Importance sampling (IS) methods are broadly used to approximate posterior distributions or their moments. In the standard IS approach, samples are drawn from a single proposal distribution and ...weighted adequately. However, since the performance in IS depends on the mismatch between the targeted and the proposal distributions, several proposal densities are often employed for the generation of samples. Under this multiple importance sampling (MIS) scenario, extensive literature has addressed the selection and adaptation of the proposal distributions, interpreting the sampling and weighting steps in different ways. In this paper, we establish a novel general framework with sampling and weighting procedures when more than one proposal is available. The new framework encompasses most relevant MIS schemes in the literature, and novel valid schemes appear naturally. All the MIS schemes are compared and ranked in terms of the variance of the associated estimators. Finally, we provide illustrative examples revealing that, even with a good choice of the proposal densities, a careful interpretation of the sampling and weighting procedures can make a significant difference in the performance of the method.
This qualitative exploratory cross‐case analysis analyzed the beliefs and practices of high school counselors related to science, technology, engineering, and mathematics (STEM) academic advisement, ...postsecondary planning, and career participation. Interviews were conducted with high school counselors (N = 13) who were purposively sampled to represent a diversity of schools in terms of demographic variables. Findings indicated that high school counselors perceived that (a) sociocultural factors influenced student preparation for STEM, career planning, and decision making; (b) students’ STEM‐related career goals and academic behaviors were sometimes misaligned, and academic advisement often mediated this tension; and (c) their professional STEM knowledge, beliefs, and practices were influenced by professional preparation, workplace characteristics, and their academic experiences. Implications include the need for early, sustained high school STEM counseling and academic advisement; accessible professional development in STEM preparation and careers to promote multiple pathways and reduce school counselor bias; and encouraging family involvement in STEM career decision making.
We present particle filtering algorithms for tracking a single target using data from binary sensors. The sensors transmit signals that identify them to a central unit if the target is in their ...neighborhood; otherwise they do not transmit anything. The central unit uses a model for the target movement in the sensor field and estimates the target's trajectory, velocity, and power using the received data. We propose and implement the tracking by employing auxiliary particle filtering and cost-reference particle filtering. Unlike auxiliary particle filtering, cost-reference particle filtering does not rely on any probabilistic assumptions about the dynamic system. In the paper, we also extend the method to include estimation of constant parameters, and we derive the posterior Cramer-Rao bounds (PCRBs) for the states. We show the performances of the proposed methods by extensive computer simulations and compare them to the derived bounds.
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step ...they generate samples from a proposal distribution and assign them weights according to the importance sampling principle. Critical issues in applying PMC methods are the choice of the generating functions for the samples and the avoidance of the sample degeneracy. In this paper, we propose three new schemes that considerably improve the performance of the original PMC formulation by allowing for better exploration of the space of unknowns and by selecting more adequately the surviving samples. A theoretical analysis is performed, proving the superiority of the novel schemes in terms of variance of the associated estimators and preservation of the sample diversity. Furthermore, we show that they outperform other state of the art algorithms (both in terms of mean square error and robustness w.r.t. initialization) through extensive numerical simulations.
In Bayesian signal processing, all the information about the unknowns of interest is contained in their posterior distributions. The unknowns can be parameters of a model, or a model and its ...parameters. In many important problems, these distributions are impossible to obtain in analytical form. An alternative is to generate their approximations by Monte Carlo-based methods like Markov chain Monte Carlo (MCMC) sampling, adaptive importance sampling (AIS) or particle filtering (PF). While MCMC sampling and PF have received considerable attention in the literature and are reasonably well understood, the AIS methodology remains relatively unexplored. This article reviews the basics of AIS as well as provides a comprehensive survey of the state-of-the-art of the topic. Some of its most relevant implementations are revisited and compared through computer simulation examples.
In this paper, we propose a novel adaptive importance sampling (AIS) algorithm for probabilistic inference. The sampler learns a proposal distribution adaptation strategy by framing AIS as a ...reinforcement learning problem. Under this structure, the proposal distribution of the sampler is treated as an agent whose state is controlled using a parameterized policy. At each iteration of the algorithm, the agent earns a reward that is related to its contribution to the variance of the AIS estimator of the normalization constant of the target distribution. Policy gradient methods are employed to learn a locally optimal policy that maximizes the expected value of the sum of all rewards. Numerical simulations on two different examples demonstrate promising results for the future application of the proposed method to complex Bayesian models.
Multiple importance sampling (MIS) methods use a set of proposal distributions from which samples are drawn. Each sample is then assigned an importance weight that can be obtained according to ...different strategies. This work is motivated by the trade-off between variance reduction and computational complexity of the different approaches (classical vs. deterministic mixture) available for the weight calculation. A new method that achieves an efficient compromise between both factors is introduced in this letter. It is based on forming a partition of the set of proposal distributions and computing the weights accordingly. Computer simulations show the excellent performance of the associated partial deterministic mixture MIS estimator.
Background
With widespread adoption of the Next Generation Science Standards (NGSS) in the USA (US), research is needed on how secondary science, technology, engineering, and mathematics (STEM) ...teachers conceptualize the integration of engineering knowledge and practices in traditional STEM classrooms. The present study explored the affective impacts of participation in an engineering education workshop for secondary STEM teachers as part of a 200-h professional development program. The workshop focused on the implementation of electrical engineering and biotechnology principles and design practices in disciplinary instruction, as well as training teachers to differentiate among engineering fields and advise on career pathways. The conceptual framework for the workshop design was based upon elements of the interconnected model of professional growth to identify influences contributing to engineering pedagogical self-efficacy and career awareness.
Results
The overarching research questions addressed how professional development in engineering education affected secondary STEM teachers’ beliefs about the value of using engineering design to support learning, their self-efficacy regarding teaching engineering in their courses, perceived obstacles to effective STEM integration, and their confidence advising students about engineering post-secondary study and careers. The convergent parallel mixed methods design involved factor analysis, comparisons of means, and phenomenology with elements of grounded theory. The survey sample included 60 STEM teachers in the treatment group and 28 teachers in the control group. Six science teachers participated in interviews before and after the engineering workshops. Findings indicated that participating teachers significantly improved their confidence in engineering pedagogy, as well as their knowledge of engineering careers and precollege preparation for post-secondary engineering. Teachers expressed their views of engineering as a potentially powerful tool in developing students’ critical thinking and problem-solving skills, particularly when integrating the practices of science and engineering with the instruction of disciplinary content.
Conclusions
The results from this study demonstrate that a university-based professional development workshop series, developed by engineering and science education faculty, is an effective first-step intervention to improve the engineering knowledge and skills of secondary STEM educators, ultimately facilitating NGSS adoption in classroom instruction. Educating teachers on engineering career pathways is another innovation for the promotion of more diverse participation in engineering fields.
Surface science methodologies for understanding thermodynamic aspects of surface processes are at an advanced level. However, instrumentation and approaches for extracting kinetic parameters from ...elementary steps are far less accessible. In this work, we present an approach combining the use of a fast gas pulsing valve synchronized with data acquisition to enable surface transient kinetics studies using infrared reflection absorption spectroscopy. This methodology applies to the study of reversible processes and borrows concepts and ideas from molecular beam scattering and temporal analysis of products. A temporal resolution of ~67 ms is achieved, and this is illustrated through the study of CO adsorption and desorption on a Pd(111) crystal in the presence and absence of background O2. The same approach can be extended to other surface spectroscopies, such as X-ray photoelectron spectroscopy, to obtain spectra with high temporal resolution and signal-to-noise ratio and enable future multimodal surface transient kinetic studies aiming at elucidating reaction mechanisms.
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•Transient Kinetics Capabilities were enabled in an infrared reflection absorption spectroscopy system.•This instrument allows taking IRRA spectra with a time resolution of 67 ms for reversible processes.•Its use is illustrated by studying the kinetics of adsorption/desorption of CO on Pd(111) using square waves of pressure.
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