Value Of Perfect Information Research Articles

Cost-effectiveness of surgical treatment of thumb carpometacarpal joint arthritis: a value of information study

BackgroundThumb carpometacarpal (CMC) joint arthritis is one of the most prevalent arthritic conditions commonly treated with trapeziectomy alone or trapeziectomy with ligament reconstruction and tendon interposition (LRTI). We evaluate the cost-effectiveness and value of perfect and sample information of trapeziectomy alone, LRTI, and non-operative treatment.MethodsA societal perspective decision tree was modeled. To understand the value of future research in comparing quality-of-life after trapeziectomy, LRTI, and non-operative management we characterized uncertainty by fitting distributions to EQ-5D utility data published from the United Kingdom hand surgery registry. We used Monte Carlo simulation for the probabilistic sensitivity analysis and to evaluate the value of perfect and sample information.ResultsBoth trapeziectomy alone and LRTI were cost-effective compared to non-operative management ($2,540 and $3,511/QALY respectively). Trapeziectomy alone (base case total cost $8,251, QALY 14.08) was dominant compared to LRTI (base case total cost $8,798, QALY 13.34). However, probabilistic sensitivity analysis suggested there is a 12.5% chance LRTI may be preferred at a willingness-to-pay of $50,000/QALY. Sensitivity analysis revealed postoperative utilities are the most influential factors in determining cost-effectiveness. The value of perfect information was approximately $1,503/person. A study evaluating the quality-of-life of 1,000 patients in each arm undergoing trapeziectomy alone or LRTI could provide an expected $1,117 of information value. With approximately 40,000 CMC arthroplasties performed each year in the U.S., the annual value is close to $45 million.ConclusionsTrapeziectomy without LRTI appears to be the most cost-effective procedure in treating late-stage CMC arthritis and should be considered as first-line surgical treatment. There is substantial societal value in conducting additional research to better understand the relative quality-of-life improvements gained from these two common hand surgeries.

A cost-effectiveness and value of information analysis to inform future research of tranexamic acid for older adults experiencing mild traumatic brain injury

BackgroundTranexamic acid reduces head injury deaths in patients with CT scan evidence of intracranial bleeding after mild traumatic brain injury (TBI). However, the cost-effectiveness of tranexamic acid for people with mild TBI in the pre-hospital setting, prior to CT scanning, is uncertain. A large randomised controlled trial (CRASH-4) is planned to address this issue, but the economic justification for it has not been established. The aim of the analysis was to estimate the likelihood of tranexamic acid being cost-effective given current evidence, the treatment effects required for cost-effectiveness, and the expected value of performing further research.MethodsAn early economic decision model compared usual care for mild TBI with and without tranexamic acid, for adults aged 70 and above. The evaluation was performed from a UK healthcare perspective over a lifetime time horizon, with costs reported in 2020 pounds (GBP) and outcomes reported as quality-adjusted life years (QALYs). All analyses used a £20,000 per QALY cost-effectiveness threshold.ResultsIn the base case analysis, tranexamic acid was associated with an incremental cost-effectiveness ratio of £4885 per QALY gained, but the likelihood of it being cost-effective was highly dependent on the all-cause mortality treatment effect. The value of perfect information was £22.4 million, and the value of perfect information for parameters that could be collected in a trial was £21.9 million. The all-cause mortality risk ratio for tranexamic acid and the functional outcomes following TBI had the most impact on cost-effectiveness.ConclusionsThere is a high degree of uncertainty in the cost-effectiveness of tranexamic acid for older adults experiencing mild TBI, meaning there is a high value of performing future research in the UK. The value in a global context is likely to be far higher.

Anticipatory scheduling of synchromodal transport using approximate dynamic programming

AbstractWe study the problem of scheduling container transport in synchromodal networks considering stochastic demand. In synchromodal networks, the transportation modes can be selected dynamically given the actual circumstances and performance is measured over the entire network and over time. We model this problem as a Markov Decision Process and propose a heuristic solution based on Approximate Dynamic Programming (ADP). Due to the multi-period nature of the problem, the one-step look-ahead perspective of the traditional approximate value-iteration approach can make the heuristic flounder and end in a local-optimum. To tackle this, we study the inclusion of Bayesian exploration using the Value of Perfect Information (VPI). In a series of numerical experiments, we show how VPI significantly improves a traditional ADP algorithm. Furthermore, we show how our proposed ADP–VPI combination achieves significant gains over common practice heuristics.

Agroforestry and reforestation with the Gold Standard-Decision Analysis of a voluntary carbon offset label

Voluntary standards can help to ensure the quality of projects eligible for carbon offsetting, i.e., selling carbon certificates. However, in deciding on whether to adopt such standards, the managers of carbon offset projects are faced with uncertainty regarding the costs and risks involved. Decision Analysis provides a helpful set of tools that can support such decisions by forecasting outcomes under different scenarios. We applied Decision Analysis methods to generate models for the decisions to certify two projects in Costa Rica with the voluntary carbon offset label “The Gold Standard”. We evaluated certifying an additional site of a partially certified reforestation project, as well as the initial certification of an agroforestry project.We calibrated and interviewed decision-makers and stakeholders of the certification projects to identify important parameters and translate these into a decision model. We ran the final decision model as a Monte Carlo simulation to project plausible ranges of decision outcomes, expressed as Net Present Values and annual cash flows. We identified critical uncertainties and research priorities by using the Expected Value of Perfect Information. The results indicate that certification of the two projects would result in a positive Net Present Value. The partially low return on investment of the certification, however, shows the need for projects to undergo thorough evaluation and generate customized strategies before participating in a voluntary carbon offset scheme. The Decision Analysis approaches we describe can help to improve the process of decision making under uncertainty and should be widely adopted for evaluating the potential impacts of certification.

Early field planning using optimisation and considering uncertainties

During early phases of oil field development, field planners must decide upon the optimal number of wells and optimal field plateau rate, usually by performing sensitivity studies. These design choices are then “frozen” in subsequent development stages. However, they often end up being suboptimal when the field is built and produced and the uncertainty is reduced. In this work, we employ non-linear numerical optimisation, latin hypercube sampling and the Schwartz & Smith oil price model to compute probability distributions of the optimal number of wells, plateau rate and project value. We also employ an analytical model to compute production profiles and project value and consider uncertainties in in-place oil volume, well productivity and oil price. Then, we study how do these distributions change from early field planning until when the field is abandoned, when uncertainties are reduced to a minimum. The variation in time of the in-place oil volume uncertainty is modelled with a random walk. The well productivity is a step function altered randomly after production startup. The actual oil price trajectory is picked randomly from possible trajectories computed with the Schwartz and Smith model. The results show that the distributions of the optimal number of wells, plateau rate and project value depend greatly on the uncertainties in the input data. Field designs based on the average of the distributions during the early phase are profitable, but suboptimal. A potential upside of such designs is that they entail less capital investment and therefore less financial risk when compared against the optimal field design. • Robust approach to consider uncertainties when computing optimal field design. • The optimal design strongly depends on the uncertainties in input parameters. • Uncertainties in input parameters are considered to vary during the field’s life. • The value of perfect information is modest for the cases studied in this paper.

Using social values in the prioritization of research: Quantitative examples and generalizations.

Identifying critical uncertainties about ecological systems can help prioritize research efforts intended to inform management decisions. However, exclusively focusing on the ecological system neglects the objectives of natural resource managers and the associated social values tied to risks and rewards of actions.I demonstrate how to prioritize research efforts for a harvested population by applying expected value of perfect information (EVPI) to harvest decisions made with a density‐independent matrix population model. Research priorities identified by EVPI diverge from priorities identified by matrix elasticity analyses that ignore social utility.Using a density‐dependent harvest model, the value of information about the intrinsic productivity of a population is shown to be sensitive to the socially determined penalty for implementing a harvest rate that deviates from the goal because of imperfection in estimation. Synthesis and applications. The effect of including social values into harvest decision‐making depends on the assumed population model, uncertainty in population vital rates, and the particular form of the utility function used to represent risk/reward of harvest. EVPI analyses that include perceived utility of different outcomes can be used by managers seeking to optimize monitoring and research spending. Collaboration between applied ecologists and social scientists that quantitatively measure peoples' values is needed in many structured decision‐making processes.

Cost-effectiveness and budget impact of venetoclax in combination with rituximab in relapsed/refractory chronic lymphocytic leukemia in Switzerland

IntroductionVenetoclax in combination with rituximab (VEN + R) demonstrated prolonged overall survival (OS) and progression-free survival (PFS) for patients with relapsed/refractory (R/R) chronic lymphocytic leukemia (CLL) in comparison to standard chemoimmunotherapy [bendamustine + rituximab (BR)]. We conducted a cost-effectiveness and budget impact analysis comparing VEN + R versus six comparators from the Swiss healthcare payer perspective.MethodsA three-state partitioned survival model, developed in accordance with NICE and ISPOR decision modelling guidelines, was adapted to Switzerland. Model inputs were informed by the MURANO trial (survival data, patient characteristics), publicly available Swiss sources (drug prices, inpatient and outpatient costs), Swiss National Institute of Cancer Epidemiology and Registration data (incidence and prevalence values), and Swiss medical expert feedback. We used published (dis-)utility values and adverse event probabilities.ResultsOver a lifetime, VEN + R resulted in an expected gain of 2.60 quality-adjusted life years (QALYs) per patient and incremental costs of Swiss Francs (CHF) 147,851 compared to BR, leading to an incremental cost-effectiveness ratio of CHF 56,881/QALY gained. Other treatment strategies (for example ibrutinib versus VEN + R) resulted in higher costs and lower QALYs. Results were not different for subgroups of patients with/without deletion of chromosome 17p/tumour protein 53 mutation. In scenario analysis, changes in post-progression treatment costs demonstrated a high impact on results. We estimated an expected value of perfect information of CHF 3,318/patient. A moderate VEN + R uptake was estimated to save CHF 12.3 million during 5 years.ConclusionsUsing a threshold of CHF 100,000 per QALY, VEN + R was projected to be cost-effective vs BR.

Cost-Effectiveness and Value of Information of Cabozantinib Treatment for Patients with Advanced Renal Cell Carcinoma After Failure of Prior Therapy in South Korea.

To estimate the cost-effectiveness and value of information of cabozantinib compared to nivolumab in advanced renal cell carcinoma (RCC) patients, who previously failed treatment from a societal perspective in South Korea. A partitioned survival model was used to evaluate the incremental cost-utility ratio (ICUR) of cabozantinib versus nivolumab. Overall survival (OS) and progression-free survival (PFS) curves were obtained from a network meta-analysis that included METEOR and CheckMate 025 trial results. Utility values for health states and adverse events were estimated based on the EQ-5D-5L data of METEOR trial with a Korean-specific tariff. Costs were estimated by a micro-costing approach using healthcare claims data and expert consultation. The impact of uncertainties in the model were explored by scenario analyses, and deterministic and probabilistic sensitivity analyses. The expected value of perfect information (EVPI) was estimated to assess the value of future research to decrease decision uncertainty. Compared to nivolumab, cabozantinib was associated with improved OS, PFS, and quality-adjusted life-years (QALYs) at greater cost. The ICUR was $34,445 per QALY. In sensitivity analysis, drug costs had the greatest influence on the ICUR. Cabozantinib had a 68.0% probability of being cost-effective at a threshold of 2 times gross domestic product (GDP) per capita. The population EVPI was $82.6 million at 2 GDP threshold. Cabozantinib was found to be cost-effective for advanced RCC patients after failure of prior therapy at a 2 GDP threshold. Future research that costs less than the estimated population EVPI would be worth considering for a comparison of cabozantinib and nivolumab.

Optimal Prognostics and Health Management-driven inspection and maintenance strategies for industrial systems

The performance of the Prognostics and Health Management (PHM) depends both on the functioning of the measurement acquisition system and on the actual state of the system being monitored. The dependencies between these systems must be considered when developing optimal inspection and maintenance strategies. This paper presents a methodology to support the definition maintenance strategies for PHM-equipped industrial systems. The methodology employs influence diagrams when seeking to maximize the expected utility of system operation. The optimization problem is solved by mixed-integer linear programming, subject to budget and technical constraints. Chance constraints can be also included, for instance to curtail risks based on measures such as the Value at Risk (VaR) and the Conditional Value at Risk (CVaR) of system operation. The viability of the methodology is demonstrated by optimizing the inspection and maintenance strategy for a gas turbine equipped with PHM solution. The computation of the Value of Perfect Information (VoPI) provides additional insights on maintenance management.

Pricing real options based on linear loss functions and conditional value at risk

The main purpose of this paper is to expand real option analysis out of the realm of pure financial option pricing techniques. To overcome many of the well-known concerns by adopting the financial option pricing techniques for modeling real options problems such as replicating portfolio concept, geometric Brownian motion as underlying stochastic process, and estimating project volatility, we propose an alternative real option valuation based on the loss function approach. The option value determined by the loss function approach is equivalent to the expected value of perfect information (EVPI) in decision analysis. It basically sets the upper bound of risk premium to pay in retaining the options. In practice, many firms utilize the concept of Value at Risk to manage their portfolio risk. If a firm sets a target VAR, then we may be able to link this VAR in refining the actual risk premium to pay in hedging the risk embedded in the investment. With this practice in mind, we present a logic to figure out an appropriate amount of real option premium to pay for a given level of risk tolerance. A comprehensive example is presented to demonstrate the computational procedures as well as economic interpretations on the outcomes.

Determining the cost-effectiveness requirements of an exoskeleton preventing second hip fractures using value of information

BackgroundFalls may lead to hip fractures, which have a detrimental effect on the prognosis of patients as well as a considerable impact on healthcare expenditures. Since a secondary hip fracture (SHF) may lead to even higher costs than primary fractures, the development of innovative services is crucial to limit falls and curb costs in high-risk patients. An early economic evaluation assessed which patients with a second hip fracture could benefit most from an exoskeleton preventing falls and whether its development is feasible.MethodsThe life-course of hip fractured patients presenting with dementia or cardiovascular diseases was simulated using a Markov model relying on the United Kingdom administrative data and complemented by published literature. A group of experts provided the exoskeleton parameters. Secondary analyses included a threshold analysis to identify the exoskeleton requirements (e.g. minimum impact of the exoskeleton on patients’ quality of life) leading to a reimbursable incremental cost-effectiveness ratio. Similarly, the uncertainty around these requirements was modelled by varying their standard errors and represented alongside population Expected Value of Perfect Information (EVPI).ResultsOur base-case found the exoskeleton cost-effective when providing a statistically significant reduction in SHF risk. The secondary analyses identified 286 cost-effective combinations of the exoskeleton requirements. The uncertainty around these requirements was explored producing further 22,880 scenarios, which showed that this significant reduction in SHF risk was not necessary to support the exoskeleton adoption in clinical practice. Conversely, a significant improvement in women quality of life was crucial to obtain an acceptable population EVPI regardless of the cost of the exoskeleton.ConclusionsOur study identified the exoskeleton requisites to be cost-effective and the value of future research. Decision-makers could use our analyses to assess not only whether the exoskeleton could be cost-effective but also how much further research and development of the exoskeleton is worth to be pursued.

Balancing Lifecycle Sustainment Cost with Value of Information during Design Phase

<div class="section abstract"><div class="htmlview paragraph">The complete lifecycle of complex systems, such as ground vehicles, consists of multiple phases including design, manufacturing, operation and sustainment (O&S) and finally disposal. For many systems, the majority of the lifecycle costs are incurred during the operation and sustainment phase, specifically in the form of uncertain maintenance costs. Testing and analysis during the design phase, including reliability and supportability analysis, can have a major influence on costs during the O&S phase. However, the cost of the analysis itself must be reconciled with the expected benefits of the reduction in uncertainty. In this paper, we quantify the value of performing the tests and analyses in the design phase by treating it as imperfect information obtained to better estimate uncertain maintenance costs. A multi-attribute decision framework for military ground vehicles acquisition is employed to illustrate the methodology and the value of performing the analysis early in the system’s lifecycle. Attributes considered are maintenance cost and operational availability, while the utility is calculated for a risk averse decision maker. Numerical methods are employed to calculate the value of sample information and reflect an increase in expected utility (EU) after collecting the information. While less than the value of perfect information that completely eliminates outcome uncertainty, results demonstrate a positive value for testing. This value determines the maximum amount that should be spent on testing given the anticipated benefits.</div></div>

Cost-effectiveness and value of information analysis of a low-friction environment following skin graft in patients with burn injury

BackgroundPatients with burn injuries may receive a skin graft to achieve healing in a timely manner. However, in around 7% of cases, the skin graft is lost (fails to attach to the wound site) and a re-grafting procedure is necessary. It has been hypothesised that low-friction (smooth, more slippery) bedding may reduce the risk of skin-graft loss. A before and after feasibility study comparing low-friction with standard bedding in skin-grafted patients was conducted in order to collect proof of concept data. The resulting relative risk on the primary outcome (number of patients with skin graft failure) for the non-randomised study provided no evidence of effect but had a large standard error. The aim of this study is to see if an appropriately powered randomised control trial would be worthwhile.MethodsA probabilistic decision-analytic model was constructed to compare low-friction bedding to standard care in a population of burn patients who have undergone skin grafting. Results from the before and after study were used as model inputs. The sensitivity of results to bias in the relative risk of graft loss was conducted. Low-friction bedding is considered optimal if expected incremental net benefit (INB) is positive. Uncertainty is assessed using cost-effectiveness acceptability curves. Expected Value of Perfect Partial Information (EVPPI) provides an upper bound for the potential net health benefits of new research for given model input.ResultsAt a willingness to pay threshold of £20,000 per QALY, INB = £151 (95% Credible Interval (CrI) −142 to 814), marginally favouring low-friction bedding but with high uncertainty (probability of being cost-effective 70.5%). Expected value of perfect information (EVPI) per patient was £20.29, which results in a population EVPI of £174,765 over a 10-year lifetime for the technology (based on 1000 patients per year who would benefit from the intervention). The parameter contributing most to the uncertainty was the inpatient care cost, i.e. information that could be obtained from the audit of practice and without an expensive trial. These findings were robust to a wide-range of assumptions about the potential bias due to the observational nature of the comparative evidence.ConclusionsOur study results suggest that an RCT (randomised controlled trial) is unlikely to be worthwhile, but there may be value in a study to estimate the re-graft rates and associated costs in this population.

Value of Improved Information about Environmental Protection Values: Toward a Benefit–Cost Analysis of Public-Good Valuation Studies

AbstractWhat is the benefit from obtaining more precise values of environmental or other public goods through surveys or other information gathering? In the value of information (VOI) problem studied here, a buyer who wishes to preserve a resource sets a price to offer a seller without knowing precisely its protection value, B, nor its value to the seller, V. The VOI from more precise information about B is important for environmental and natural resource valuation, but is typically not quantified nor compared to valuation costs. More precise environmental values reduce the frequency of two types of mistakes (protecting the resource when it should not be; and not protecting it when it should), and increases ex ante welfare. We apply our analysis to Amazon rainforest protection, focusing on the “value of perfect information,” VOPI, which, we show through simulations, typically exceeds realistic valuation costs, justifying significant valuation expenditures. VOPI also depends on the nature of buyer–seller interactions, and takes its highest value when the buyer has full concern for the seller’s outcome. Our paper proposes and prepares the base for a new, needed, field in applied welfare economics, the “benefit–cost analysis of public-good valuation studies.”

Value of perfect information in stock picking

Portfolio picking is an important aspect in investmtent management. Before deciding what stock to pick, an investor will consider many aspect of the stock, the fundamental and the trend of the market. Knowing what to expect is an important science and art in investment. Expected value of perfect information – EVPI is the difference between two payoff that predicted to be the best of some certain condition. For portfolio management, we could employ Capital Asset Pricing Model to provide clearer view of each securities and using treynor ratio to optimize the investment result. Description in this paper about performance analysis of stocks in LQ-45 index in Indonesian Stock Index in 1-st quartil period of 2015, based on return and risk to reach the group of stocks which optimum using the model of Capital Asset Pricing Model (CAPM). Our finding suggests that using CAPM and Treynor Ratio analysis could optimize the portfolio outcome, while changing business and economic environment create limitation on the portfolio.

Thou shalt be given… but how? A replication study and extended cost-effectiveness analysis of a randomized experiment on food assistance in Northern Ecuador

ABSTRACTThe original cluster-randomised controlled trial took place in two provinces of Northern Ecuador. The trial compared cash, food or voucher assistance and found them to be effective. The results of the original paper are completely replicable and the findings of the original analysis are robust; however, we additionally find that treatments are more effective in the poorer province. We then extend the cost-effectiveness analysis by taking into account the parameter uncertainty in a probabilistic sensitivity analysis (PSA). Moreover, we provide information about the usefulness of additional research to reduce uncertainty concerning the cost-effectiveness analysis by calculating the expected value of perfect information (EVPI). Our extended cost-effectiveness analysis reveals that for some outcomes decision makers with a relatively small willingness-to-pay maybe a risk to choose a less cost-effective intervention. Furthermore, our findings indicate that further research into the comparative cost-effectiveness of these interventions could be worthwhile. This is in particular true for low-resource settings where decision makers face stricter budget constraints to finance interventions. In particular, policy makers with a small budget have a high risk of choosing a comparably less cost-effective treatment. Hence, further research to reduce uncertainty of effect estimates could aid decision-making.

The cost-effectiveness of omega-3 polyunsaturated fatty acids – The Australian healthcare perspective

ObjectivesTo examine the cost-effectiveness of a triglyceride lowering medication–icosapent ethyl added on to statin from Australian healthcare system perspective. MethodsA Markov-model was developed using data from the pivotal trial of icosapent ethyl in a secondary prevention population. Probabilities of CVD events were derived and extrapolated from the published Kaplan-Meier curve using a valid algorithm. Management cost of CVD, health-related quality of life, and background non-CVD mortality were extracted from publicly available sources. Acquisition cost of icosapent ethyl from the United States was used in the current analysis. Australian patients with histories of CVD were modelled for a 25 year time horizon and costs and benefits were discounted. Sensitivity analyses (SA) were undertaken. Value of perfect information (VPI) was quantified. ResultsTreatment with icosapent ethyl was associated with both higher costs and benefits (i.e. quality-adjusted life year [QALY] and life year [LY]), resulting in an incremental cost-effectiveness ratio (ICER) of AUD59,036/QALY or AUD54,358/LY. Using the often quoted willingness-to-pay (WTP)/QALY of AUD50,000/QALY, icosapent ethyl was not considered cost-effective. SA showed that time horizon, drug cost, and discount rate were the key drivers of the ICER. Total monetary VPI for icosapent ethyl was over AUD15 million over 5 years. ConclusionsPatients with established CVD in whom level of triglycerides is high would benefit from the treatment using icosapent ethyl, however, it is not a cost-effective from an Australian healthcare system perspective. The government may consider subsidising this medication given the clinical need but at a discounted acquisition cost.

Within trial cost-utility analysis of disease management program for patients hospitalized with atrial fibrillation: results from the SAFETY trial

Background: The potential impact of disease management to optimize quality of care, health outcomes, and total healthcare costs across a range of cardiac disease states is unknown.Methods: A trial-based cost-utility analysis was conducted alongside a randomized controlled trial of 335 patients with chronic, non-valvular AF (without heart failure; the SAFETY Trial) discharged to home from three tertiary referral hospitals in Australia. A home-based disease management intervention (the SAFETY intervention) that involved community-based AF care including home visits was compared to routine primary healthcare and hospital outpatient follow-up (standard management). Bootstrapped incremental cost-utility ratios were computed based on quality-adjusted life-years (QALYs) and total healthcare costs. Cost-effectiveness acceptability curves were constructed to explore the probability of the SAFETY intervention being cost-effective. Sub-group analyses were performed based on age and sex to determine differential cost-effectiveness.Results: During median follow-up of 1.75 years, the SAFETY intervention was associated with a non-statistically significant increase in QALYs (0.02 per person) and lower total healthcare costs (–$4,375 per person). Although each of these findings were not statistically significant, the SAFETY intervention was found to be dominant (more effective and cost saving) in 58.8% of the bootstrapped iterations and cost-effective (more effective and gains in QALYs achieved at or below $50,000 per QALY gained) in 61.5% of the iterations. Males and those aged less than 78 years achieved greater gains in QALYs and savings in healthcare costs. The estimated value of perfect information in Australia (the monetized value of removing uncertainty in the cost-effectiveness results) was A$51 million, thus demonstrating the high potential gain from further research.Conclusions: Compared with standard management, the SAFETY intervention is potentially a dominant strategy for those with chronic, non-valvular AF. However, there would be substantial value in reducing the uncertainty in these estimates from further research.Trial registration: Australian New Zealand Clinical Trials Registry identifier: ACTRN12610000221055.

Bayesian Decision Modeling in Watershed Management - Cross River Basin, Nigeria

This paper aimed at examining simulation modeling in Bayesian Decision theory and its application in day to day decision making as well as planning in water resources and Environmental engineering. It also gives more insight in the validation of prior probability. The research objectives deals with the multi-objective value of water for its wide range of purposes such as Power generation, water supply, Navigation, Irrigation, and Flood control, in the Cross River basin using Bayesian Modeling. In line with foregoing objectives, the research aim to achieve the following: (i) to lay bare the usefulness of the Bayesian theory that gives more than point estimation. It measures the magnitude of the difference between alternative actions and provides a variety of estimates for consideration, (ii) to present selected empirical results of a study employing decision-making theory as a framework for considering decision making under uncertainty. (iii) to evaluate the optimal policy or strategy or action that maximizes the expected benefit in the River Basin within the available limited resources and funds over the planning period of a course of action or alternatives. The multi-objectives arising from the development that were optimized include: Economic Efficiency, Regional Economic Distribution, State and Local Economic Redistribution, Youth Employment and Environmental Quality Improvement, which are primarily essential in Cross Rivers State and Nigeria. Methodology applied involving methods, experiments and data were collected for the River Basin Engineering Development, from Parastatals and Ministries. The conceptual framework on Bayesian Decision Model (BDM) as presented captured the iterative updates of prior probability toward achieving an optimum solution of a set problem. The analysis and presentation of results were based on simulation of Bayesian Models Iterations. Chi-square, Contingency and association and Pearson Product Moment Correlation were carried out as Interaction, reliability and Validity tests respectively. The study applied Bayesian Decision Model, where the following parameters were obtained:: (a)Posterior Probabilities of the States of Nature (b) Marginal Probability of the Courses of action, (c) Maximum Expected Monetary Value[EMV*] (d) Expected Profit in a Perfect Information[EPPI], (e) Expected Value of Perfect Information[EVPI], and (f) Expected Value of System Information[EVSI]. In the process of Iteration, and at some point the Prior becomes equal to the Posterior Probability, when this occurs an optimum solution is said to be achieved. However, the correlation of prior and posterior probability is equal to one (1) at the optimum solution. In conclusion, the efficiency of system information is 50%. Table 25 indicates monetary allocation to the multi-objectives which gave a clear indication that the life wire of the watershed/dam lies on it; and therefore should be comparatively considered; because without it, it will be difficult to maintain the watershed. The Basin Authority is expected to pay the researcher the Expected Value of System Information (EVSI) value of = ₦0.1billion for information generated using the Bayesian Decision theory model spreadsheet. The value of Economic efficiency optimized from 1 st iteration to 2 nd Iteration with the EMV values of ₦2.54billion to ₦2.74billion respectively as in [ Table 4 & 15] Keywords : Optimum Solution, Prior-posterior, Probability, River Basin. DOI : 10.7176/CER/11-2-11 Publication date :March 31 st 2019

Simulation Modeling in Prior-Posterior Decision Theory- A Case Study of Farmers’ Decision Problem

This study aims at applying Prior-Posterior decision theory based models to analyze and solve the farmers’ decision problem who are faced with decision of determining among alternatives crops [Sorghum, Rice, Wheat & Corn] the best crop to invest on, that will give a highest yield and profit under the prevailing state of nature on each of a 100 acres land located in Obudu LGA in Cross River State for each of the Farm Settler. However, the study has the following objectives (i) laying bare the usefulness of the theory, (ii) measuring the magnitude of the difference between alternative actions (iii) presenting experimental results for considering decision making under uncertainties, and (iv) evaluating the optimal policy or strategy or action that maximizes the expected yield of cereal crop within the study area. The methodology involves experiments and data were compared to United State Department of Agriculture (USDA). The analysis and presentation of results were based on Simulation of Prior-Posterior decision models, Policy iterations, and Pearson Product Moment Correlation as interaction, validity, reliability tests respectively. Consequently, from the results of prior probabilities of the state of nature and the likelihood of the alternatives courses of action, and applying Prior-Posterior Decision Models to the uncertain system, the following decision were generated: (a)Posterior Probabilities of the States of Nature (b) Marginal Probability of the Course of Action, (c) Maximum Expected Monetary Value[EMV*] (d) Expected Profit in a Perfect Information[EPPI], (e) Expected Value of Perfect Information[EVPI], and (f) Expected Value of System Information[ EVSI]. The results gave a clear indication that Rice has the [EMV*] value of $17,178.21 at 40 th model iteration, making it the most suitable crop for each of the Farmer Settlers to invest on, for maximum yield. EMV* of rice was also observed to be optimized from the 1 st and 40 th model iteration at the value of $14,175.66 and $17,178.21 respectively. The results of the analyses attest to the fact that rice production in Obudu study area is currently the most yielding crop. The performance of Prior-Posterior decision models on the farmers’ decision was evaluated which gave Pearson Product Moment Coefficient(r) of = 1.0. This shows applicability of Prior-Posterior Decision Model Excel Algorithms in River Basin Multi-projects/objectives Planning and Management. Keywords : Prior-Posterior, Modeling, Farm- Settlers -Decision, investment, Optimization. DOI : 10.7176/CER/11-2-07 Publication date :March 31 st 2019