IN ANALYZING A TEMPORAL DATA SET FROM A CONTINUOUS VARIABLE, DIFFUSION PROCESSES CAN BE SUITABLE UNDER CERTAIN CONDITIONS, DEPENDING ON THE DISTRIBUTION OF INCREMENTS. WE ARE INTERESTED IN PROCESSES WHERE A SEMI-PERMEABLE BARRIER SPLITS THE STATE SPACE, PRODUCING A SKEWED DIFFUSION THAT CAN HAVE DIFFERENT RATES ON EACH SIDE. IN THIS WORK, THE ASYMPTOTIC BEHAVIOR OF SOME BAYESIAN INFERENCES FOR THIS CLASS OF PROCESSES IS DISCUSSED AND VALIDATED THROUGH SIMULATIONS. AS AN APPLICATION, WE MODEL THE LOCATION OF SOUTH AMERICAN SEA LIONS (OTARIA FLAVESCENS) ON THE COAST OF CALBUCO, SOUTHERN CHILE, WHICH CAN BE USED TO UNDERSTAND HOW THE FORAGING BEHAVIOR OF APEX PREDATORS VARIES TEMPORALLY AND SPATIALLY.

A COMMON PROBLEM IN THE PRACTICE OF REGRESSION ANALYSIS IS MULTICOLLINEARITY. ITS NEGATIVE EFFECTS ON THE LEAST SQUARES ESTIMATOR ARE WELL KNOWN. A NUMBER OF SHRINKAGE ESTIMATORS HAVE BEEN DEVELOPED TO CORRECT THIS PROBLEM, PROMINENT AMONG THEM IS RIDGE REGRESSION. WE DISCUSS THE BAYESIAN INTERPRETATION OF THE ESTIMATOR AND IN PARTICULAR WE PROPOSE A BAYESIAN STRATEGY TO SELECT THE SHRINKAGE PARAMETER. WE PROVIDE AN EXAMPLE OF THE RESULTING RIDGE REGRESSION ESTIMATOR. ALSO, TO COMPARE THE ESTIMATION AND PREDICTION PROPERTIES OF THE BAYESIAN SHRINKAGE RIDGE REGRESSION WITH OTHER WELL KNOWN RIDGE REGRESSION AND ORDINARY LEAST SQUARES ESTIMATORS, WE PERFORM A SIMULATION STUDY.

THIS PAPER DISCUSSES A NEW APPROACH FOR SYSTEM RELIABILITY PARAMETER. ACTUALLY, WE PROVIDE EXPECTATION BAYESIAN (E-BAYESIAN) ESTIMATION OF SYSTEM RELIABILITY FOR SERIES AND PARALLEL SYSTEMS BASED ON PASCAL DISTRIBUTION. THE DEFINITION AND PROPERTIES OF E-BAYESIAN ESTIMATION ARE GIVEN. ALSO WE APPLIED THREE DIFFERENT DISTRIBUTIONS FOR THE PARAMETERS IN PRIOR DISTRIBUTION TO INVESTIGATE THE INFLUENCE OF THE DIFFERENT PRIOR DISTRIBUTIONS ON THE E-BAYESIAN ESTIMATION. THE CONFIDENCE INTERVALS OF R, BASED ON E-BAYESIAN AND BOOTSTRAP METHODS, ARE DEVELOPED. THE PERFORMANCE OF THESE CONFIDENCE INTERVALS IS STUDIED THROUGH EXTENSIVE SIMULATION. TWO NUMERICAL PRACTICAL EXAMPLES, IS PRESENTED TO ILLUSTRATE THE IMPLEMENTATION OF THE PROPOSED PROCEDURE.

THE MAIN PURPOSE OF THIS PAPER IS TO PROVIDE A METHODOLOGY FOR DISCUSSING THE FUZZY. THIS APPROACH WILL BE USED TO CREATE THE FUZZY E-BAYESIAN AND HIERARCHICAL BAYESIAN ESTIMATIONS OF KUMARASWAMY DISTRIBUTION UNDER CENSORING DATA BY INTRODUCING AND APPLYING A THEOREM CALLED "RESOLUTION IDENTITY" FOR FUZZY SETS. IN OTHER WORDS, MODEL PARAMETERS ARE ASSUMED TO BE FUZZY RANDOM VARIABLES. THE AUTHORS ALSO USE COMPUTATIONAL METHODS WU 2003. FOR THIS PURPOSE, THE ORIGINAL PROBLEM IS TRANSFORMED INTO A NONLINEAR PROGRAMMING PROBLEM WHICH IS THEN DIVIDED UP INTO FOUR SUB-PROBLEMS TO SIMPLIFY COMPUTATIONS. FINALLY, THE RESULTS OBTAINED FOR THE SUB-PROBLEMS CAN BE USED TO DETERMINE THE MEMBERSHIP FUNCTIONS OF THE FUZZY E-BAYESIAN AND HIERARCHICAL BAYESIAN ESTIMATIONS.