Including Systematic Uncertainties in Confidence Interval Construction for Poisson Statistics

One way to incorporate systematic uncertainties into the calculation of confidence intervals is by integrating over probability density functions parametrizing the uncertainties. In this note we present a development of this method which takes into account uncertainties in the prediction of background processes, uncertainties in the signal detection efficiency and background efficiency and allows for a correlation between the signal and background detection efficiencies. We implement this method with the Feldman & Cousins unified approach with and without conditioning. We present studies of coverage for the Feldman & Cousins and Neyman ordering schemes. In particular, we present two different types of coverage tests for the case where systematic uncertainties are included. To illustrate the method we show the relative effect of including systematic uncertainties the case of dark matter search as performed by modern neutrino tel escopes.Comment: 23 pages, 10 figures, replaced to match published versio

Doctor of Philosophy

dissertationMarketers invest significantly in generating consumer action, with curiosity one of many ways to pique interest. This is the topic of our first essay, in which we discuss how discounted price displays arouse curiosity, thus affecting information search behavior. This essay moves beyond the assumption that any prediscounted price will elicit the same consumer response and considers four moderating factors, including i) absolute price, ii) dispositional curiosity, iii) expected price and iv) drive states such as hunger. In a series of examinations, we propose that higher (lower) prices generate greater (less) curiosity. Findings inform psychology-based accounts of curiosity and provide implications for marketers in understanding pricing`s effect on information seeking. Essays 2 and 3 explore the long-term impact of a referral on sender and receiver behavior. Marketers have long sought to harness the influence of existing customers, with much literature focusing on a referral`s worth. While prior research has extensively examined referral value, less is known about how the specific information within the referral itself differentially influences behavior. Thus, Essay 2 focuses on the degree of customization within the referral, examining for both senders and receivers the influence of custom (sender-generated) versus standard (company-generated on behalf of sender) referrals. To test our predictions, we utilize email referrals from retail customers and compare purchase behavior between these referral types, testing the underlying theories of spotlight effect and reciprocity. In our third essay, we ask whether the act of referring changes long term purchase behavior of referrers. Extensive literature has proved the value of customers acquired through referral efforts of existing customers. However, while much is known about the incremental value of referrals, less is known about the intervening role of the referral itself. Therefore, in our research we seek to understand how a referral influences future sender behavior and ask whether the act of referring results in an increase, decrease, or consistency in purchases for senders. We explore opposing predictions based on i) dissonance and ii) market mavens and explore these predictions through an empirical examination of transaction data, offering implications for marketers and theorists alike

Efficient propagation of systematic uncertainties from calibration to analysis with the SnowStorm method in IceCube

Efficient treatment of systematic uncertainties that depend on a large number of nuisance parameters is a persistent difficulty in particle physics and astrophysics experiments. Where low-level effects are not amenable to simple parameterization or re-weighting, analyses often rely on discrete simulation sets to quantify the effects of nuisance parameters on key analysis observables. Such methods may become computationally untenable for analyses requiring high statistics Monte Carlo with a large number of nuisance degrees of freedom, especially in cases where these degrees of freedom parameterize the shape of a continuous distribution. In this paper we present a method for treating systematic uncertainties in a computationally efficient and comprehensive manner using a single simulation set with multiple and continuously varied nuisance parameters. This method is demonstrated for the case of the depth-dependent effective dust distribution within the IceCube Neutrino Telescope

Atmospheric and Astrophysical Neutrinos above 1 TeV Interacting in IceCube

The IceCube Neutrino Observatory was designed primarily to search for high-energy (TeV--PeV) neutrinos produced in distant astrophysical objects. A search for $\gtrsim 100$~TeV neutrinos interacting inside the instrumented volume has recently provided evidence for an isotropic flux of such neutrinos. At lower energies, IceCube collects large numbers of neutrinos from the weak decays of mesons in cosmic-ray air showers. Here we present the results of a search for neutrino interactions inside IceCube's instrumented volume between 1~TeV and 1~PeV in 641 days of data taken from 2010--2012, lowering the energy threshold for neutrinos from the southern sky below 10 TeV for the first time, far below the threshold of the previous high-energy analysis. Astrophysical neutrinos remain the dominant component in the southern sky down to 10 TeV. From these data we derive new constraints on the diffuse astrophysical neutrino spectrum, $\Phi_{\nu} = 2.06^{+0.4}_{-0.3} \times 10^{-18} \left({E_{\nu}}/{10^5 \,\, \rm{GeV}} \right)^{-2.46 \pm 0.12} {\rm {GeV^{-1} \, cm^{-2} \, sr^{-1} \, s^{-1}} }$, as well as the strongest upper limit yet on the flux of neutrinos from charmed-meson decay in the atmosphere, 1.52 times the benchmark theoretical prediction used in previous IceCube results at 90\% confidence.Comment: 18 pages, 12 figure

Time-Integrated Neutrino Source Searches with 10 Years of IceCube Data.

This Letter presents the results from pointlike neutrino source searches using ten years of IceCube data collected between April 6, 2008 and July 10, 2018. We evaluate the significance of an astrophysical signal from a pointlike source looking for an excess of clustered neutrino events with energies typically above ∼1  TeV among the background of atmospheric muons and neutrinos. We perform a full-sky scan, a search within a selected source catalog, a catalog population study, and three stacked Galactic catalog searches. The most significant point in the northern hemisphere from scanning the sky is coincident with the Seyfert II galaxy NGC 1068, which was included in the source catalog search. The excess at the coordinates of NGC 1068 is inconsistent with background expectations at the level of 2.9σ after accounting for statistical trials from the entire catalog. The combination of this result along with excesses observed at the coordinates of three other sources, including TXS 0506+056, suggests that, collectively, correlations with sources in the northern catalog are inconsistent with background at 3.3σ significance. The southern catalog is consistent with background. These results, all based on searches for a cumulative neutrino signal integrated over the 10 years of available data, motivate further study of these and similar sources, including time-dependent analyses, multimessenger correlations, and the possibility of stronger evidence with coming upgrades to the detector

Search for Prompt Neutrino Emission from Gamma-Ray Bursts with IceCube

We present constraints derived from a search of four years of IceCube data for a prompt neutrino flux from gamma-ray bursts (GRBs). A single low-significance neutrino, compatible with the atmospheric neutrino background, was found in coincidence with one of the 506 observed bursts. Although GRBs have been proposed as candidate sources for ultra-high energy cosmic rays, our limits on the neutrino flux disfavor much of the parameter space for the latest models. We also find that no more than $\sim1\%$ of the recently observed astrophysical neutrino flux consists of prompt emission from GRBs that are potentially observable by existing satellites.Comment: 15 pages, 3 figure

Combined sensitivity to the neutrino mass ordering with JUNO, the IceCube Upgrade, and PINGU

The ordering of the neutrino mass eigenstates is one of the fundamental open questions in neutrino physics. While current-generation neutrino oscillation experiments are able to produce moderate indications on this ordering, upcoming experiments of the next generation aim to provide conclusive evidence. In this paper we study the combined performance of the two future multi-purpose neutrino oscillation experiments JUNO and the IceCube Upgrade, which employ two very distinct and complementary routes toward the neutrino mass ordering. The approach pursued by the 20 kt medium-baseline reactor neutrino experiment JUNO consists of a careful investigation of the energy spectrum of oscillated νe produced by ten nuclear reactor cores. The IceCube Upgrade, on the other hand, which consists of seven additional densely instrumented strings deployed in the center of IceCube DeepCore, will observe large numbers of atmospheric neutrinos that have undergone oscillations affected by Earth matter. In a joint fit with both approaches, tension occurs between their preferred mass-squared differences Δm312=m32-m12 within the wrong mass ordering. In the case of JUNO and the IceCube Upgrade, this allows to exclude the wrong ordering at >5σ on a timescale of 3-7 years - even under circumstances that are unfavorable to the experiments' individual sensitivities. For PINGU, a 26-string detector array designed as a potential low-energy extension to IceCube, the inverted ordering could be excluded within 1.5 years (3 years for the normal ordering) in a joint analysis

Observation of High-Energy Astrophysical Neutrinos in Three Years of IceCube Data

A search for high-energy neutrinos interacting within the IceCube detector between 2010 and 2012 provided the first evidence for a high-energy neutrino flux of extraterrestrial origin. Results from an analysis using the same methods with a third year (2012-2013) of data from the complete IceCube detector are consistent with the previously reported astrophysical flux in the 100 TeV - PeV range at the level of $10^{-8}\, \mathrm{GeV}\, \mathrm{cm}^{-2}\, \mathrm{s}^{-1}\, \mathrm{sr}^{-1}$ per flavor and reject a purely atmospheric explanation for the combined 3-year data at $5.7 \sigma$. The data are consistent with expectations for equal fluxes of all three neutrino flavors and with isotropic arrival directions, suggesting either numerous or spatially extended sources. The three-year dataset, with a livetime of 988 days, contains a total of 37 neutrino candidate events with deposited energies ranging from 30 to 2000 TeV. The 2000 TeV event is the highest-energy neutrino interaction ever observed.Comment: 8 pages, 5 figures. Accepted by PRL. The event catalog, event displays, and other data tables are included after the final page of the article. Changed from the initial submission to reflect referee comments, expanding the section on atmospheric backgrounds, and fixes offsets of up to 0.9 seconds in reported event times. Address correspondence to: J. Feintzeig, C. Kopper, N. Whitehor