Probability Research Articles

Machine learning for corporate default risk: Multi-period prediction, frailty correlation, loan portfolios, and tail probabilities

We model multi-period cumulative and forward corporate default probabilities using machine learning methods and introduce a novel hybrid econometric-machine learning model which combines tree-boosting with a latent frailty model. The latter allows for modeling correlation that is not accounted for by observable predictor variables. We find that machine learning methods have higher prediction accuracy compared to linear models with the differences being larger for longer prediction horizons. The likely reason for this is the presence of stronger interaction effects for longer prediction horizons compared to short horizons. Among all methods, tree-boosting has the highest prediction accuracy. Further, the frailty component of the newly proposed “LaGaBoost frailty model” is overall large and exhibits strong variation over time. In contrast to prior research, we find that upper tail predictions of loan portfolio losses of frailty models are not consistently higher throughout time compared to models ignoring frailty correlation, but they show more temporal variation.

Probabilistic cooperative coded forwarding for broadcast transmissions in industrial mobile edge communications

Mobile edge computing (MEC) is considered as a key enabler for the industrial internet of things (IIoT) to cope with the ever-increasing communication and computing demands of nodes. In consideration of the limited resource of the IIoT nodes, it is necessary to design cost-effective multi-hop data transmission schemes for mobile edge IIoTs. However, most of the traditional schemes have to spend enormous cost to meet the reliability requirement, which cannot support timely information processing of MEC-based IIoT. In this article, the probabilistic cooperative coded forwarding (PCCF) scheme for multi-hop data transmission in mobile edge IIoTs is proposed to address the above problem. First, the data packets are encoded at a source IIoT node using the systematic sparse network coding (SSNC) mechanism, then the source broadcasts the coded packets to its one-hop neighbors. To minimize the required number of redundant coded packets, the sparsity of coded packets is optimized. Second, the nodes which received the packets will become volunteer relay nodes and forward the coded packets using the cooperative coded forwarding (CCF) mechanism. The volunteer relays first forward the received coded packets with a forwarding probability, and then re-encode a pair of received coded packets and broadcast the re-encoded packet with a re-encoding probability. To guarantee the broadcast performance while minimizing the transmission number at relay nodes, the feasible forwarding and re-encoding probability are provided. Third, the receiver nodes will try to decode the received coded and re-encoded packets and recover data packets without sending acknowledgments. Finally, through a series of experiments, we verify the accuracy of analytical approximations and also find out the optimal sparsity of coded packets and the existence of minimum transmission numbers. These provide insights for further optimization of multi-hop data transmission in mobile edge IIoTs.

Bile acids directly bind and allosterically regulate the epithelial sodium channel

Bile acids are critical for the digestion and absorption of dietary fats and have important roles as signaling molecules. Bile acids are normally restricted to the enterohepatic circulation, but can be elevated in the blood and urine of patients with advanced liver diseases. The epithelial sodium channel (ENaC) mediates Na+ transport in the biliary epithelium, where it regulates bile viscosity, and in the aldosterone‐sensitive distal nephron, where it regulates extracellular fluid volume. We previously showed that bile acid regulation of ENaC depends on the position and stereochemistry of specific functional groups, but not on their chemico‐physical properties. To determine whether bile acids regulate ENaC in ex vivo native tissues, we performed patch clamp experiments on isolated split open renal tubules from mice, using recording pipettes backfilled with taurocholic acid (t‐CA) or taurohyodeoxycholic acid (t‐HDCA). Consistent with in vitro experiments, t‐CA increased ENaC open probability (PO) by 2‐fold while t‐HDCA decreased ENaC PO by nearly two‐thirds. To determine whether bile acids regulate ENaC through direct binding, we performed photoaffinity labeling experiments. We employed a bile acid derivative (p‐DCA) with diazirine and terminal alkyne groups that facilitate uv‐crosslinking and affinity purification, respectively. Using cultured Fisher Rat Thyroid cells transfected with ENaC, we found that the deoxycholic acid derivative (p‐DCA) crosslinked to the α, β, and γ subunits. To determine whether crosslinking was specific, we performed experiments in the presence of competing bile acids. Crosslinking to the β subunit was significantly reduced in the presence of deoxycholic acid (DCA). Crosslinking to the γ subunit was significantly reduced by taurocholic acid (t‐CA). These data suggest direct binding and multiple sites. To determine the effect of subunit composition on regulation, we measured the effect of t‐CA on Li+ currents in Xenopusoocytes expressing different functional ENaC subunit combinations. Channels composed of α subunits alone were strongly activated by t‐CA, followed by αβγ‐ and αβ‐ channels, suggesting that the α subunit is sufficient for ENaC sensitivity to t‐CA. Our data are consistent with bile acids directly binding all three ENaC subunits at multiple sites. Bile acid moieties provide for selective preferences for each of the sites, resulting in distinct effects for each bile acid.

Measurement equivalence in probability and nonprobability online panels

Nonprobability online panels are commonly used in the social sciences as a fast and inexpensive way of collecting data in contrast to more expensive probability-based panels. Given their ubiquitous use in social science research, a great deal of research is being undertaken to assess the properties of nonprobability panels relative to probability ones. Much of this research focuses on selection bias, however, there is considerably less research assessing the comparability (or equivalence) of measurements collected from respondents in nonprobability and probability panels. This article contributes to addressing this research gap by testing whether measurement equivalence holds between multiple probability and nonprobability online panels in Australia and Germany. Using equivalence testing in the Confirmatory Factor Analysis framework, we assessed measurement equivalence in six multi-item scales (three in each country). We found significant measurement differences between probability and nonprobability panels and within them, even after weighting by demographic variables. These results suggest that combining or comparing multi-item scale data from different sources should be done with caution. We conclude with a discussion of the possible causes of these findings, their implications for survey research, and some guidance for data users.

Non-Cooperative Game Forwarding Leveraging User Trustworthiness in Mobile Edge Networks

Given frequent changes of network topology caused by limited computing power, strong mobility and weak reliability of most nodes in mobile edge computing (MEC) networks, a Non-Cooperative Game forwarding strategy based on user Trustworthiness (NCGT) is proposed to deal with low security and efficiency of data transmission. NCGT firstly considers device residual energy ratio, contact probability, service degree and link stability between devices to measure the reliability of nodes. Then, leverages Entropy Weight (EW) method and Golden Section Ratio (GSR) to develop a security optimal neighbors screening model based on multi-attribute decision-making, which ensures that high-performance security nodes are selected as forwarding game objects. Third, NCGT takes forwarding and non-forwarding as the policy set, designs the benefit function, and gets forwarding probability of nodes through Nash equilibrium, to reduce a large number of redundancy, competition and conflict in forwarding requests and improve its broadcasting efficiency. The simulation results show, NCGT is more effective against black hole and witch attacks than S-MODEST and AODV+FDG when there exists malicious nodes. Meanwhile, with the increasing of network load, NCGT with or without GSR always performs best in the terms of data delivery rate, delay, transmission energy consumption and system throughput in MEC environment.

Evaluating the Performance of Zero-Inflated and Hurdle Poisson Models for Modeling Overdispersion in Count Data

A Poisson regression model is commonly used to model count data. The Poisson model assumes equidispersion, that is, the mean is equal to the variance. This assumption is often violated. In count data, overdispersion (the variance is larger than the mean) occurs frequently due to excessive zeroes in the response variable. Zero-inflated Poisson (ZIP) and Hurdle models are commonly used to fit data with excessive zeros. Although some studies have compared the ZIP and Hurdle models, the results are inconsistent. This paper aims to evaluate the performance of ZIP and Hurdle Poisson models for overdispersion data through both simulation study and real data. Data were simulated with three different sample sizes, six different means, and three different probabilities of zero with 500 replications. Model goodness-of-fit measures were compared by using Akaike Information Criteria (AIC). Overall, the ZIP model performed relatively the same or better than the Hurdle Poisson model under different scenarios, but both ZIP and Hurdle models are better than the standard Poisson model for overdispersion in count data .

But that’s possible! Infants, pupils, and impossible events

Infants’ expectations of the world around them have been extensively assessed through the violation of expectation paradigm and related habituation tasks. Typically, in these tasks, longer looking to impossible events following familiarisation with possible equivalents is taken to reflect surprise at their occurrence, thus revealing infants’ knowledge. In this study, the role of learning during the task itself is explored by switching the archetypal approach on its head and familiarising infants to impossible events. In a partial replication of Jackson and Sirois (2009), nine-month-old infants were presented with short video clips of toy trains moving around a circular track. A tunnel over a short section of the track meant trains were briefly occluded as they completed a circuit. In impossible versions of events, the train switched colours while occluded by the tunnel. Both looking times and pupil dilation were used as dependent measures. Using a factorial design in which perceptual (novelty-familiarity) and conceptual (possible-impossible) variables were independently and jointly analysed, we show that infants showed greater responding to possible events than to impossible events following familiarisation. Pupil dilation data successfully allowed for more precise interpretation of infants’ perception of events than could have been achieved through looking times alone. These findings suggest a central role for learning in violation of expectation tasks, and also further support the use of pupil dilation as a dependent measure in infancy work.

A Proposed Method for Predicting User Disinformation Forwarding Behavior

At present, social network sites (SNSs) have become the major channels by which disinformation is released and disseminated. Without the effective control of disinformation on social media, a serious threat to social stability may occur. Different from traditional media, forwarding has become the key approach to propagating information on social media. Therefore, if the users who will forward the disinformation are identified in advance, they can be prevented from forwarding the disinformation and the harmful effects of disinformation will be minimized. To identify the users who will forward the disinformation, we should predict the probability of an individual forwarding disinformation. We propose a novel method to predict the disinformation forwarding probability of individuals on a social network. The proposed method extracts the features that affect individual disinformation forwarding, especially extracting features related to the susceptibility of users to disinformation. With combining bootstrap sampling and expectation-maximization (EM) algorithm to learn unobserved features, the proposed method utilizes both observed and unobserved features to predict the disinformation forwarding probability of individuals. Using data from “Weibo,” which is the largest social media platform in China, we demonstrate the effectiveness of the proposed method.

Securing localization-free underwater routing protocols against depth-spoofing attacks

Localization-free depth-based opportunistic routing protocols are an energy efficient choice for underwater wireless sensor networks (UWSNs). However, most depth-based routing protocols are vulnerable to sinkhole attacks caused by depth spoofing. In this paper, we propose an energy-efficient depth-based probabilistic routing protocol (DPR) that is resilient against depth spoofing. By encouraging unqualified (suboptimal) relay nodes to randomly forward data packets, the adversarial effects of depth-spoofing can be mitigated. As the randomized forwarding probability increases, a better packet delivery ratio can be achieved when under depth-spoofing attacks. To keep energy consumption in check, we propose a simulation-based methodology for finding the optimal forwarding probability. By adjusting the unqualified node forwarding probability, the proposed DPR protocol can effectively resist depth-spoofing attacks with a reasonably efficient energy overhead. A delivery ratio exceeding 90% can be achieved under attack with energy overhead as low as 35% under normal conditions. In comparison with relevant existing protocols, the proposed protocol achieves better energy efficiency, resilience efficiency, and scalability.

Miraculous, magical, or mundane? The development of beliefs about stories with divine, magical, or realistic causation.

Children's naïve theories about causal regularities enable them to differentiate factual narratives describing real events and characters from fictional narratives describing made-up events and characters (Corriveau, Kim, Schwalen, & Harris, Cognition 113 (2): 213-225, 2009). But what happens when children are consistently presented with accounts of miraculous and causally impossible events as real occurrences? Previous research has shown that preschoolers with consistent exposure to religious teaching tend to systematically judge characters involved in fantastical or religious events as real (Corriveau et al., Cognitive Science, 39 (2), 353-382, 2015; Davoodi et al., Developmental Psychology, 52 (2), 221, 2016). In the current study, we extended this line of work by asking about the scope of the impact of religious exposure on children's reality judgments. Specifically, we asked whether this effect is domain-general or domain-specific. We tested children in Iran, where regular exposure to uniform religious beliefs might influence children's reasoning about possibility in non-religious domains, in addition to the domain of religion. Children with no or minimal schooling (5- to 6-year-olds) and older elementary school students (9- to 10-year-olds) judged the reality status of different kinds of stories, notably realistic, unusual (but nonetheless realistic), religious, and magical stories. We found that while younger children were not systematic in their judgments, older children often judged religious stories as real but rarely judged magical stories as real. This developmental pattern suggests that the impact of religious exposure on children's reality judgments does not extend beyond their reasoning about divine intervention. Children's justifications for their reality judgments provided further support for this domain-specific influence of religious teaching.

Revisiting asynchronous fault tolerant computation with optimal resilience

The celebrated result of Fischer, Lynch and Paterson is the fundamental lower bound for asynchronous fault tolerant computation: any 1-crash resilient asynchronous agreement protocol must have some (possibly measure zero) probability of not terminating. In 1994, Ben-Or, Kelmer and Rabin published a proof-sketch of a lesser known lower bound for asynchronous fault tolerant computation with optimal resilience in face of a Byzantine adversary: if $$n\le 4t$$ then any t-resilient asynchronous verifiable secret sharing protocol must have some non-zero probability of not terminating. Our main contribution is to revisit this lower bound and provide a rigorous and more general proof. Our second contribution is to show how to avoid this lower bound. We provide a protocol with optimal resilience that is almost surely terminating for a strong common coin functionality. Using this new primitive we provide an almost surely terminating protocol with optimal resilience for asynchronous Byzantine agreement that has a new fair validity property. To the best of our knowledge this is the first asynchronous Byzantine agreement with fair validity in the information theoretic setting.

A Fuzzy Knowledge-Based Approach for End-2-End Behavioural Analysis of Wormhole Attacks on Mobile Ad-Hoc Networks

Mobile Ad hoc Networks (MANETs) involves series of travelling nodes communicating with each other without a fixed Set-up. Certainly, MANETs are networks that utilize communication peripatetic nodes such as; Personal Digital Assistants (PDAs), mobile phones, laptops which enable wireless transmission across an area and forwarding data packets to the other nodes resulting in frequent change in topology. MANETs are exposed to several communication assaults such as active attack and passive attack. The active attack disrupts network operations while the passive attack obtains information without upsetting normal networks operation. Wormhole is a typical case of active attack. Indeed, an attacker receives packets at one end of the network, tunnels them to another end of the network, and then replays them into the networks from that point resulting in a collapse in communication across wireless setups. This research work simulates and models a typical wormhole attack in MANET using Network Simulator (NS-2.35) and Fuzzy Inference System (FIS). The End-2-End behavioural analysis of wormhole attacks on the transmitting networks layer of MANET was realized. To detect the level of wormhole attack in the network several parameters such as Packet Delivery Ratio, Packet Forwarding Probability and Packet Dropping Probability were considered by determining the degree of severity of wormhole attack which may upset the Quality of Service (QOS) delivery. The aim of this research paper is in the direction of Network security optimization.

Rational Reasons, Counterfactual Statements and “Impossible Worlds” in the Philosophical Justifications of Thought Experiments

In his theory of natural laws David Lewis rejects the authenticity of impossible worlds on the grounds that the contradiction contained within his modifier "in (the world) w" is tantamount to a contradiction in the whole theory, which seems unacceptable. At the same time, in philosophical discourse very often researchers use counterfactual situations and thought experiments with impossible events and objects. There is a need to apply the theory of worlds to genuine, concrete, but impossible worlds. One way to do this is to reject Lewis's classical negation on the grounds that it leads to problems of completeness and inconsistency inside the worlds. The proposed extension for impossibility is compatible with Lewis's extensional metaphysics, although it leads to some loss for description completeness in semantics.

Is What Mickey Mouse Says Impossible? Informant Reality Status and Children’s Beliefs in Extraordinary Events

ABSTRACT As children get older, they become better able to discriminate between impossible and improbable statements and they realize that improbable events can occur in reality while impossible ones cannot. However, when children hear about extraordinary events from fictional entities (e.g., popular characters from children’s media), they may be more likely to doubt that the events can occur in reality. The current studies examine how an informant’s reality status and familiarity influence children’s belief in statements about improbable and impossible events. Across two studies, children ages 4, 6, and 8 (N = 362) heard impossible and improbable statements from an unfamiliar person, a familiar character, or an unfamiliar character (Study 1) or a real or pretend person (Study 2) and judged whether each statement could happen in reality. As in previous studies, older children were more likely than younger children to believe improbable events could occur. Additionally, for both types of statements, children’s judgments about the possibility of the events were similar regardless of the informant. These results suggest that when children hear extraordinary statements described by fictional characters, they pay more attention to the content of the statement than to the source.

Youth risk profiles and their prediction of distal cannabis and tobacco co-use in the Population Assessment of Tobacco Health (PATH)

Background: Co-use of cannabis and tobacco is common and increases negative behavioral, physical and mental health consequences. This study aimed to describe latent profiles of youth internalizing and externalizing problems, sensation seeking, and family environment in the US and their relationships with substance co-use. Methods: Data come from the Population Assessment of Tobacco Health (PATH). Using latent profile analysis with a distal outcome, we conducted a secondary data analysis examining relationships between latent profiles and the distal outcome of cannabis/tobacco use and co-use one year later. Participants were a nationally representative sample of youth ages 12–17 (N = 13,651). Results: We identified five youth subgroups: (1;11%) Family Risk, (2;32%) Family Protection with Very Low Internalizing, (3;21%) Family Protection with High Youth Risk, (4;24%) Family Protection with Moderate Youth Risk, (5;12%) Family Risk with High Youth Risk. Relationships between group membership and tobacco/cannabis outcomes, one year later, indicated that the least likely tobacco/cannabis users were the Family Protection with Very Low Internalizing class (no lifetime use probability (PR)=0.86, standard error (SE)=0.007; no 30-day use PR = 0.96, SE = 0.004). In contrast, the Family Risk with High Youth Risk class had the highest probability of both co-use (lifetime co-use PR = 0.33; SE = 0.014; 30-day co-use PR = 0.10; SE = 0.010) and single substance use (probability of lifetime single substance use PR = 0.30; SE = 0.013; 30-day single substance use PR = 0.24; SE = 0.014). Conclusions: A “protective but reactive” risk buffering pattern effect of family factors on youth factors was observed in that the lowest rates of co-use were observed in the three classes with family protection. These findings highlight the need for interventions addressing multiple domains and focusing on youth and family risk factors.

Data Dissemination in VANETs Using Clustering and Probabilistic Forwarding Based on Adaptive Jumping Multi-Objective Firefly Optimization

Data dissemination in a VANETs network requires a meticulous process to ensure a high quality of service and eliminate hazardous conditions due to congestion or a broadcast storm. Considering multi-metric approaches and their implicit conflicting nature, it is necessary to handle this through effective multi-objective optimization algorithms. An effective optimization can be handled using a meta-heuristic approach with a high level of solution interactions. For this purpose, firefly was selected, which is a type of meta-heuristic search algorithm. Several developments of the firefly optimization were added to increase its capability to find more dominating solutions, namely, objective decomposition, archive management, and controlled mutation for exploration and exploitation balance. This developed multi-objective optimization was designated as adaptive jumping multi-objective firefly algorithm (AJ-MOFA). Afterwards, AJ-MOFA was integrated with a clustering and forwarding mechanism (CFM). This mechanism includes three main components. The first is clustering, which uses arbitration based on the cluster head score; the second is a forwarding mechanism that uses probabilistic forwarding and the third is AJ-MOFA. The solution space design in CFM combined two variables: the first is the probability of forwarding and the second is the maximum number of nodes within one cluster. The metrics to be incorporated in the multi-objective optimizations are the packet delivery ratio (PDR), the end-to-end delay (E2E-delay) and the number of dropped packets. Comparing both AJ-MOFA and CFM with benchmarks using multi-objective optimization and networking metrics reveals the superiority in most evaluation measures, which makes them promising algorithms for data dissemination in VANETs. The results showed an accomplished PDR of 60% and an E2E delay of 6.6 seconds, while the number of dropped packets was almost nine for the entire running time of the experiment, comparing a similar or lower performance of the benchmarks for these metrics.

Decision prioritization and causal reasoning in decision hierarchies.

From cooking a meal to finding a route to a destination, many real life decisions can be decomposed into a hierarchy of sub-decisions. In a hierarchy, choosing which decision to think about requires planning over a potentially vast space of possible decision sequences. To gain insight into how people decide what to decide on, we studied a novel task that combines perceptual decision making, active sensing and hierarchical and counterfactual reasoning. Human participants had to find a target hidden at the lowest level of a decision tree. They could solicit information from the different nodes of the decision tree to gather noisy evidence about the target’s location. Feedback was given only after errors at the leaf nodes and provided ambiguous evidence about the cause of the error. Despite the complexity of task (with 107 latent states) participants were able to plan efficiently in the task. A computational model of this process identified a small number of heuristics of low computational complexity that accounted for human behavior. These heuristics include making categorical decisions at the branching points of the decision tree rather than carrying forward entire probability distributions, discarding sensory evidence deemed unreliable to make a choice, and using choice confidence to infer the cause of the error after an initial plan failed. Plans based on probabilistic inference or myopic sampling norms could not capture participants’ behavior. Our results show that it is possible to identify hallmarks of heuristic planning with sensing in human behavior and that the use of tasks of intermediate complexity helps identify the rules underlying human ability to reason over decision hierarchies.

The probability of the existence of defects that lead to the destruction of the pressure vessel without leak

Relevance. To ensure the safety of a nuclear power plant on the basis of the requirements of norms and rules in the field of the use of atomic energy for pipelines of the primary circuit of a nuclear reactor, the design should apply the leak before break concept. The main idea of the concept is to prevent a sudden rupture of the pipelines of the reactor coolant loop, and consists in substantiating the fact that the rupture is preceded by the formation of a stable through crack, which is detected by the provided leak control means. When substantiating the concept, it is assumed that break without leak is an impossible event. This article provides a method for determining the probability of a failure event without a leak. Purpose - estimate the probability of the existence of a defect that can lead to the destruction of the vessel or pressure pipeline without leakage, as well as the probability of failure without leakage for a known number of loading cycles. Methods. To systematize the data obtained by different methods of non-destructive testing, conservative assumptions were used to determine the area of detected defects. On the basis of the obtained defect sizes, the defect size regions were determined, which can determine the scenarios of crack growth. Using the methods of mathematical statistics, the probability of the existence of a defect, which can lead to failure without leakage, was determined. Based on the methods of the theory of reliability, a comparison of the obtained probability of destruction with the admissible value is carried out. Results. A method for processing non-destructive testing data based on an assessment of the area of detected defects has been developed to systematize the data obtained by different non-destructive testing methods. The criterion for the development of cracks according to the scheme leak before destruction is determined. A method has been developed for determining the probability of a defect that can lead to failure without leakage. An example of calculation based on feed water pipelines is considered.

Usage-Based Individual Differences in the Probabilistic Processing of Multi-Word Sequences

While it is widely acknowledged that both predictive expectations and retrodictive integration influence language processing, the individual differences that affect these two processes and the best metrics for observing them have yet to be fully described. The present study aims to contribute to the debate by investigating the extent to which experienced-based variables modulate the processing of word pairs (bigrams). Specifically, we investigate how age and reading experience correlate with lexical anticipation and integration, and how this effect can be captured by the metrics of forward and backward transition probability (TP). Participants read more and less strongly associated bigrams, paired to control for known lexical covariates such as bigram frequency and meaning (i.e., absolute control, total control, absolute silence, total silence) in a self-paced reading (SPR) task. They additionally completed assessments of exposure to print text (Author Recognition Test, Shipley vocabulary assessment, Words that Go Together task) and provided their age. Results show that both older age and lesser reading experience individually correlate with stronger TP effects. Moreover, TP effects differ across the spillover region (the two words following the noun in the bigram).

An empirical approach to estimating hydrocarbon column heights for improved predrill volume prediction in hydrocarbon exploration

Estimating pre-drill volumes in hydrocarbon exploration involves dealing with geological and technical uncertainties. The prediction of the hydrocarbon column height is widely recognized as the primary driver of uncertainty in volumetric estimates. The oil and gas industry continues to renew efforts to limit such uncertainties because of the potential economic costs of inaccurate estimation, yet estimation of pre-drill volumes remains an in-exact science. This study introduces new empirical data from the Norwegian Continental Shelf, and aims to improve accuracy in hydrocarbon column height prediction. We use column height, trap height and burial depth data to calculate the degree of hydrocarbon trap fill for each of the 242 studied discovery wells. The data is aggregated into a simple forward probability model to calculate the probability of encountering different ranges of trap-fill, based on burial depth and trap height. The distribution of trap-fill ratios clearly correlates with both trap height and burial depth, thus indicating that the same pre-drill column height distribution should not be used for all prospects. These findings strongly suggest that the prospect’s dimensions and burial depth are used alongside other technical subsurface factors to determine the most suitable pre-drill hydrocarbon column height distribution. This method contributes to reducing the largest source of uncertainty, which in turn reduces the overall uncertainty associated with pre-drill volume estimation. Such an approach will increase the accuracy of pre-drill volume estimation, leading to more appropriate future development plans. We recommend that the presented methods and lessons learnt are applied in basins settings worldwide.