Let $n\geq 2$ random lines intersect a planar convex domain D. Consider the probabilities $p_{nk}$, $k=0,1, \ldots, {n(n-1)}/{2}$ that the lines produce exactly k intersection points inside D. The objective is finding $p_{nk}$ through geometric invariants of D. Using Ambartzumian’s combinatorial algorithm, the known results are instantly reestablished for $n=2, 3$. When $n=4$, these probabilities are expressed by new invariants of D. When D is a disc of radius r, the simplest forms of all invariants are found. The exact values of $p_{3k}$ and $p_{4k}$ are established.

This study investigates the asymptotic properties of the Bayesian empirical likelihood (BEL), which uses the empirical likelihood as an alternative to a parametric likelihood for Bayesian inference. We establish two asymptotic equivalence results based on the Bernstein–von Mises (BvM) theorem by introducing a new formulation of the moment restriction model. First, the limiting posterior distribution of the BEL is the same as that of a parametric Bayesian method that uses the likelihood of a least favorable model of the moment restriction model. Second, the limiting posterior distribution is also the same as that of a semiparametric Bayesian method that places priors on both a finite-dimensional parameter of interest and an infinite-dimensional nuisance parameter. Because parametric and semiparametric Bayesian methods are legitimate Bayesian procedures, the equivalence results provide a large sample justification for the BEL as a Bayesian inference method. Moreover, the BvM theorem provides a frequentist justification for BEL posterior inference.

The spread of Severe Acute Respiratory Syndrome Coronavirus 2 new variants increased the number of subjects in home isolation and quarantine. The aim of this study was to assess the compliance with coronavirus disease 2019 home isolation rules for 32 subjects in home care in Marche Region, Italy. The results showed that subjects in home isolation were better informed about isolation rules (P = 0.007) than those who were in quarantine. They had lower educational level (P < 0.001) and none/single income (P < 0.001) and higher rate of clinical manifestation. The education for a safe quarantine should be strengthened widely, especially among disadvantaged subjects.

Antimicrobial-resistant (AMR) bacteria are a threat to public health as they can resist treatment and pass along genetic material that allows other bacteria to become drug-resistant. To assess foodborne AMR risk, the Codex Guidelines for Risk Analysis of Foodborne AMR provide a framework for risk profiles and risk assessments. Several elements of a risk profile may benefit from a scoping review (ScR). To contribute to a larger risk profile structured according to the Codex Guidelines, our objective was to conduct a ScR of the current state of knowledge on the distribution, frequency and concentrations of extended-spectrum β-lactamase (ESBL)-producing Enterobacteriaceae in salmon and shrimp. Articles were identified via a comprehensive search of five bibliographic databases. Two reviewers screened titles and abstracts for relevance and characterised full-text articles with screening forms developed a priori. Sixteen relevant studies were identified. This review found that there is a lack of Canadian data regarding ESBL-producing Enterobacteriaceae in salmon and shrimp. However, ESBL- producing Escherichia coli, Klebsiella pneumoniae and other Enterobacteriaceae have been isolated in multiple regions with a history of exporting seafood to Canada. The literature described herein will support future decision-making on this issue as research/surveillance and subsequent assessments are currently lacking.

Fiduciary agents and trust-based institutions are increasingly proposed and considered in legal, regulatory, and ethical discourse as an alternative or addition to a control-based model of data management. Instead of leaving it up to the citizen to decide what to do with her data and to ensure that her best interests are met, an independent person or organization will act on her behalf, potentially also taking into account the general interest. By ensuring that these interests are protected, the hope is that citizens’ willingness to share data will increase, thereby allowing for more data-driven projects. Thus, trust-based models are presented as a win–win scenario. It is clear, however, that there are also apparent dangers entailed with trust-based approaches. Especially one model, that of data trusts, may have far-reaching consequences.

It is well known that, under suitable regularity conditions, the normalized fractional process with fractional parameter d converges weakly to fractional Brownian motion (fBm) for $d>\frac {1}{2}$. We show that, for any nonnegative integer M, derivatives of order $m=0,1,\dots ,M$ of the normalized fractional process with respect to the fractional parameter d jointly converge weakly to the corresponding derivatives of fBm. As an illustration, we apply the results to the asymptotic distribution of the score vectors in the multifractional vector autoregressive model.

This paper proposes a new test for a class of conditional moment restrictions (CMRs) whose parameterization involves unknown, unrestricted conditional expectation functions. Motivating examples of such CMRs arise from models of discrete choice under uncertainty including certain static games of incomplete information. The proposed test may be viewed as a semi-/nonparametric extension of the Bierens (1982, Journal of Econometrics 20, 105–134) goodness-of-fit test of a parametric model for the conditional mean. Estimating conditional expectations using series methods and employing a Gaussian multiplier bootstrap to obtain critical values, the test is shown to be asymptotically correctly sized and consistent. Simulation studies indicate good finite-sample properties. In an empirical application, the test is used to study the validity of a game-theoretical model for discount store market entry, treating equilibrium beliefs as nonparametric conditional expectations. The test indicates that Walmart and Kmart entry decisions do not result from a static discrete game of incomplete information with linearly specified profits.