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MCPherson_et_al

Course: CPSY 8101, Fall 2008
School: U. Memphis
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Psychology's Counseling Ambivalent Relationship With Master's-Level Training Robert H. McPherson Stewart Pisecco University of Houston Nancy S. Elman University of Pittsburgh Margaret Crosbie-Burnett University of Miami Thomas V. Sayger University of Memphis Inspired by efforts by those who seek to redefine the practice of psychology as a master'slevel specialty, the authors examine counseling psychology's...

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Psychology's Counseling Ambivalent Relationship With Master's-Level Training Robert H. McPherson Stewart Pisecco University of Houston Nancy S. Elman University of Pittsburgh Margaret Crosbie-Burnett University of Miami Thomas V. Sayger University of Memphis Inspired by efforts by those who seek to redefine the practice of psychology as a master'slevel specialty, the authors examine counseling psychology's heightened ambivalence regarding master's-level training. First, they present a historical review of this issue. Next, they discuss current social and political pressures that, they suggest, have resulted in renewed tensions in the training of master's-level practitioners for the field of counseling psychology. They conclude with specific recommendations regarding the manner in which counseling psychology should (a) train master'-level providers, (b) attempt to document the added value doctoral training, and (c) politically respond to this issue. Within the American Psychological Association (APA), the master'sversus doctoral-level issue has traditionally been conceptualized as a debate regarding the allocation of responsibilities. Although the field of psychology has at times varied in its stance, there is a great deal of consistency with the position that (a) master's-level professionals should work under the supervision of psychologists and be assigned duties commensurate with their education and (b) that the doctorate is the requisite degree for the title of psychologist and independent practice (APA, 1947; APA Committee on Subdoctoral Education, 1955). Consequently, for many psychologists, distinctions between doctoral- and master's-level professionals seem self-evident: The psychologist is the primary provider of psychological services, and the person with a master's degree is a supervised extender of these services. Within the subspecialty of counseling psychology, a more specific debate transpired that focused on defining appropriate roles, responsibilities, and McPherson et al. / MASTER'S-LEVEL / September THE COUNSELING PSYCHOLOGISTTRAINING 2000 Correspondence concerning this article and requests for reprints should be addressed to Robert H. McPherson, chairperson of the Department of Educational Psychology, University of Houston, 4800 Calhoun Rd., Houston, TX 77204-5874; e-mail: bmcph@uh.edu. THE COUNSELING PSYCHOLOGIST, Vol. 28 No. 5, September 2000 687-700 2000 by the Division of Counseling Psychology. 687 688 THE COUNSELING PSYCHOLOGIST / September 2000 professional titles for master's- and doctoral-level providers (Fretz & Simon, 1992). These discussions represented a period of identity formation for counseling psychology, which led to the embracing of (a) the tenets of a scientistprofessional training model and (b) the APA's standard of the doctoral degree for independent practice. In turn, master's-level graduates in counseling have defined themselves as members of a separate profession and are more likely to identify professionally with the standards and values endorsed by the American Counseling Association (ACA). Today, there is a decreased tension between the two related but distinctive professions of counseling and counseling psychology, as illustrated by our subspecialty's close affiliation with master's-level counselors and their training programs in many colleges of education (McPherson & Sayger, 1997). Recently, however, a subgroup of master's-level practitioners have launched aggressive efforts to change established psychology licensure so that they may call themselves psychologists and practice independently (APA, 1999; Northamerican Association of Masters in Psychology [NAMP], 1999). The effect of such an amendment would redefine the practice of psychology as a subdoctoral profession, establish an indifference to the distinctiveness of doctoral training for psychological practice, and devalue the scientist-practitioner training model. As a consequence, we suggest that the more contemporary issue has shifted from a concern related to the allocation of duties to a justification of distinctiveness. Thus, as we move into the next millennium, the field of counseling psychology is once again faced with the dilemma of reexamining its role in the training of master's-level clinicians and the implications of that relationship for the future of the field. The purpose of this article is to (a) provide a historical overview, (b) examine the social and political pressures that are shaping this issue, (c) discuss implications for training, and (d) propose specific recommendations. HISTORICAL OVERVIEW OF THE ROLE OF MASTER'S-LEVEL TRAINING IN COUNSELING PSYCHOLOGY Master's-level training has long been a source of concern and, at times, debate within the field of psychology (Moore, 1954; Woods, 1971). Although the history of this issue can be traced back several decades, it has long been the position of the APA that the minimal educational requirement for the granting of the title psychologist should be a doctoral degree (APA, 1947; APA, 1987a; Armstrong, 1947, Hess, 1977; Robiner, Arbisi, & Edwall, 1994). This opinion was reflected in the model act for state licensure of psy- McPherson et al. / MASTER'S-LEVEL TRAINING 689 chologists (APA, 1987a) and has been supported each time it has been raised at various graduate training conferences (APA, 1987b; Woods, 1971). Just as APA has maintained that the doctoral degree is the requisite level of training for a psychologist, APA has historically suggested that individuals with the master's degree are best prepared to serve as psychological technicians (APA Committee on Subdoctoral Education, 1955). The responsibilities of psychological technicians, who would work under the supervision of psychologists, could include a variety of duties such as (a) administering and interpreting psychological tests, (b) guidance counseling, (c) delivering psychoeducational instruction, and (d) constructing basic statistics and tests (APA Education and Training Board, 1952). The Committee on Subdoctoral Education also recommended a specific 2-year training curriculum, with the goal of providing education in the basic areas of psychology and developing important technical skills (APA Committee on Subdoctoral Education, 1955). Their recommendations were largely based on the belief that there is and will continue to be a great social demand for psychological services and that there are important duties that do not require the doctoral degree. The committee also sought to recommend a curriculum that would eliminate existing ambiguity related to the quality of various master's degree programs and foster an inclusive atmosphere for master's-level technicians within the field of psychology and APA. This is an important point because it was a departure from earlier suggestions that graduate programs in psychology discontinue the granting of a master's degree for "lower level" work (APA, 1947). The committee's position on subdoctoral training was generally reaffirmed at most subsequent graduate training conferences. However, during the late 1960s and early 1970s, there was a serious departure from the traditional platform, which led to the reconceptualization of graduate training at the Vail conference in 1973. Instead of continuing to support the graded progression of training and complexity of duties afforded to doctoral-level psychologists, Korman (1974) reported that the idea of a career ladder should be replaced by the more inclusive concept of a career lattice--an open-ended occupational structure which encourages broader skill acquisition at any given level in addition to upward professional movement; this would encourage continued training and development, leading to functional differentiation of skills at every performance level. (p. 443) Although the Vail statement continued to support the differentiation of skill levels, the concept of an inclusive model was a departure from the previously described graded approach to training. Bickman (1987) attributes the change in philosophy to the social atmosphere of the early 1970s. More specifically, 690 THE COUNSELING PSYCHOLOGIST / September 2000 he suggested that the previous training model was rejected because it was a "product of the establishment." Indeed, Korman's (1974) statement that there was a general dissatisfaction with psychology's response to the social issues of the times is consistent with Bickman's (1987) hypothesis. As would be expected, there was a great deal of concern regarding the conference's recommendations, and ultimately, the suggestion that master'slevel clinicians receive increased recognition was rejected by the APA (Bickman, 1987). More consistent with previous statements, the subsequent national graduate education conference at the University of Utah in Salt Lake City (APA, 1987b) proposed resolutions that were framed within the more typical career ladder model. Although specific guidelines for master's-level training were not articulated, it was proposed that a national conference focusing on this issue be convened (APA, 1987b); however, now 12 years later, the APA has yet to formally sponsor or endorse such a conference. Although various aspects of this issue have been debated, there seems to be some consistency in psychology's stance toward the distinction between psychologists and master's -level providers. First, it has been accepted within the field of psychology that the title of psychologist should be afforded exclusively to individuals with a doctorate. Second, master's-level clinicians provide a service for which there are real and necessary demands. Finally, the work of these individuals should be under the supervision of doctoral-level psychologists. Although the field of psychology typically is united in its stance toward master's-level training and the role of counselors, there are powerful social and political forces that have led to more contemporary challenges to the previously established distinctions between master's- and doctoral-level professionals. SOCIAL AND POLITICAL FACTORS One obvious social factor, which has stirred tension regarding the doctoral and master's-level service providers, is the ever-growing presence of managed care. Although the term insurance elicits a strong negative reaction today (Phelps, Eisman, & Kohout, 1998), there was a time when psychologists embraced the concept. Indeed, during the early years of managed care, Belar (1989, as cited in Fretz & Simon, 1992) reported that there was a 300% increase in the number of health maintenance organizations (HMOs) offering comprehensive mental health services. Consequently, there was speculation that the increase would result in more demand for mental health clinicians and greater competition and tension between master's and doctoral-level providers (Anderson, Parente, & Gordon, 1981; Fretz & Simon, 1992). McPherson et al. / MASTER'S-LEVEL TRAINING 691 Contributing to this tension was the fact that until the 1990s, most states did not have independent licensing laws for master's-level clinicians (Fretz & Simon, 1992). Master's-level providers, in the private sector, were then left to seek the credential of a psychological examiner and/or associate. Although these individuals were functioning within the range of APA's earlier stated expectations (see APA Committee on Subdoctoral Education, 1955), there was a growing dissatisfaction with the limitations of that particular license (Trent, 1993). Many master's-level practitioners felt indentured to their supervising psychologists, who were enjoying handsome incomes from the services provided by the supervisee. Others claimed that supervision was nonexistent or superfluous to their function, and some suggested that their competency exceeded that of their supervisors. More recently, trends in managed care company practices have led to the denial of payment of claims submitted for services provided by supervised personnel, whether these practitioners are licensed or otherwise credentialed as psychological associates (or under other titles). In addition, psychologists are sometimes but one of a few identified professional provider groups eligible to provide and receive certain reimbursement in certain state or federal health care programs. In an effort to disentangle themselves from the restrictions of supervisory relationships and to extend their presence in the mental health field, master'slevel clinicians have joined the lobbying efforts of master's-level counselors for the right to practice independently. In fact, these efforts have been very successful, as evidenced by legislation in 46 states, which allows for independent practice by master's-level professionals (National Board for Certified Counselors, 1999). This legislation generally recognizes an individual's ability to function independently as a licensed professional counselor or under an equivalent title (e.g., mental health counselor, psychotherapist, etc.). Individuals with this credential generally represent a heterogeneous group of mental health practitioners. Although the managed care movement was an important economic catalyst, which we suggest eventually led to political lobbying for the right of master's-level providers to practice independently, it is also our opinion that there are other critical economic and social pressures that should be acknowledged. For instance, psychopathology affects individuals across the range of socioeconomic levels and is not limited to any particular race or ethnic population (Kessler, 1989). However, it has been long recognized that several groups of individuals continue to suffer from restricted access to mental health services (Kessler, 1989). The abundance of master's-level professionals represents one type of provider who could potentially offer services to individuals who may not otherwise have access. However, this assertion is only speculative. Research is necessary to determine distribution of mental health service providers by geographic location, job setting, and treatment 692 THE COUNSELING PSYCHOLOGIST / September 2000 population expertise. It is also necessary to determine racial and gender representation of both counseling and psychological service providers by level of training in accordance to these distributions. In addition, it is important to note that individuals from disadvantaged backgrounds may be drawn to the economic advantages of a 2-year versus 5-year degree program. Similarly, the profusion of master's programs allows for widespread educational opportunities for individuals who are restricted to areas without doctoral degree programs and for whom relocating is financially prohibited. Thus, the master's degree could be considered an attractive and financially feasible alternative for many individuals, resulting in very real benefits to society through greater access to mental health services. The creation of independent practice legislation for master's-level providers resulted in decreased tension between doctoral and master's-level clinicians and created recognizable and professionally acknowledged distinctions between the duties of a psychologist versus those of a counselor (Fretz & Simon, 1992). Although one may speculate that the right to practice independently would appease the master's-level provider, a subgroup of individuals (e.g., members of NAMP) continue to aggressively lobby for additional practice rights and the title of psychologist (APA, 1999; NAMP, 1999; Saeman, 1997). This group does not define itself as professional counselors and holds passionately to the notion that they were trained by psychologists to practice psychology (NAMP, 1999). Although psychologists and other counselor-oriented organizations (e.g., ACA) clearly understand the distinctions between professionals with master's degrees versus those with doctorates, some state legislatures have begun to question the need for differentiated licensing of mental health professionals on the basis of degree title alone (McPherson, 1997). In the past, psychology has responded to questions regarding the legitimacy of distinctions between master's- and doctoral-level providers by empirically examining the advantages of doctoral training, with most studies concluding that there were no significant therapeutic outcome differences between the two levels of training (Elman & Crosbie-Burnett, 1997). Unfortunately, many have concluded that the few studies that have addressed differences in clinical practice are inconclusive, contradictory, or methodologically flawed (Berman & Norton, 1985; Christensen & Jacobson, 1994; Dawes, 1994; Hill, Charles, & Reed, 1981; Lumpkin, 1997; Mallinckrodt & Nelson, 1991; Robiner, Arbisi, & Edwall, 1994). However, a consistent pattern of differences between master's- and doctoral-level professionals has been documented on the Examination for Professional Psychology Practice (EPPP) (Shrader, 1980; Terris, 1973). More specifically, master's-level professionals account for the vast majority of failures on the EPPP and typically earn lower scores than doctoral-level McPherson et al. / MASTER'S-LEVEL TRAINING 693 psychologists. They also note that the pass rates for master's-level clinicians are well below the 80% rate more typical of psychologists (Robiner et al., 1994). Although some may argue that the use of the EPPP is not appropriate because many master's-level professionals seek licensure through other credentials or that it is a measure of knowledge rather than competence, we contend that it is particularly relevant because obtaining the right to the title of psychologist is an important goal for a significant subgroup of master's-level professionals (APA, 1999; NAMP, 1999). Unfortunately, whereas counseling psychology has focused on parity with clinical psychology, the national movement by master's-level professionals has received relatively little attention. Consequently, we contend that psychology and, especially, counseling psychology has to consider the implications of this issue when examining their role in the training of master's students today and in the next millennium. IMPLICATIONS FOR THE TRAINING OF MASTER'S-LEVEL PROFESSIONALS One clear implication of the current social and political atmosphere is that there exists a very real threat to APA's long-standing position that the title of psychologist be afforded solely to individuals with the doctoral degree. In turn, it is likely that arguments disavowing the privileges of master's-level professionals to practice independently will continue. However, we suggest that the independent practice issue has largely been resolved in that 46 states have legislation that recognizes the rights of master's-level providers to practice without supervision. In addition, we contend that it is time to concede the point that there is a great social need for the delivery of mental health services that psychiatrists and psychologists, alone, cannot meet. Therefore, we believe that the more important remaining issue is counseling psychology's role in training clinicians with a master's degree in psychology and the latter group's efforts to obtain practice and title parity with psychologists. In reaction to this threat, some may argue that the field should discontinue granting a practice-oriented terminal master's degree. The rationale would be that without a degree in psychology, these individuals would have a more difficult time lobbying the legislature for the title of psychologist. Indeed, this possibility has been raised before (APA, 1947), and others have asked the question, "Is there a place for the master's-level professional in counseling psychology?" (Watkins & Schneider, 1990). Watkins and Schneider's (1990) question is particularly given relevant today's political atmosphere, and it is especially difficult to answer given counseling psychology's relationship with master's training programs. As 694 THE COUNSELING PSYCHOLOGIST / September 2000 previously indicated, counseling psychology has long maintained administrative and training linkages with master's-level training programs in counseling, counselor education, or counseling psychology (McPherson, Crosbie-Burnett, Elman, & Sayger, 1997). Although this association may not be as important to those programs housed within departments of psychology, the relationship is vital for those units assigned to colleges of education. For instance, master's programs generate a significant amount of revenue for both the college and university by commonly admitting relatively large numbers of students (Elman & Crosbie-Burnett, 1997; R. Goodyear, personal e-mail communication, October, 1997). More specifically, master's programs in counseling admitted, on average, 30 students for the fall of 1996 (APA, 1999). In contrast, clinical psychology programs admitted, on average, 18 students for that same academic year (APA, 1999). We suggest that the higher enrollment rates of counseling master's programs serve to offset the high cost associated with running a doctoral program by compensating for the relatively low enrollment rates more typical of doctoral-level courses. (For example, in 1996, the average number of doctoral students accepted into a counseling psychology program was 8.) Because doctoral programs in clinical psychology are usually assigned to departments of psychology, they financially benefit from the existence of an undergraduate curriculum and hence are unlikely to experience the admissions pressures more typical of programs that do not serve an undergraduate population (e.g., counseling psychology programs in colleges of education). We must also face the fact that there is great demand for master's training (Richert & Fulkerson, 1987). Data from APA indicated that on average, a master's program in counseling received 112 applicants for admission in 1996. As would be expected, that number was higher than the average number of applicants to master's-level clinical programs, which was 56. It is surprising that the average number of applicants to master's counseling programs was also greater than the average number of applicants to master's programs in school psychology, which was 34 (APA, 1999). It is safe to assume that the applicants to a master's counseling program would not cease applying if training at the master's level was discontinued. Rather, individuals would likely apply and receive training elsewhere. Darley, Elliott, Hathaway, and Paterson (1948) made the following similar prediction 50 years ago: If, by our actions, we shun responsibility for MA [master's] training, we shall soon see it taken over by education, social work, engineering, and business schools, without assurance that such programs will include sufficient basic psychotechnological training to insure competence on the job. (p. 55) McPherson et al. / MASTER'S-LEVEL TRAINING 695 The other issue is that the field of psychology probably is best qualified to train master's-level professionals. From a social perspective, ending master'slevel training would be the academic equivalent of the school-yard tactic of taking our ball and going home. Although it is easy to become entrapped in adversarial debates about doctoral- and master's-level issues, we must consider the best interests of the field and those of the communities for whom our students (master's and doctoral graduates) will provide services. Finally, it is important to recognize the long-term implications of any amendment that would grant to master's-level providers the title of psychologist. Obviously, any such revision to the licensing act would result in the practice of psychology shifting to a subdoctoral specialty. Not only does this shift represent a challenge to psychology's inherent right to define its legitimate entry-level educational requirements but it is also a serious threat to the field's training model. Adhering to the principles of a scientist-practitioner training model dictates that psychologists acquire a foundation in both the practice and legitimate science of the field. As educators, we understand that this requires a dedication, by the student and university, to engage in a comprehensive discourse and carefully planned exposure to advanced research techniques, theory, and principles of application. We believe that a 2- or 3-year curriculum is not sufficient to provide a student with the skills necessary to be competent in both the practice and science of the field. MASTER'S-LEVEL TRAINING RECOMMENDATIONS Before discussing specific recommendations, we believe it is important to recognize the basic principles that have significantly influenced our current position. First, we firmly believe that the doctoral degree should continue to serve as the requisite educational requirement for the title of psychologist. Second, we suggest that the APA Division 17Counseling Psychology develop a plan of action sensitive to the social and political pressures that are shaping this issue. Third and related to the second point, we recognize the fact that master's-level professionals, with appropriate education and training, can independently and adequately provide a specific, albeit limited, range of services. Thus, our recommendations for counseling psychology represent the following three interdependent categories of action: (a) research, (b) training, and (c) political advocacy. RECOMMENDATIONS SPECIFIC TO RESEARCH Surprisingly absent from research that has examined differences between master's-level providers and psychologists are studies that focus on responsi- 696 THE COUNSELING PSYCHOLOGIST / September 2000 bilities other than counseling. As a field, we recognize that psychologists in the health service domains are trained to provide a variety of duties--hence, the advanced level of education and training experiences. Therefore, we suggest that researchers interested in studying this issue expand the range of their focus. For instance, the ability to approach problems from the scientific method is a critical goal of doctoral-level training and an important point of distinction between master's-level providers and psychologists. Consequently, it is expected that psychologists would be better equipped to understand the clinical implications of empirical research and/or detect flaws in treatment studies. In addition, doctoral students usually receive more advanced training in specific types of assessment techniques than do students at the master's level. Consequently, one would expect that psychologists would be better prepared to identify problems and errors with various types of psychological assessment data than would master's-level providers. Third, we believe that there is a need to conduct functional job analyses regarding the duties and responsibilities of psychologists and master's-level providers to further illustrate identifiable areas of distinction. RECOMMENDATIONS SPECIFIC TO TRAINING Our training recommendations represent an attempt to (a) create a stronger affiliation of terminal master's degree programs with the profession of counseling and (b) provide a mechanism by which there are clear and identifiable distinctions between the training experiences of students in a master's program versus those seeking a doctorate. First, we encourage faculty to consider adopting the title(s) of counselor education or mental health counseling for all terminal master's degree programs. We also suggest that faculty encourage those students who aspire to enter the practice arena with master'slevel training to professionally identify with counselor-oriented professional organizations (e.g., ACA). In addition, we recommend that faculty encourage the Council for Accreditation of Counseling and Related Educational Programs (CACREP) accreditation of these terminal master's degree programs to facilitate quality-of-training standards and promote distinctiveness between these standards and APA accreditation standards for counseling psychology. We also recommend that faculty carefully review their current degree programs at both the master's and doctoral levels with the intention of understanding how the training models produce distinct professionals. We contend that it is important for terminal master's programs to avoid simply increasing the number of credit-hour requirements in reaction to independent license legislation for master's-level providers. Doing so, we speculate, results in a McPherson et al. / MASTER'S-LEVEL TRAINING 697 master's degree that some will argue is simply the training equivalent of an "all-but-dissertation" educational experience. We consider this a particularly important point because academic institutions and professional fields (e.g., law, medicine, psychology) are experiencing increased pressures from the legislature and public to provide evidence that degree programs yield professionals who possess meaningfully distinct skills. Most important, we fear the training curriculum creep of master's-level programs will place heavy emphasis on the practitioner side of the ledger at the expense of scientific training. Quite simply, we fear that not only will the title of psychologist be threatened but also the value of the scientist-practitioner model will be minimized and discounted, ultimately relegating psychological practice and science as technician skill enterprises. RECOMMENDATIONS SPECIFIC TO POLITICAL ADVOCACY The recommendations of this section are based on the experiences of the lead author who has served as president of a state psychological association and has been faced with the issue of master's-level practitioners seeking title and practice parity since 1991. Faculty of counseling psychology programs are encouraged to become active in responding to challenges of psychology title and practice issues. The aggressive political advocacy efforts to redefine the practice of psychology are led by a small but very vocal band of practitioners and trainers. Their battlegrounds are not professional journals but rather the state legislature. In this political arena, title and scope of practice issues abound and are considered "can't win" nuisance issues by politicians. However, practitioners and trainers claiming threats of job loss, increased potential for underserved populations, and underdog status (master's constituents versus state psychology associations) can and have made substantial changes in psychology licensure laws when the opposition is weak. Although the state associations typically take the lead in defending assaults against the doctoral standard for psychology practice, their influence is limited by the fact that some inexperienced state representatives view the interests of psychologists to be self-serving. In contrast, academic psychologists, especially those who train both doctoral- and master's-level providers, are viewed as experts regarding the distinctiveness and relative strengths and weaknesses of each level of training. Representatives have also indicated that they view the opinions of academic psychologists as less biased because we are interested in providing professional opportunities for our students regardless of their levels of education. 698 THE COUNSELING PSYCHOLOGIST / September 2000 It is also important for those who engage in advocacy efforts to avoid political compromises that imply that on-the-job training is equivalent to the formal educational process. For example, one proposal that has surfaced in a number of state legislatures calls for licensing opportunities as a psychologist for individuals with master's-degree training and a specified number of years of postd...

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Stat 8931, Fall 2005 Homework 2 Due Oct 5, 2005Q1 Do a Gibbs sampler for the problem described in Section 10.6 (or whatever the Examples subsection of The Gibbs Update section has turned into) of the lecture notes. The likelihood is a function of t
Minnesota - STAT - 8931
Stat 8931 Fall 2005 Class Notes c 2005 Charles J. Geyer Some More Markov Chain Theory Version of November 16, 2005 Contents1 Markov Transition Matrices 1.1 Eigenvectors Associated with Eigenvalue 1.1.1 Right Eigenvectors . . . . . . . . 1.1.2 Left E
Minnesota - HW - 8931
Stat 8931, Fall 2005 Homework 5 Hint Homework Problem 5 Hint A much more complicated problem from which some techniques for this problem can be stolen was solved by Hobert, J. P. and Geyer, C. J. (1998). Geometric ergodicity of Gibbs and block Gibbs
Minnesota - HW - 8931
Stat 8931 Flu Homework Solution, Part 1Charles J. Geyer October 26, 20051SetupFirst we load the library.> library(mcmc) Then we load the data, copied from Table 1 in Coull and Agresti (2000). > > > > > > data <- read.table("flu.txt", header =
Minnesota - HW - 8931
Stat 8931 Spin Glass Homework Solution, Part 1Charles J. Geyer December 14, 20051SetupRead betas.> > + + + > > >foo <- try(scan("betas.txt") if (inherits(foo, "try-error") { write(c(br, bd), file = "betas.txt") foo <- scan("betas.txt") } n
Minnesota - MATH - 2374
1. Suppose I give you the linear transformationsS(x, y) = (x + y, y, 2x y) T (x, y) = (x + y, 2x 3y) (a) Write both S and T in matrix form.(b) Compute S T .(c) Compute T S.(d) Compute T 1 .(e) Compute T T 1 and T 1 T . Try and explain
Minnesota - MATH - 2374
1. Let c(t) be the parametric equations given by cos(2t) sin(2t) c(t) = t Parameterize the line tangent to the path at time t = 0.2. Find the derivative of g f at the point (0, 1, 0) where g(x, y) = (x3 y, y) f (x, y, z) = (4x + y + z 3 , xy) (
Minnesota - MATH - 2374
1. Find both rst-order partial derivatives of f (x, y) = e3y sin(x) xy 2 ln(3x)g(x, y) =2. Now nd the four second order partial derivatives of f (x, y) and g(x, y).3. A function f (x, y) is harmonic if it satises the Laplace equation: Show that
Minnesota - MATH - 2374
Let S denote the closed cylinder with bottom given by z = 0 and top given by z = 4 and the lateral surface given by x2 + y 2 = 9. Orient S without outward normals. Determine the Surface Integral ydSS1. Is this a vector or a scalar surface integral
Minnesota - MATH - 2283
Quiz 3 Math 2283 TA: Edman February 14, 2008NAME:1. Find an example of a sequence (sn ) for which each term sn is irrational, but lim sn is rational. No proof is required.2. Correct at least two of the errors in the following proof of that limi
Minnesota - TFALL - 2004
HOMEWORK 7 SOLUTIONS The Way of Analysis p. 163: 1.) Suppose f, g are diff. on (a, b) and g(a) = g(b). Show there exists x0 between a and b with f (b) - f (a) f (x0 ) = . g(b) - g(a) g (x0 ) Following the hint, we define, h(x) = (f (b) - f (a) g(x) -
Minnesota - MATH - 4707
Math 4707Introduction to Combinatorics and Graph Theory Homework 2 SolutionsFall 2006Exercises: 6.5.2 Which graphs have Euler circuits? (a) does not, because it is not connected. (b) has Euler circuit a-c-b-f-h-i-l-j-k-g-e-d-c-f-i-j-g-d-a, for
Minnesota - MATH - 5707
TournamentsDrew Armstrong armstron@math.umn.edu September 29, 2006Suppose we have a collection of n commercial products or n sports teams and we want to compare them to determine which is the strongest? or which is the weakest?. Ideally, we would l
Minnesota - STAT - 8102
Stat8102 HW #4 (Due 02/18/09)Problem 1. Suppose that the random variables Y1 , . . . , Yn satisfy Yi = 1 + 2 xi + i , where x1 , . . . , xn are fixed constants, and sufficient statistic for = (1 , 2 , 2 ) . i = 1, . . . , n, are iid n(0, 2 ), 2
Minnesota - STAT - 8102
Stat8102 HW #2 (Due 02/04/09)Problem 1 Suppose that the random variables Y1 , . . . , Yn satisfy Yi = xi + i , where x1 , . . . , xn are fixed constants, and i = 1, . . . , n, are iid n(0, 2 ), 2 unknown.1, . . . , n(a) Find the MLE of and s
Minnesota - STAT - 8111
Final Exam Statistics 8111 Fall 2007 Name: SID:1. Consider the measurable space (, A) where = {1 , 2 , 3 , 4 } and A = {, , {1 , 2 }, {3 , 4 } . Give an example of a function f : which is not A-measurable but such that the composite function
Minnesota - STAT - 8701
Homework 4 STAT 8701 Spring 2007 G ENERAL I NSTRUCTIONS: As usual use Sweave to document your code and report your results. 1. Suppose X Gamma(3/2, 1). Let =E 1 (X + 1) log(X + 3) .(a) Let q(y) = pf1 (y) + (1 p)f2 (y) where 0 < p < 1, f1 is the
Minnesota - CSCI - 4011
SET THEORY 101INHERENT LIMITATIONS OF COMPUTER PROGRAMSCSci 4011A function f : A B is: 1-1 (or injective) if f(x)=f(y) x=y onto (or surjective) if y x: y = f(x) bijective if it is 1-1 and onto. f can help us count. If f is: 1-1 then |A| |B|
Minnesota - CSCI - 5471
Modern Cryptography Lecture 1Yongdae KimWhos who?2Some movies :-)3IntroductionClass Information Title:Modern Cryptography Course Number: CSci 5471 Lectures: MW 2:30 PM - 3:45 PM, EE/CSci 3-111Has been experimental and challengin
Minnesota - CSCI - 5271
CSci 5271: Introduction to Computer SecurityExercise 23 due: December 10, 2007 Ground Rules. You may choose to complete this problem with a partner or by yourself. If you work with a partner, turn in one copy with both of your names on it. You may c
Minnesota - CSCI - 5271
CSci 5271: Introduction to Computer SecurityExercise 22 due: December 10, 2007 Ground Rules. You may choose to complete this problem with a partner or by yourself. If you work with a partner, turn in one copy with both of your names on it. You may c
Minnesota - CSCI - 5271
CONTROL HIJACKING(or, Why to Avoid C Like the Plague)INTRODUCTION TO COMPUTER SECURITYCSCI 5271A control hijacking attack injects new code into a running process.There are many ways to hijack a C program.Most common is the buffer overflow:
Minnesota - CSCI - 4011
QUIZ 2INHERENT LIMITATIONS OF COMPUTER PROGAMSCSci 4011Under G = (V,R,S) we say that a b if: a = uVy and b = uvy and (V v) R. A CFG is ambiguous if: it can derive some string s in two ways. The regular pumping lemma says that. if w L and |w|
U. Memphis - PSYC - 7701
Movement Fig 1Fig 2MOTOR SYSTEMS - Evolutionary ConsiderationsPrimitive Aquatic Invertebrates - whole body movements (e.g. protozoa, hydrozoan jellyfish) Primitive Aquatic Vertebrates - whole and partial body movements (e.g. fish) Primitive Amph
U. Memphis - PSYC - 7701
Fig. 1 Lec 5Fig. 2Fig. 3Fig. 4Fig. 5Fig. 6Fig. 7Fig. 8Fig. 9Fig. 10Fig. 11Fig. 12Fig. 13Fig. 14Fig. 15Fig. 16Fig. 17. Fig. 18Fig. 19Fig. 20Fig. 21Fig. 22Fig. 23
U. Memphis - CE - 7137
1Documentation for the 2002 Update of the National Seismic Hazard Mapsby Arthur D. Frankel1, Mark D. Petersen1, Charles S. Mueller1, Kathleen M. Haller1, Russell L. Wheeler1, E.V. Leyendecker1, Robert L. Wesson1, Stephen C. Harmsen1, Chris H. Cra
U. Memphis - CE - 1112
Whitney Rectangular Stress Distribution The computation of flexural strength Mn based on the approximately parabolic stress distribution shown in Figure 1 may be done using given values of k2/(k1k3). However, it is desirable to have a simple method i
U. Memphis - CE - 1112
CIVL 1112Excel LOOKUP Functions1/4Excel Lookup Functions Lookup-type functions can return particular information from a series of a table of data The two most common lookup functions are:Excel Lookup Functions The VLOOKUP function moves ve
U. Memphis - CE - 1112
CIVL 1112Water Treatment - Aeration and Disinfection1/6Treatment ProcessesScreeningCoarse bar racks and fine traveling racks are employed at intake structure, on reservoirs and rivers. Coarse bar screen racks usually have clear spaces up to
U. Memphis - CE - 1112
CIVL 1112Excel IF Function1/3Excel IF Function The logical functions in Excel are a small group consisting of six functions These functions are noted for their blackor-white results A logical function can return only one of two values: TRUE
U. Memphis - CE - 1112
CIVL 1112Water Treatment - Sedimentation Group Problem1/1Sedimentation ExampleGroup ProblemEstimate the settling velocity of of the floc particles that have an estimated density and size of:Pp = 1,050 kg/m3 d = 0.1 mmSedimentation Example
U. Memphis - CE - 1112
CIVL 1112Excel - Goal Seek1/2Excel Goal Seek Function When you use the Goal Seek command, Excel changes the value in one cell until the value in a second cell reaches a number that you desire To use Goal Seek, go to the Tools command If Goal
U. Memphis - CE - 1112
CIVL 1112 Civil Engineering Analysis Detention Pond Project Report Spring 2008Section Introduction Topic Background ObjectivesName:Check Project scenario Why is a pond important? At least 100,000 gallon Balanced cut-and-fill cost Low total proje
U. Memphis - CE - 1112
CIVL 1112ACI Mix Design - Group Problem 21/3ACI Mix Design ExampleThe 28-day compressive strength should be 7,000 lb/in2. The slump should be between 3 and 4 in. and the maximum aggregate size should not exceed in. The properties of the mater
U. Memphis - CE - 1112
CIVL 1112Detention Pond - Part 11/9Detention Ponds A detention basin is an artificial flow control structure that is used to contain flood water for a limited period of a time. Detention basins are best management practices (BMPs) used to mit