Mixing of MCMC algorithms

We analyse MCMC chains focusing on how to find simulation parameters that give good mixing for discrete time, Harris ergodic Markov chains on a general state space X having invariant distribution π. The analysis uses an upper bound for the variance of the probability estimate. For each simulation parameter set, the bound is estimated from an MCMC chain using recurrence intervals. Recurrence intervals are a generalization of recurrence periods for discrete Markov chains. It is easy to compare the mixing properties for different simulation parameters. The paper gives general advice on how to improve the mixing of the MCMC chains and a new methodology for how to find an optimal acceptance rate for the Metropolis-Hastings algorithm. Several examples, both toy examples and large complex ones, illustrate how to apply the methodology in practice. We find that the optimal acceptance rate is smaller than the general recommendation in the literature in some of these examples.     

Goal setting in recovery: families where a parent has a mental illness or a dual diagnosis

Goal setting is an important element within mental health recovery models; however, parenting and children are rarely recognized in such approaches. This study outlines a family recovery planning model where a parent has a mental health or dual substance and mental health problem. The differences between family types (parent with a mental illness or parent with dual diagnosis) and family members (parent and children) are illustrated in terms of goals across 11 domains. There were a total of 33 parents and 50 children from 10 mental illness and 10 dual diagnosis families. Education and specifically mental health knowledge are important goals across all families and appear especially important for children whose parent has a dual diagnosis. Specific goals and achievement levels for each type of family and parents and children are also outlined. Clear areas for action by clinicians and family members are indicated by this study.     

Social security,age of retirement,and economic well-being: Intertemporal and demographic patterns among retired-worker beneficiaries

We examine the economic status of a sample of new recipients of social security retired-worker benefits shortly after their first receipt of benefits (1982) and 10 years later (1991). The probability that these retired-worker beneficiaries were poor or near-poor is positively and strongly associated with their acceptance of early retired-worker benefits. Early retirees, women who remained single, and women who lost their spouses experienced large declines in economic status over the decade following their first receipt of benefits. Although both women and men who first received benefits at younger ages had lower economic status than did those who became beneficiaries at older ages, this retirement age-related disadvantage increased over the decade for women but not for men.     

Emulation and interpretation of high-dimensional climate model outputs

Running complex computer models can be expensive in computer time, while learning about the relationships between input and output variables can be difficult. An emulator is a fast approximation to a computationally expensive model that can be used as a surrogate for the model, to quantify uncertainty or to improve process understanding. Here, we examine emulators based on singular value decompositions (SVDs) and use them to emulate global climate and vegetation fields, examining how these fields are affected by changes in the Earth's orbit. The vegetation field may be emulated directly from the orbital variables, but an appealing alternative is to relate it to emulations of the climate fields, which involves high-dimensional input and output. The SVDs radically reduce the dimensionality of the input and output spaces and are shown to clarify the relationships between them. The method could potentially be useful for any complex process with correlated, high-dimensional inputs and/or outputs.     

401(k) plan asset allocation, account balances, and loan activity in 2009

CONSISTENT SAMPLE: Because 401(k) balances can fluctuate with market returns from year to year, meaningful analysis of 401(k) plans must examine how participants' accounts have performed over the long term. Looking at consistent participants in the EBRI/ICI 401(k) database over the six-year period from 2003 to 2009 (which included one of the worst bear markets for stocks since the Great Depression), the study found: After rising in 2003 and for the next four consecutive years, the average 401(k) retirement account fell 27.8 percent in 2008, before rising 31.9 percent in 2009. The average 401(k) account balance moved up and down with stock market performance, but over the entire six-year time period increased at an average annual growth rate of 10.5 percent, attaining $109,723 at year-end 2009. The median (or midpoint, half above and half below) 401(k) account balance increased at an average annual growth rate of 14.7 percent over the 2003-2009 period to $59,381 at year-end 2009. THE BULK OF 401(K) ASSETS CONTINUED TO BE INVESTED IN STOCKS: On average, at year-end 2009, 60 percent of 401(k) participants' assets were invested in equity securities through equity funds, the equity portion of balanced funds, and company stock. Thirty-six percent was in fixed-income securities such as stable-value investments and bond and money funds. MORE THAN THREE-QUARTERS OF 401(K) PLANS INCLUDED TARGET-DATE FUNDS IN THEIR INVESTMENT LINEUP AT YEAR-END 2009: At year-end 2009, nearly 10 percent of the assets in the EBRI/ICI 401(k) database was invested in target-date funds and 33 percent of 401(k) participants held target-date funds. Also known as lifecycle funds, they are designed to simplify investing and to automate account rebalancing. NEW EMPLOYEES CONTINUED TO USE BALANCED FUNDS, INCLUDING TARGET-DATE FUNDS: Across all but the oldest age group, more new or recent hires invested their 401(k) assets in balanced funds, including target-date funds. At year-end 2009, about 42 percent of the account balances of recently hired participants in their 20s were invested in balanced funds, compared with 36 percent in 2008, and about 7 percent in 1998. At year-end 2009, 31 percent of the account balances of recently hired participants in their 20s was invested in lifecycle funds, compared with almost 23 percent at year-end 2008. 401(K) PARTICIPANTS CONTINUED TO SEEK DIVERSIFICATION OF THEIR INVESTMENTS: The share of 401(k) accounts invested in company stock continued to shrink, falling by half of a percentage point (to 9.2 percent) in 2009. That continued a steady decline that started in 1999. Recently hired 401(k) participants contributed to this trend: They tended to be less likely to hold employer stock. PARTICIPANTS' 401(K) LOAN ACTIVITY ROSE IN 2009: In 2009, 21 percent of all 401(k) participants eligible for loans had a loan outstanding against their 401(k) account, compared with 18 percent at year-end 2008 and year-end 2007. Loans outstanding amounted to 15 percent of the remaining account balance, on average, at year-end 2009, compared with 16 percent at year-end 2008. Loan amounts remained in line with the past few years in terms of typical dollar amounts.     

Generation,resistance, and survival: African-American children and the Southampton Rebellion of 1831

The Southampton Rebellion of 1831, Nat Turner’s Rebellion, stands as the most famous slave rebellion in American History. Historians have studied the rebellion extensively often focusing on Turner’s biography, the incident’s violent sequence of events, and the wide social, cultural, and political impact of the rebellion. The most recent scholarship on the Southampton Rebellion focuses on the wider community that produced the violent event that resulted in the death of nearly 60 whites and an uncountable number of people of color. African-American children made up a significant demographic in antebellum Southampton. They were present everywhere, just as children were present in most antebellum communities. Yet their appearances in the trial records associated with the Southampton Rebellion are all but unstudied. The Southampton Rebellion was not the result of Nat Turner’s singular genius focused on immediate results. It was a rebellion constituted in the community with future liberation in mind. Children, the literal embodiment of slavery’s future, then were necessarily included and involved. This article engages the extensive court documents associated with the Southampton Rebellion’s aftermath to investigate the possible role of children in the rebellion and their significance to the resistance of enslaved communities.