallicity) of the stellar populations of a ring-like tidal stellar stream (or streams) around the edge-on galaxy SPRC047 (z = 0.031) using spectral energy distribution (SED) fits to integrated broad-band aperture flux densities. We used visual images in six different bands and Spitzer/IRAC 3.6 micron data. We have attempted to derive best-fit stellar population parameters (metallicity, age) in three non-contiguous segments of the stream. Due to the very low surface brightness of the stream, we have performed a deconvolution with a Richardson-Lucy type algorithm of the low spatial resolution 3.6 micron IRAC image, thereby reducing the effect of the point-spread-function (PSF) aliased "emission" from the bright edge-on central galaxy at the locations of our three stream segments. Our SED fits that used several different star formation history priors, from an exponentially decaying star formation burst to continuous star formation, indicate that the age-metallicity-dust degeneracy is not resolved, most likely because of inadequate wavelength coverage and low signal-to-noise ratios of the low surface brightness features. We also discuss how future deep visual-near-infrared observations, combined with absolute flux calibration uncertainties at or below the 1 per cent level, complemented by equally well absolute flux calibrated observations in ultraviolet and mid-infrared bands, would improve the accuracy of broad-band SED fitting results for low surface brightness targets, such as stellar streams around nearby galaxies that are not resolved into stars.

astro-ph.GA

eDIG-CHANGES I: Extended Hα Emission from the Extraplanar Diffuse Ionized Gas (eDIG) around CHANG-ES Galaxies

The extraplanar diffuse ionized gas (eDIG) represents the cool/warm ionized gas reservoir around galaxies. We present a spatial analysis of H$α$ images of 22 nearby edge-on spiral galaxies from the CHANG-ES sample (the eDIG-CHANGES project), taken with the APO 3.5m telescope, in order to study their eDIG. We conduct an exponential fit to the vertical intensity profiles of the sample galaxies, of which 16 can be decomposed into a thin disk plus an extended thick disk component. The median value of the scale height (h) of the extended component is $1.13\pm 0.14$ kpc. We find a tight sublinear correlation between h and the SFR. Moreover, the offset of individual galaxies from the best-fit SFR-h relation shows significant anti-correlation with SFR_SD. This indicates that galaxies with more intense star formation tend to have disproportionately extended eDIG. Combined with data from the literature, we find that the correlations between the eDIG properties and the galaxies' properties extend to broader ranges. We further compare the vertical extension of the eDIG to multi-wavelength measurements of other CGM phases. We find the eDIG to be slightly more extended than the neutral gas (HI 21-cm line), indicating the existence of some extended ionizing sources. Most galaxies have an X-ray scale height smaller than the h, suggesting that the majority of the X-ray emission detected in shallow observations are actually from the thick disk. The h is comparable to the L-band radio continuum scale height, both slightly larger than that at higher frequencies (C-band), where the cooling is stronger and the thermal contribution may be larger. The comparable H$α$ and L-band scale height indicates that the thermal and non-thermal electrons have similar spatial distributions. This further indicates that the thermal gas, the cosmics rays, and the magnetic field may be close to energy equipartition.

astro-ph.GA

Multi-epoch variability of AT 2000ch (SN 2000ch) in NGC 3432 -- A radio continuum and optical study

AT 2000ch is a highly variable massive star and supernova imposter in NGC 3432 first detected in 2000. It is similar and often compared to SN 2009ip, and it is therefore expected to undergo a core-collapse supernova -- a SN imposter of similar brightness -- in the near future. We characterize the long-term variability of AT 2000ch in the radio and optical regimes with archival data reaching back to the year 1984. We use these newly reduced observations in addition to observations in the literature to restrict the mass-loss rates of AT 2000ch at multiple epochs based on different approaches, and to infer the general properties of its circumstellar nebula with respect to the detected radio brightness. We extend the known optical light curve of AT 2000ch up to the beginning of 2022 by performing point spread function photometry on archival data from the Palomar Transient Factory and the Zwicky Transient Facility. We reduced archival radio continuum observations obtained with the Very Large Array using standard calibration and imaging methods and complemented these with pre-reduced \changes observations as well as observations obtained with the Westerbork Synthesis Radio Telescope and LOw Frequency ARray. For the analysis of AT 2000ch, we consider the optical light curve and color evolution, its radio continuum brightness at different frequencies and times, and the corresponding spectral indices. We estimated mass-loss rates and optical depths based on radio continuum brightnesses and Ha fluxes. We report two newly detected outbursts of AT 2000ch similar to those found in the 2000s and 13 re-brightening events, of which at least four are not conclusively detected because of insufficient sampling of the light curve. The dates of all outbursts and significant, well-sampled re-brightening events are consistent with a period of $\sim 201 \pm 12\,$days over a total time-span of two decades. Such a behavior has never been found for any SN imposter, especially not for candidate SN~2009ip analogs. During 2010 to 2012 and 2014 to 2018, we only have a few detections, which is insufficient to come to any conclusion as to a possible less eruptive phase of the transient. We find steady dimming after the most recent re-brightening events and possible evidence of porosity in the circumstellar envelope, suggesting AT~2000ch may currently be in transition to a state of relative calm. We identified a second, unrelated source at a projected distance of $\sim 23\,$pc ($\sim0.5^{\prime\prime}$) that has contaminated the optical measurements of AT~2000ch at its minimum luminosity over the last two decades probably on a $5\%-10\,\%$ level, but this does not affect our overall findings and is negligible during re-brightening. We are able to restrict the mass-loss rate of AT~2000ch to range between several $10^{-6}\,\textrm{M}_{\odot}/\textrm{yr}$ and several $10^{-5}\,\textrm{M}_{\odot}/\textrm{yr}$. The fresh ejecta appear to be optically thick to radio continuum emission at least within the first $\sim 25\,$days after significant re-brightening.

astro-ph.SR

A Systematic Approach to Constructing Families of Incremental Topology Control Algorithms Using Graph Transformation

In the communication systems domain, constructing and maintaining network topologies via topology control (TC) algorithms is an important cross-cutting research area. Network topologies are usually modeled using attributed graphs whose nodes and edges represent the network nodes and their interconnecting links. A key requirement of TC algorithms is to fulfill certain consistency and optimization properties to ensure a high quality of service. Still, few attempts have been made to constructively integrate these properties into the development process of TC algorithms. Furthermore, even though many TC algorithms share substantial parts (such as structural patterns or tie-breaking strategies), few works constructively leverage these commonalities and differences of TC algorithms systematically. In previous work, we addressed the constructive integration of consistency properties into the development process. We outlined a constructive, model-driven methodology for designing individual TC algorithms. Valid and high-quality topologies are characterized using declarative graph constraints; TC algorithms are specified using programmed graph transformation. We applied a well-known static analysis technique to refine a given TC algorithm in a way that the resulting algorithm preserves the specified graph constraints. In this paper, we extend our constructive methodology by generalizing it to support the specification of families of TC algorithms. To show the feasibility of our approach, we reneging six existing TC algorithms and develop e-kTC, a novel energy-efficient variant of the TC algorithm kTC. Finally, we evaluate a subset of the specified TC algorithms using a new tool integration of the graph transformation tool eMoflon and the Simonstrator network simulation framework.

cs.SE

A Systematic Approach to Constructing Incremental Topology Control Algorithms Using Graph Transformation

Communication networks form the backbone of our society. Topology control algorithms optimize the topology of such communication networks. Due to the importance of communication networks, a topology control algorithm should guarantee certain required consistency properties (e.g., connectivity of the topology), while achieving desired optimization properties (e.g., a bounded number of neighbors). Real-world topologies are dynamic (e.g., because nodes join, leave, or move within the network), which requires topology control algorithms to operate in an incremental way, i.e., based on the recently introduced modifications of a topology. Visual programming and specification languages are a proven means for specifying the structure as well as consistency and optimization properties of topologies. In this paper, we present a novel methodology, based on a visual graph transformation and graph constraint language, for developing incremental topology control algorithms that are guaranteed to fulfill a set of specified consistency and optimization constraints. More specifically, we model the possible modifications of a topology control algorithm and the environment using graph transformation rules, and we describe consistency and optimization properties using graph constraints. On this basis, we apply and extend a well-known constructive approach to derive refined graph transformation rules that preserve these graph constraints. We apply our methodology to re-engineer an established topology control algorithm, kTC, and evaluate it in a network simulation study to show the practical applicability of our approach

cs.SE

Construction and Characterization of a Frequency-Controlled, Picometer-Resolution, Displacement Encoder-Actuator

We have constructed an actuator/encoder whose generated displacement is controlled through the resonance frequency of a microwave cavity. A compact, 10-micrometer-range, digitally-controlled actuator executing frequency-coded displacement with picometer resolution is described. We consider this approach particularly suitable for metrologic-precision scanning probe microscopy.

physics.ins-det

Local likelihood estimation of local parameters for nonstationary random fields

We develop a weighted local likelihood estimate for the parameters that govern the local spatial dependency of a locally stationary random field. The advantage of this local likelihood estimate is that it smoothly downweights the influence of far away observations, works for irregular sampling locations, and when designed appropriately, can trade bias and variance for reducing estimation error. This paper starts with an exposition of our technique on the problem of estimating an unknown positive function when multiplied by a stationary random field. This example gives concrete evidence of the benefits of our local likelihood as compared to naïve local likelihoods where the stationary model is assumed throughout a neighborhood. We then discuss the difficult problem of estimating a bandwidth parameter that controls the amount of influence from distant observations. Finally we present a simulation experiment for estimating the local smoothness of a local Matérn random field when observing the field at random sampling locations in $[0,1]^2$.

stat.ME