We consider a sequential treatment problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision-maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socioeconomic functional such as an inequality, welfare, or poverty measure. We develop expected regret lower bounds for this problem and construct a near minimax optimal sequential assignment policy.

This paper studies control function (CF) approaches in endogenous threshold regression where the threshold variable is allowed to be endogenous. We first use a simple example to show that the structural threshold regression (STR) estimator of the threshold point in Kourtellos, Stengos and Tan (2016, Econometric Theory 32, 827–860) is inconsistent unless the endogeneity level of the threshold variable is low compared to the threshold effect. We correct the CF in the STR estimator to generate our first CF estimator using a method that extends the two-stage least squares procedure in Caner and Hansen (2004, Econometric Theory 20, 813–843). We develop our second CF estimator which can be treated as an extension of the classical CF approach in endogenous linear regression. Both these approaches embody threshold effect information in the conditional variance beyond that in the conditional mean. Given the threshold point estimates, we propose new estimates for the slope parameters. The first is a by-product of the CF approach, and the second type employs generalized method of moment (GMM) procedures based on two new sets of moment conditions. Simulation studies, in conjunction with the limit theory, show that our second CF estimator and confidence interval for the threshold point together with the associated second GMM estimator and confidence interval for the slope parameter dominate the other methods. We further apply the new estimation methodology to an empirical application from international trade to illustrate its usefulness in practice.

Syndromic surveillance was originally developed to provide early warning compared to laboratory surveillance, but it is increasing used for real-time situational awareness. When a potential threat to public health is identified, a rapid assessment of its impact is required for public health management. When threats are localised, analysis is more complex as local trends need to be separated from national trends and differences compared to unaffected areas may be due to confounding factors such as deprivation or age distributions. Accounting for confounding factors usually requires an in-depth study, which takes time. Therefore, a tool is required which can provide a rapid estimate of local incidents using syndromic surveillance data.

Here, we present ‘DiD IT?’, a new investigation tool designed to measure the impact of local threats to public health. ‘DiD IT?’ uses a difference-in-differences statistical approach to account for temporal and spatial confounding and provide a direct estimate of impact due to incidents. Temporal confounding differences are estimated by comparing unaffected locations during and outside of exposure periods. Whilst spatial confounding differences are estimated by comparing unaffected and exposed locations outside of the exposure period. Any remaining differences can be considered to be the direct effect of the local incident.

We illustrate the potential utility of the tool through four examples of localised health protection incidents in England. The examples cover a range of data sources including general practitioner (GP) consultations, emergency department (ED) attendances and a telehealth call and online health symptom checker; and different types of incidents including, infectious disease outbreak, mass-gathering, extreme weather and an industrial fire. The examples use the UK Health Security Agency's ongoing real-time syndromic surveillance systems to show how results can be obtained in near real-time.

The tool identified 700 additional online difficulty breathing assessments associated with a severe thunderstorm, 53 additional GP consultations during a mumps outbreak, 2–3 telehealth line calls following an industrial fire and that there was no significant increase in ED attendances during the G7 summit in 2021.

DiD IT? can provide estimates for the direct impact of localised events in real-time as part of a syndromic surveillance system. Thus, it has the potential for enhancing surveillance and can be used to evaluate the effectiveness of extending national surveillance to a more granular local surveillance.

This study aimed to evaluate the contrast-enhanced ultrasound (CEUS) features of ureteral tuberculosis (UTB) and ureteral malignant tumour and to explore its application value in the differentiation of UTB from ureteral tumour. The ultrasound (US) and CEUS imaging features of 33 and 12 cases of pathologically confirmed UTB and ureteral malignant tumour, respectively, were retrospectively evaluated, and echo of the ureteral wall, abnormal echo of the lumen, degree of ureteral dilation and CEUS patterns of the two diseases were statistically analysed. The results revealed that the lumen echo of UTB was hyperechoic or anechoic, whereas that of ureteral tumour lesions was hypoechoic (χ2 = 28.22, P < 0.001). The wall echo of the obstruction site differed between the two diseases; in UTB, the ureteral wall was thickened but the outer wall remained intact, whereas in ureteral tumour, both the malignant tumour wall and outer wall were irregular (χ2 = 30.25, P < 0.001). CEUS of UTB revealed nonenhancement or heterogeneous enhancement in the lumen, whereas that of ureteral tumours revealed significant homogeneous enhancement (χ2 = 30.25, P < 0.001). Thus, CEUS can reveal lesion microcirculation and be used to evaluate blood supply characteristics in the lesion, indicating that it has high potential for differentiating the two diseases.

In this paper, we introduce the 3-step hedge-based valuation for the valuation of hybrid claims. We consider an insurance portfolio which is exposed to traded risks, diversifiable risks and non-traded systematic risks. The class of 3-step hedge-based valuations is equivalent with the class of fair valuations. Closed-form solutions are derived for a portfolio of unit-linked contracts under the assumption of independence between financial and non-financial risks. We also consider the additive 3-step valuation and show that this additive valuation is a member of the more general class of 3-step hedge-based valuations.

Despite promising steps towards the elimination of hepatitis C virus (HCV) in the UK, several indicators provide a cause for concern for future disease burden. We aimed to improve understanding of geographical variation in HCV-related severe liver disease and historic risk factor prevalence among clinic attendees in England and Scotland. We used metadata from 3829 HCV-positive patients consecutively enrolled into HCV Research UK from 48 hospital centres in England and Scotland during 2012–2014. Employing mixed-effects statistical modelling, several independent risk factors were identified: age 46–59 y (ORadj 3.06) and ≥60 y (ORadj 5.64) relative to <46 y, male relative to female sex (ORadj 1.58), high BMI (ORadj 1.73) and obesity (ORadj 2.81) relative to normal BMI, diabetes relative to no diabetes (ORadj 2.75), infection with HCV genotype (GT)-3 relative to GT-1 (ORadj 1.75), route of infection through blood products relative to injecting drug use (ORadj 1.40), and lower odds were associated with black ethnicity (ORadj 0.31) relative to white ethnicity. A small proportion of unexplained variation was attributed to differences between hospital centres and local health authorities. Our study provides a baseline measure of historic risk factor prevalence and potential geographical variation in healthcare provision, to support ongoing monitoring of HCV-related disease burden and the design of risk prevention measures.

We prove some estimates for the variations of transition probabilities of the (1+1)-affine process. From these estimates we deduce the strong Feller and the ergodic properties of the total variation distance of the process. The key strategy is the pathwise construction and analysis of several Markov couplings using strong solutions of stochastic equations.

This paper proposes a two-phase deep reinforcement learning approach, for hedging variable annuity contracts with both GMMB and GMDB riders, which can address model miscalibration in Black-Scholes financial and constant force of mortality actuarial market environments. In the training phase, an infant reinforcement learning agent interacts with a pre-designed training environment, collects sequential anchor-hedging reward signals, and gradually learns how to hedge the contracts. As expected, after a sufficient number of training steps, the trained reinforcement learning agent hedges, in the training environment, equally well as the correct Delta while outperforms misspecified Deltas. In the online learning phase, the trained reinforcement learning agent interacts with the market environment in real time, collects single terminal reward signals, and self-revises its hedging strategy. The hedging performance of the further trained reinforcement learning agent is demonstrated via an illustrative example on a rolling basis to reveal the self-revision capability on the hedging strategy by online learning.

Ross River virus (RRV) is the most common mosquito-borne infection in Australia. RRV disease is characterised by joint pain and lethargy, placing a substantial burden on individual patients, the healthcare system and economy. This burden is compounded by a lack of effective treatment or vaccine for the disease. The complex RRV disease ecology cycle includes a number of reservoirs and vectors that inhabit a range of environments and climates across Australia. Climate is known to influence humans, animals and the environment and has previously been shown to be useful to RRV prediction models. We developed a negative binomial regression model to predict monthly RRV case numbers and outbreaks in the Darling Downs region of Queensland, Australia. Human RRV notifications and climate data for the period July 2001 – June 2014 were used for model training. Model predictions were tested using data for July 2014 – June 2019. The final model was moderately effective at predicting RRV case numbers (Pearson's r = 0.427) and RRV outbreaks (accuracy = 65%, sensitivity = 59%, specificity = 73%). Our findings show that readily available climate data can provide timely prediction of RRV outbreaks.

Hand, foot and mouth disease (HFMD) is a common infection in the world, and its epidemics result in heavy disease burdens. Over the past decade, HFMD has been widespread among children in China, with Shanxi Province being a severely affected northern province. Located in the temperate monsoon climate, Shanxi has a GDP of over 2.5 trillion yuan. It is important to have a comprehensive understanding of the basic features of HFMD in those areas that have similar meteorological and economic backgrounds to northern China. We aimed to investigate epidemiological characteristics, identify spatial clusters and predict monthly incidence of HFMD. All reported HFMD cases were obtained from the Shanxi Center for Disease Control and Prevention. Overall HFMD incidence showed a significant downward trend from 2017 to 2020, increasing again in 2021. Children aged < 5 years were primarily affected, with a high incidence of HFMD in male patients (relative risk: 1.316). The distribution showed a seasonal trend, with major peaks in June and July and secondary peaks in October and November with the exception of 2020. Other enteroviruses were the predominant causative agents of HFMD in most years. Areas with large numbers of HFMD cases were primarily in central Shanxi, and spatial clusters in 2017 and 2018 showed a positive global spatial correlation. Local spatial autocorrelation analysis showed that hot spots and secondary hot spots were concentrated in Jinzhong and Yangquan in 2018. Based on monthly incidence from September 2021 to August 2022, the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) of the long short-term memory (LSTM) and seasonal autoregressive integrated moving average (SARIMA) models were 386.58 vs. 838.25, 2.25 vs. 3.08, and 461.96 vs. 963.13, respectively, indicating that the predictive accuracy of LSTM was better than that of SARIMA. The LSTM model may be useful in predicting monthly incidences of HFMD, which may provide early warnings of HFMD epidemics.

The Bruss–Robertson–Steele (BRS) inequality bounds the expected number of items of random size which can be packed into a given suitcase. Remarkably, no independence assumptions are needed on the random sizes, which points to a simple explanation; the inequality is the integrated form of an $\omega$-by-$\omega$ inequality, as this note proves.

This paper introduces a flexible risk decomposition method for life insurance contracts embedding several risk factors. Hedging can be naturally embedded in the framework. Although the method is applied to variable annuities in this work, it is also applicable in general to other insurance or financial contracts. The approach relies on applying an allocation principle to components of a Shapley decomposition of the gain and loss. The implementation of the allocation method requires the use of a stochastic on stochastic algorithm involving nested simulations. Numerical examples studying the relative impact of equity, interest rate and mortality risk for guaranteed minimal maturity benefit (GMMB) policies conclude our analysis.

The model uncertainty issue is pervasive in virtually all applied fields but especially critical in insurance and finance. To hedge against the uncertainty of the underlying probability distribution, which we refer to as ambiguity, the worst case is often considered in quantifying the underlying risk. However, this worst-case treatment often yields results that are overly conservative. We argue that, in most practical situations, a generic risk is realized from multiple scenarios and the risk in some ordinary scenarios may be subject to negligible ambiguity so that it is safe to trust the reference distributions. Hence, we only need to consider the worst case in the other scenarios where ambiguity is significant. We implement this idea in the study of the worst-case moments of a risk in the hope to alleviate the over-conservativeness issue. Note that the ambiguity in our consideration exists in both the scenario indicator and the risk in the corresponding scenario, leading to a two-fold ambiguity issue. We employ the Wasserstein distance to construct an ambiguity ball. Then, we disentangle the ambiguity along the scenario indicator and the risk in the corresponding scenario, so that we convert the two-fold optimization problem into two one-fold problems. Our main result is a closed-form worst-case moment estimate. Our numerical studies illustrate that the consideration of partial ambiguity indeed greatly alleviates the over-conservativeness issue.

We introduce a new measure of inaccuracy based on extropy between distributions of the nth upper (lower) record value and parent random variable and discuss some properties of it. A characterization problem for the proposed extropy inaccuracy measure has been studied. It is also shown that the defined measure of inaccuracy is invariant under scale but not under location transformation. We characterize certain specific lifetime distribution functions. Nonparametric estimators based on the empirical and kernel methods for the proposed measures are also obtained. The performance of estimators is also discussed using a real dataset.

We consider a model of binary opinion dynamics where one opinion is inherently “superior” than the other, and social agents exhibit a “bias” toward the superior alternative. Specifically, it is assumed that an agent updates its choice to the superior alternative with probability α > 0 irrespective of its current opinion and opinions of other agents. With probability $1-\alpha$, it adopts majority opinion among two randomly sampled neighbors and itself. We are interested in the time it takes for the network to converge to a consensus on the superior alternative. In a complete graph of size n, we show that irrespective of the initial configuration of the network, the average time to reach consensus scales as $\Theta(n\,\log n)$ when the bias parameter α is sufficiently high, that is, $\alpha \gt \alpha_c$ where αc is a threshold parameter that is uniquely characterized. When the bias is low, that is, when $\alpha \in (0,\alpha_c]$, we show that the same rate of convergence can only be achieved if the initial proportion of agents with the superior opinion is above certain threshold $p_c(\alpha)$. If this is not the case, then we show that the network takes $\Omega(\exp(\Theta(n)))$ time on average to reach consensus.

Consider Bernoulli bond percolation on a graph nicely embedded in hyperbolic space $\mathbb{H}^d$ in such a way that it admits a transitive action by isometries of $\mathbb{H}^d$. Let $p_{\text{a}}$ be the supremum of all percolation parameters such that no point at infinity of $\mathbb{H}^d$ lies in the boundary of the cluster of a fixed vertex with positive probability. Then for any parameter $p < p_{\text{a}}$, almost surely every percolation cluster is thin-ended, i.e. has only one-point boundaries of ends.