![]() In the next sections we define Wald’s 4 SPRT, Hall’s 6 SPRT, and our simple heuristic modifications of these SPRTs. 4 A recent publication on SPRTs is the book on sequential statistics by Govindarajulu, 5 which we shall use repeatedly in this paper. For example, a 1975 textbook on simulation (Kleijnen, 3 pp.503–505) has already discussed the SPRT originally developed by Wald. We claim that SPRTs may be useful in simulation, because most computer systems proceed sequentially. However, until now these methods have not used SPRTs. This simulation optimization may use many statistical methods (see Kleijnen, 1 pp.241–300). In these situations, we may try to estimate which system is optimal. ![]() Actually, the number of systems may be a given small number (e.g., 10), infinite (if continuous input variables define the system), or nearly infinite (if many discrete variables define the system). This need for efficient design and analysis of simulation experiments arises not only if we must choose between two hypothesized values for the mean simulation output (which is the focus of this paper), but also if we must choose among more than two simulated systems. In simulation, we should also strive for efficiency in the case where we need relatively much more computer time to obtain a single observation on the response (or output) of the given simulation model (this case is called “expensive simulation”). Indeed, testing drugs on humans should minimize the number of necessary observations, and SPRTs do so that is, SPRTs are more efficient than classic tests such as the Student’s t-test. While sequential probability ratio tests (SPRTs) are popular in application areas such as the testing of drugs on humans, they are virtually unknown in simulation. For these two experiments, we provide details on their design and analysis these details may also be useful for simulation experiments in general. In experiment #2, we estimate the robustness of these SPRTs for non-normal output. Furthermore, our experiment shows that the most efficient SPRT is Hall’s modified SPRT. Whereas Wald’s SPRT with estimated variance gives too high error rates, Hall’s original and modified SPRTs are “conservative” that is, the actual error rates are smaller than those prespecified (nominal). In experiment #1, simulation outputs are normal. ![]() In this paper, we quantify the performance of the various SPRTs, using several Monte Carlo experiments. A modification uses a fully sequential variance estimator. Biometrika 1962 49: 367–378) developed a SPRT that assumes normal distributions with unknown variances estimated from a pilot sample. Some sequential analogs of Stein’s two-stage test. A modification permits unknown variances that are estimated. Ann Math Stat 1945 16: 117–186) allows general types of distribution, including normal distributions with known variances. Sequential tests of statistical hypotheses. For this case, the classic SPRT of Wald (Wald A. To change this situation, we review SPRTs for the simplest case namely, the case of choosing between two hypothesized values for the mean simulation output. However, until now simulation analysts have ignored SPRTs. All subjects Allied Health Cardiology & Cardiovascular Medicine Dentistry Emergency Medicine & Critical Care Endocrinology & Metabolism Environmental Science General Medicine Geriatrics Infectious Diseases Medico-legal Neurology Nursing Nutrition Obstetrics & Gynecology Oncology Orthopaedics & Sports Medicine Otolaryngology Palliative Medicine & Chronic Care Pediatrics Pharmacology & Toxicology Psychiatry & Psychology Public Health Pulmonary & Respiratory Medicine Radiology Research Methods & Evaluation Rheumatology Surgery Tropical Medicine Veterinary Medicine Cell Biology Clinical Biochemistry Environmental Science Life Sciences Neuroscience Pharmacology & Toxicology Biomedical Engineering Engineering & Computing Environmental Engineering Materials Science Anthropology & Archaeology Communication & Media Studies Criminology & Criminal Justice Cultural Studies Economics & Development Education Environmental Studies Ethnic Studies Family Studies Gender Studies Geography Gerontology & Aging Group Studies History Information Science Interpersonal Violence Language & Linguistics Law Management & Organization Studies Marketing & Hospitality Music Peace Studies & Conflict Resolution Philosophy Politics & International Relations Psychoanalysis Psychology & Counseling Public Administration Regional Studies Religion Research Methods & Evaluation Science & Society Studies Social Work & Social Policy Sociology Special Education Urban Studies & Planning BROWSE JOURNALSīecause computers (except for parallel computers) generate simulation outputs sequentially, we recommend sequential probability ratio tests (SPRTs) for the statistical analysis of these outputs.
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