A Study in Multistage Decision Making for Odisha State Avionic Infrastructure Development

Influence diagrams are a powerful graphic representation for decision models, complementary to decision trees. Influence diagrams and decision trees are different graphic representations for the same underlying mathematical model and operations. This article describes the elements of an influence diagram, and shows several familiar decision problems represented as decision trees and as influence diagrams. The authors also contrast the information highlighted in each graphic representation, demonstrate how to calculate the expected utilities of decision alternatives modeled with an influence diagram, provide an overview of the conceptual basis of the solution algorithms that have been developed for influence diagrams, discuss the strengths and limitations of influence diagrams relative to decision trees, and describe the mathematical operations that are used to evaluate both decision trees and influence diagrams. They use clinical examples to illustrate the mathematical operations of the influence-diagram-evaluation algorithm; these operations are arc reversal, chance node removal by averaging, and decision node removal by policy determination. Influence diagrams may be helpful when problems have a high degree of conditional independence, when large models are needed, when communication of the probabilistic relationships is important, or when the analysis requires extensive Bayesian updating. The choice of graphic representation should be governed by convenience, and will depend on the problem being analyzed, on the experience of the analyst, and on the background of the consumers of the analysis.

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 127761, ’Probabilistic Modeling for Decision Support in Integrated Operations,’ by Martin Giese, University of Oslo, and Reidar B. Bratvold, SPE, University of Stavanger, prepared for the 2010 SPE Intelligent Energy Conference and Exhibition, Utrecht, Netherlands, 23-25 March. The paper has not been peer reviewed. A system was designed to assist operational decisions on the basis of real-time sensor readings in a typical scenario: While drilling close to the transition to a high-pressure formation, gas influx is observed. The technology used Bayesian networks and influence diagrams (IDs) to apply the method of decision analysis. The resulting ID was tested with a simulation. Introduction An assumption of integrated operations is that all information provided by the technology will help to make better decisions faster. But for this to happen, information must be presented in an accessible, useful, and decision-relevant format. Decision-analysis tools provide decision makers with logical and consistent recommendations based on the available data. This decision-analysis method was applied to a real case, representative of a typical scenario in drilling operations. The tool enabled good decisions consistently. However, effort is required and challenges exist in the modeling process along with problems regarding the way decision making is treated in the industry. Modeling and Solving A decision tree provides a graphical illustration of all the uncertainties, decisions, and payoffs associated with a decision situation. Although application of decision trees is intuitive for simple problems, the method loses its appeal for complex decisions. A symmetric decision tree grows exponentially with the number of variables in the decision domain, which often makes its use impractical. For complex decisions, the ID can provide a level of insight and transparency that cannot be achieved with the equivalent decision tree. The ID is a compact graphical-model representation for reasoning under uncertainty and was developed to assist structuring and analysis of complex decisions. The ID has two advantages—structuring and probabilistic evaluation. The structuring provides a graphical representation of the inter-relationships among the decision-basis elements (i.e., alternatives, information, and preferences), while the evaluation appraises the resulting decision structure and provides an assessment of its expected utility given the quantified decision basis. The representational framework of an ID captures the probabilistic relationships among decisions (alternatives), key uncertainties (information), and utilities (values or preferences). The ID model comprises four types of nodes. Decision nodes specify a set of alternatives. Chance nodes represent the key uncertainties in the decision domain. Deterministic nodes represent either constants or intermediate calculations. Value nodes represent the criteria used to make the decisions.

TWO ALGORITHMS THAT LEARN DNF BY DISCOVERING RELEVANT FEATURES

Corrigendum.

Increased demand for natural gas in Venezuela has led to an intensified search for additional supply from mature oil fields in Eastern Venezuela. The search has involved the ranking of oil reservoirs that could be converted to gas producing reservoirs. Unreliable reservoir and historical production data introduced high uncertainties to the ranking based on gas reserves only. A fuzzy model was therefore constructed and used for ranking 45 reservoirs. Eight input variables were used to evaluate each of the reservoirs. The variables included remaining petroleum reserves, remaining gas reserves, gas cap volume, oil production per psi, gas production per psi, flow capacity, storage capacity and the distance to existing gas transmission lines. Membership functions were developed for each variable and 20 fuzzy rules were used to capture the non-linear relationship amongst the input and output variables. The output variable was represented by 5 membership functions and presented in a 0 - 1 range after defuzzification. The reservoirs were then ranked on the basis of their output range values. The results from the fuzzy model were compared to those obtained from a conventional methodology using a Decision Tree - Monte Carlo model. In this conventional model, the 8 input variables were normalized and represented as events in a decision tree. The variables were then weighted by using Monte Carlo simulation to generate the mean probability of each event occurring. A rolling netback calculation produced an output value for each reservoir. The output values were used to rank the 45 reservoirs. The paper concludes that although the two models handled the uncertainties of the impact of the 8 input variables on the output variable, the fuzzy model best capture the vagueness in the non-linear relationships between these variables. Introduction Venezuela has 147.5 TCF of gas reserves with 91% as associated gas and the remaining 9% as non-associated gas. In the Eastern part of the country, gas reserves are about 105 TCF with over 94% as associated gas. Gas demand is 1.92 BCF per day with a 7.5% annual growth rate. There is an on-going intensive search for gas to enhance the national gas supply. This search involved the conversion of mature oil reservoirs to gas producing reservoirs. Budget constraints limited the number of mature reservoirs that could be converted. Therefore, the reservoirs were ranked on the basis of Remaining Gas Reserves and the top ranked reservoirs were assumed to have the best gas opportunities. However, there was a high degree of uncertainty with the gas data. Furthermore, some of the reservoirs with large Remaining Gas Reserves had very low reservoir pressure and flow capacity. Others were located very far from any gas pipelines and surface infrastructure. There was therefore a need to use more sophisticated methods to rank the reservoirs. Conventional ranking techniques include the Net Present Value (NPV), the Internal Rate of Return (IRR), the Expected Monetary Value (EMV), Value of Information (VOI) and hydrocarbon volume such as the Remaining Gas Reserves. 1 Moore and Tucker 2 used NPV and the Economic Chance Factor to rank exploration opportunities. Zammerilli 3 used the EMV to rank horizontal well locations in tight, naturally fractured reservoirs. Variables such as reservoir pressure, net thickness, success ratio, well length, drainage area, azimuth, well radius and topography were fixed at the beginning of the project. Variables like gas price and drilling costs were allowed to vary. Kelkar 4 also used EMV to rank independent projects in the presence of uncertainties. Demirmen 5 used Decision Tree and the Value of Information (VOI) analyses for screening and ranking subsurface appraisal projects. VOI captures uncertainties arising from volumetric parameters and hydrocarbon quality parameters. Gottardi et al 6 gave a good summary of the new conventional tools for ranking R & D projects using multivariate analysis.

Conversion of a colorectal cancer guideline into clinical decision trees with assessment of validity

Chapter 5 - Decision Analysis Fundamentals

Motivation and Objectives Neuroblastoma (NB) is the most common pediatric solid tumor characterized by clinical and molecular risk factors. The mortality is about fifty percent and this makes exploration of new and more effective risk factors for improving stratification mandatory. Hypoxia is a condition of low oxygen tension occurring in poorly vascularized areas of the tumor associated with poor prognosis. We had previously defined a robust gene expression signature measuring the hypoxic component of NB tumors (NB-hypo) that is a novel, independent risk factor (Fardin et al., 2010). Integrating classical risk factors with NB-hypo could improve the stratification of NB patients. We wanted to develop a prognostic classifier of NB patients’ outcome blending existing knowledge on clinical and molecular risk factors with the prognostic NB-hypo signature. Furthermore, we were interested in the decision tree classifier that outputs explicit rules easily translated into the clinical setting. Methods A total of 182 NB patients were enrolled on the bases of availability of gene expression profile by Affymetrix GeneChip HG-U133plus2.0, clinical and molecular information. NB tumor stage was defined according to the International NB Staging System (INSS). Age at diagnosis was dichotomized as greater or equal than 1 year and less than one year. MYCN status was amplified or normal. Good and poor outcome were defined as the patient’s status alive or dead 5 years after diagnosis respectively. The risk group was assigned according to the International Neuroblastoma Risk Group (INRG) Consensus Pretreatment Classification Schema. The 182 NB patients cohort was clustered in High and low hypoxia by k-means analysis of the 62 probsets constituting the NB-hypo signature previously described to measure tumor hypoxia (Fardin et al., 2009). We utilized the k-means algorithm implemented in the WEKA software (Hall et al., 2009) setting up number of clusters to 2, 500 iterations, preserving instances order and using Manhattan distance. The classification was performed by induction of decision trees. We utilized the Weka J48 implementation of the popular C4.5 algorithm (Kotsiantis, 2007; Murthy, 1998) and we set up the following options: pruning parameter was 0.25, pruning method was sub-tree raising and minimum number of instances per leaf was 2. Each leaf of the decision tree classifier identifies a non overlapping group of patients and each decision node identifies a branch which splits the dataset. We utilized Fisher’s exact test to measure the statistical significance of groups and branches. Fisher’s test was utilized in the context of decision trees to design a top-down approach to prune out non statistically significant branches (Liu et al., 2010). For each leaf we counted the number of correctly classified (named n) and the number of incorrectly classified instances (named m). We considered the marginal totals y and ¬y which represent poor and good outcome patients respectively. We designed a 2x2 contingency table of the two possible outcomes (Good or Poor) against the number of instances included in a give leaf and the remaining instances. Application of the Fisher exact test to this table generates a p value giving the probability of observing 2x2 table, or more extreme tables, knowing the marginal totals (y, ¬y) and assuming independency among the patients in a specific leaf and those in other leaves. Results and Discussion Patients were stratified in good and poor outcome on the bases of the following risk factors: Age at diagnosis, INSS stage, MYCN status and NB-hypo. The algorithm generated a decision tree classifier composed by 3 decision nodes and 7 leaves covering 87% of non overlapping good outcome patients and 100% of non overlapping poor outcome patients. Each path from the root to a leaf utilizes some, but not all, considered risk factors. Interestingly NB-hypo was included in the decision node that stratified stage 3 tumors demonstrating its usefulness in NB patients’ stratification. The leaves classifying good outcome patients had the very low error of 2% indicating a good performance of the algorithm in predicting this class. In contrast, the classification of poor outcome patients produced the leaf with the highest error of 13%. This leaf includes stage 4 tumors that are traditionally difficult to stratify by any known risk factor. To test statistical significance of the splits performed by the algorithm and the groups of patients, we utilized the Fisher’s exact test with a confidence set at 95%. The results showed that the groups obtained at each split were statistically significant. Furthermore, analysis of single groups of patients identified by leaves demonstrated that some, but no all reached the significance threshold. The significant leaves included the NB-hypo among the utilized risk factors. These results further strengthen the value of NB-hypo in predicting patients’ outcome. Lack of significance was often associated with a rather low number of patients in the leaf. This is a limitation of the divide-and-conquer approach of the algorithm, applied to relatively small patients’ cohorts, that recurrently splits the dataset. We then assessed the concordance of the predictions with INRG risk assessment. High Risk patients were correctly included in the leaves classifying poor outcome patients and Low Risk patients mapped correctly in the good outcome leaves. Interestingly, NB-hypo generated a leaf identifying a new group of poor outcome patients, sharing the high NB-hypo, whose characteristic fell into both High and Intermediate Risk. We collected and analyzed the results of 1000 10-fold cross validations and we observed that most classifiers had 7 leaves and only 5 out of 10^4 deviated from this pattern. The recurrence of 7 leaves demonstrated the high stability of the decision tree classifier that we generated. Analysis of the pruning parameters revealed optimal performance in the range of 0.1-0.3 in line with what used in this study. The path to reach each leaf can be easily transposed into a “if…than…” rule that, in turn provides an easy readout of the classifier, precious for translating the classification into the clinical setting. In conclusion, we demonstrated that the decision tree algorithm C4.5 can derive explicit rules for NB patients stratification if classical risk factors are blended with the NB hypo signature. These rules are statistically significant and quite stable and suitable to be conveyed to the clinic to design new therapies perhaps taking hypoxia into consideration as a potential target. Acknowledgements The work was supported by the Fondazione Italiana per la Lotta al Neuroblastoma, the Associazione Italiana per la Ricerca sul Cancro, the Società Italiana Glicogenosi, the Fondazione Umberto Veronesi and the Ministero della Salute Italiano. Davide Cangelosi and Fabiola Blengio are recipients of a fellowship from the Fondazione Italiana per la Lotta al Neuroblastoma. References Fardin P, Barla A, Mosci S, Rosasco L, Verri A, Varesio L. (2009) The l1-l2 regularization framework unmasks the hypoxia signature hidden in the transcriptome of a set of heterogeneous neuroblastoma cell lines. BMC Genomics, 10:474. doi:10.1186/1471-2164-10-474 Fardin P, Barla A, Mosci S, Rosasco L, Verri A, et al. (2010) A biology-driven approach identifies the hypoxia gene signature as a predictor of the outcome of neuroblastoma patients, Journal of Molecular Cancer 9:1. 185. doi:10.1186/1476-4598-9-185 Hall M, Eibe F, Holmes G, Pfahringer B, Reutemann P, Witten IH. (2009) The WEKA Data Mining Software: An Update: SIGKDD Explorations. doi: 10.1145/1656274.1656278 Kotsiantis S.B. (2007) Supervised Machine Learning: A Review of Classification Techniques. Informatica 31:249-268. Liu W, Chawla S, Cieslak D, Chawla N. (2010) A Robust Decision Tree Algorithm for Imbalanced Data Sets. In: SDM. 766-777. Murthy S.K. (1998) Automatic Construction of Decision Trees from Data: A Multi-Disciplinary Survey, Data Mining Knowledge Discovery 2:4. 345-389. doi: 10.1023/A:1009744630224

Decision Model for Acute Appendicitis Treatment With Decision Tree Technology—A Modification of the Alvarado Scoring System

Biceps Tenodesis Has Greater Expected Value Than Repair for Isolated Type II SLAP Tears: A Meta-analysis and Expected-Value Decision Analysis

We investigate the problem of learning Boolean functions with a short DNF representation using decision trees as a concept description language. Unfortunately, Boolean concepts with a short description may not have a small decision tree representation when the tests at the nodes are limited to the primitive attributes. This representational shortcoming may be overcome by using Boolean features at the decision nodes. We present two new methods that adaptively introduce relevant features while learning a decision tree from examples. We show empirically that these methods outperform a standard decision tree algorithm for learning small random DNF functions when the examples are drawn at random from the uniform distribution.

AimsThis study aimed to clarify the different topographical distribution of tau pathology between progressive supranuclear palsy (PSP) and corticobasal degeneration (CBD) and establish a machine learning‐based decision tree classifier.MethodsParaffin‐embedded sections of the temporal cortex, motor cortex, caudate nucleus, globus pallidus, subthalamic nucleus, substantia nigra, red nucleus, and midbrain tectum from 1020 PSP and 199 CBD cases were assessed by phospho‐tau immunohistochemistry. The severity of tau lesions (i.e., neurofibrillary tangle, coiled body, tufted astrocyte or astrocytic plaque, and tau threads) was semi‐quantitatively scored in each region. Hierarchical cluster analysis was performed using tau pathology scores. A decision tree classifier was made with tau pathology scores using 914 cases. Cross‐validation was done using 305 cases. An additional ten cases were used for a validation study.ResultsCluster analysis displayed two distinct clusters; the first cluster included only CBD, and the other cluster included all PSP and six CBD cases. We built a decision tree, which used only seven decision nodes. The scores of tau threads in the caudate nucleus were the most decisive factor for predicting CBD. In a cross‐validation, 302 out of 305 cases were correctly diagnosed. In the pilot validation study, three investigators made a correct diagnosis in all cases using the decision tree.ConclusionRegardless of the morphology of astrocytic tau lesions, semi‐quantitative tau pathology scores in select brain regions are sufficient to distinguish PSP and CBD. The decision tree simplifies neuropathologic differential diagnosis of PSP and CBD.

In this paper, we consider decision trees that use two types of queries: queries based on one attribute each and queries based on hypotheses about values of all attributes. Such decision trees are similar to the ones studied in exact learning, where membership and equivalence queries are allowed. We present dynamic programming algorithms for minimization of the depth and number of nodes of above decision trees and discuss results of computer experiments on various data sets and randomly generated Boolean functions. Decision trees with hypotheses generally have less complexity, i.e., they are more understandable and more suitable as a means for knowledge representation.

There are two very similar problems in development of an oil field related to recompletion or to sidetrack of an existing producing well to an undeveloped horizon or fault block. In both cases, one has drilled and is producing an horizon, and one also knows from exploration drilling that a shallower horizon, or an adjacent fault block is present that is oilbearing. As the first horizon progressively yields its recoverable reserves, corporate attention shifts to the question of producing the remaining horizon in order to bolster cash flow. There is some risk that the recompletion or sidetrack will fail, so there is a chance that one will stop production in the currently producing zone and also fail to get production from the new zone. The economic question of interest concerns the expectation of total recoverable oil and the likely cash flow that could accrue. In other words, the economic potential of the recompletion or sidetrack must be tied to the chances of success and failure. The economic worth of a sidetrack or recompletion are frequently evaluated by using deterministic decision tree analyses to determine the expected monetary value (EMV) generated by the new expenditure. This technique can be extended in several ways as is shown here. Firstly, with deterministic inputs into the decision tree, one can estimate the uncertainty in the EMV, and the probability of exceeding some minimum value. Secondly, with uncertainty in the inputs, such as cost and production, one can calculate the full net present value distribution, both approximately and using Monte Carlo simulation. The second case provides a realistic view of the uncertainty in the economic potential of the recompletion or sidetrack, given inherent uncertainties in the project. Some examples are presented to illustrate these points succinctly and sharply.

Warning and evacuation are among the most effective ways for saving human lives and properties from landslide dam hazards. A new warning decision model for landslide dam break is developed using Influence Diagrams to minimize the total losses. An Influence Diagram is a simple visual representation of a decision problem. It analyzes the qualitative (causal) relationships between the variables via a logic diagram and determines the quantitative relationships via conditional probability and Bayes’ theorem. The model is applied for the warning decision-making of the 2008 Tangjiashan landslide dam. The new model unifies the dam failure probability, evacuation, life loss, and flood damage in an Influence Diagram. Besides, a warning criterion is proposed for efficient decision-making. The model is more advanced than the decision tree since the inter-relationships of influence factors are qualitatively analyzed with causality connections and quantitatively analyzed with conditional probabilities. It is more efficient than a dynamic decision-making model (DYDEM) as it can directly calculate the three types of flood loss (i.e., evacuation cost, flood damage, and monetized life loss) and the expected total loss. Moreover, the probabilities of the influence factors leading to known results can be obtained through inversion analysis based on Bayesian theory. The new warning decision model offers an efficient way to save lives from landslide dam breaking and avoid unnecessary expenses from premature warning and evacuation.