Bayesian Regression of Piecewise Constant Functions

We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers. We derive simple but good estimates for the in-segment variance. We also propose a Bayesian regression curve as a better way of smoothing data without blurring boundaries. The Bayesian approach also allows straightforward determination of the evidence, break probabilities and error estimates, useful for model selection and significance and robustness studies. We discuss the performance on synthetic and real-world examples. Many possible extensions will be discussed.Comment: 27 pages, 18 figures, 1 table, 3 algorithm

Three Models of Retirement: Computational Complexity Versus Predictive Validity

Empirical analysis often raises questions of approximation to underlying individual behavior. Closer approximation may require more complex statistical specifications, On the other hand, more complex specifications may presume computational facility that is beyond the grasp of most real people and therefore less consistent with the actual rules that govern their behavior, even though economic theory may push analysts to increasingly more complex specifications. Thus the issue is not only whether more complex models are worth the effort, but also whether they are better. We compare the in-sample and out-of-sample predictive performance of three models of retirement -- "option value," dynamic programming, and probit -- to determine which of the retirement rules most closely matches retirement behavior in a large firm. The primary measure of predictive validity is the correspondence between the model predictions and actual retirement under the firm's temporary early retirement window plan. The "option value" and dynamic programming models are considerably more successful than the less complex probit model in approximating the rules individuals use to make retirement decisions, but the more complex dynamic programming rule approximates behavior no better than the simpler option value rule.

Identification at the Zero Lower Bound

I show that the Zero Lower Bound (ZLB) on interest rates can be used to identify the causal effects of monetary policy. Identification depends on the extent to which the ZLB limits the efficacy of monetary policy. I propose a simple way to test the efficacy of unconventional policies, modelled via a `shadow rate'. I apply this method to U.S. monetary policy using a three-equation SVAR model of inflation, unemployment and the federal funds rate. I reject the null hypothesis that unconventional monetary policy has no effect at the ZLB, but find some evidence that it is not as effective as conventional monetary policy

Deep Distributional Time Series Models and the Probabilistic Forecasting of Intraday Electricity Prices

Recurrent neural networks (RNNs) with rich feature vectors of past values can provide accurate point forecasts for series that exhibit complex serial dependence. We propose two approaches to constructing deep time series probabilistic models based on a variant of RNN called an echo state network (ESN). The first is where the output layer of the ESN has stochastic disturbances and a shrinkage prior for additional regularization. The second approach employs the implicit copula of an ESN with Gaussian disturbances, which is a deep copula process on the feature space. Combining this copula with a non-parametrically estimated marginal distribution produces a deep distributional time series model. The resulting probabilistic forecasts are deep functions of the feature vector and also marginally calibrated. In both approaches, Bayesian Markov chain Monte Carlo methods are used to estimate the models and compute forecasts. The proposed deep time series models are suitable for the complex task of forecasting intraday electricity prices. Using data from the Australian National Electricity Market, we show that our models provide accurate probabilistic price forecasts. Moreover, the models provide a flexible framework for incorporating probabilistic forecasts of electricity demand as additional features. We demonstrate that doing so in the deep distributional time series model in particular, increases price forecast accuracy substantially

Retention Analysis Modeling for the Acquisition Workforce II

Acquisition Research Program Sponsored Report SeriesSponsored Acquisition Research & Technical ReportsTo support the modern warfighters tasked with increasing demands in a constantly changing global environment, it is imperative that the defense acquisition system continue to evolve to maintain its capability and flexibility. In this effort, growing a talented, experienced, and well-qualified civilian workforce will be vital. As part of this broad effort, the Section 809 Panel has recommended change to the DoD’s career management framework to grow and augment the workforce, and the DoD AWF Strategic Plan — FY 2016 – FY 2021 has emphasized efforts since 2010 to restore and restructure the AWF after a period of twenty years of shrinkage. This technical research report is the second in a proposed series of three linked studies to provide a cutting-edge modeling and simulation tool that leverages the increase in availability of AWF data and the large increases in computing power in the last decades. Building on the proof-of-concept model created as part of the first-year effort, we continue our development of a “Dynamic Retention Model (DRM)” designed from the ground-up for the AWF. Using a large personnel dataset of the acquisition workforce as well as a representative dataset of the civilian population from the Bureau of Labor Statistics, we estimate our DRM. DRM is a leading-edge technique that uses a powerful mathematical/econometric technique called dynamic programming. It takes a complex, multi-period problem (such as the lifetime labor market decisions of an acquisition worker) and breaks it down into simpler, one-period sub-problems in a recursive manner. Solving a single-period problem “nests” the future decisions that the worker will make, allowing the estimation and prediction of complex behavior in a surprisingly manageable framework. With estimates from the model, we simulate how various modifications in personnel policies, such as changes in salary structure and bonuses, would have affected the labor market decisions of the workforce. In particular, our model takes into account civilian positions the AWF may move into upon the decision to separate from DoD, allowing a more accurate prediction of the impact of monetary personnel policies, which must be evaluated in relation to what the worker could realistically earn in the civilian sector. In doing so, the model can help the AWF leadership in achieving the desired workforce size and structure. We conclude this report by expanding on possible extensions to enrich the model to provide yet more accurate estimation and richer simulations, including evaluating the potential impact of COVID-19 on the long-run career trajectory of the workforce.Approved for public release; distribution is unlimited.Approved for public release; distribution is unlimited

Individualized and Optimal Talent-Management of the AWF in Response to COVID-19: Dynamic Programming Approach

Acquisition Research Program Sponsored Report SeriesSponsored Acquisition Research & Technical ReportsThis report is an extension of the originally proposed sequence of three studies that developed a cutting-edge modeling and simulation tool for the Acquisition Workforce (AWF). The initial objective of that sequence was to build a Dynamic Retention Model (DRM) from the ground-up for the AWF to restore and maintain a capable and flexible acquisition workforce in support of the needs of the modern warfighter. The current report uses the previous model to analyze the phenomenal and unprecedented impact of COVID-19 pandemic on the U.S. civilian sector and its potential effects on the size and composition of the AWF in the coming years. After going steadily down for almost a decade and being at the historical low of 3.5% in February 2020, the U.S. unemployment rate spiked to almost 15% in April 2020. This event represented an unparalleled increase of more than 11% in just two months. As surprising as the initial increase was the sharp fall in the U.S. unemployment rate that followed. As of November 2021, just a year and a half after the peak, the unemployment rate is hovering around 4.6%, barely more than one percentage point above the previous historical low. While the impact of COVID-19 has been so far much harsher on the civilian sector employment than on the government sector (i.e., and the AWF), it is unclear how the latter will evolve in the mid- and long-run after the fast, ongoing recovery of the private sector. We take advantage of the DRM developed in the previous studies and extend it to explore the potential consequences of economy-wide shocks (such as COVID-19) on the AWF as the economy shows signs of strong recovery. We start analyzing the behavior of a representative AWF worker at the beginning of the pandemic, when the strength of the economic recovery was highly uncertain. We find that, under a number of different scenarios regarding the speed of recovery, it takes several years (in expectation) before the AWF employee returns to the pre-pandemic behavior. The main effect of the COVID-19 shock is to make the AWF job temporarily more attractive than a similar job in the private sector, inducing the AWF worker to stay much longer in the government. A caveat of the previous analysis is that it assumes that the AWF employee is able to predict (in expectation) the recovery path of the economy. To address that unrealistic feature of the analysis, we extend the initial study by “forcing” the AWF worker to go through the strong economic recovery path observed after the outset of the pandemic. That is, we predict the agent behavior when the recovery paths are much more positive than originally forecasted. Not surprisingly, the initial higher valuation of the AWF job compared to the private sector quickly dissipates, and AWF attrition rates surge above pre-pandemic levels as employees who were planning to move to the private sector (and froze their plans due to the pandemic) resume their original courses of action. An important take-away is that, while the COVID-19 shock may initially induce more employees to stay longer in the AWF, it is not a permanent solution to retain valuable workers. To this end, traditional personnel policy actions will be required by the AWF leadership. We conclude the report by describing different possibilities to continue extending the model even further. These extensions will augment the DRM to provide the AWF leadership more accurate and powerful predictions of future AWF worker behavior.Approved for public release; distribution is unlimited.Approved for public release; distribution is unlimited

Biological-based models of carcinogenesis in the lung from radiation and smoking

Lung adenocarcinoma and squamous cell carcinoma are the deadliest cancers worldwide. Smoking and ionizing radiation are potent carcinogens affecting strongly both lung cancer subtypes. Several biological analyses have been performed to characterise the genetic mutations leading to adenocarcinoma and squamous cell carcinoma, and different genomic spectra have been observed. Biological markers of smoking related damage could be found, leading to a deep knowledge of cellular smoking effects. Less is known about the biological effects of radiation in human carcinogenesis. Risks have been quantified with epidemiological studies of these carcinogens. Based on the biologically substantiated assumption that the number of mutations is linearly related to the dose, in radiation epidemiology it is standard to model effects linearly. These models do however not have a biological interpretation and are disconnected from general statistical methods. Here we fill both gaps. First we apply statistical generalised additive models to examine the functional relation between risk and smoking and radiation effects. Secondly, with mechanistic multi-scale models we integrate molecular biology and epidemiology to describe the carcinogenesis of lung adenocarcinoma and squamous cell carcinoma. To investigate the incidence of lung adenocarcinoma and lung squamous cell carcinoma we analysed two cohorts: first the Life Span Study cohort of atomic bomb survivors of Hiroshima and Nagasaki, and second the Eldorado cohort of Canadian Uranium miners. Exposures differed strongly between cohorts. Residents of Hiroshima and Nagasaki were exposed to a relative high dose of gamma radiation for a short time, while the miners were exposed to a protracted and lower exposure to alpha and gamma radiation. Information about smoking habits is available only for the former cohort. Three types of models were applied to analyse the effects of radiation and smoking: state-of-the-art statistical risk models of radiation protection, statistical generalized additive models and mechanistic risk models. Although there were quantitative differences in effect size and significance, each result is presented below only for a single model. For lung adenocarcinoma the best mechanistic model was a two pathway model. Smoking and radiation effects showed markedly different patterns: both acted on the apoptosis rate of precancerous cells but on different pathways without any interaction. A linear radiation effect was found in one pathway and a linear-exponential smoking effect in the other pathway. Independently of these results we analysed genomic data of American patients. It is known that the genetic damage of people with adenocarcinoma can be grouped into three pathways: the receptor mutant (RMUT ) pathway, the transducer mutant pathway (TMUT ), and other signatures (OWT ). We could show that signatures of TMUT and the OWT pathways do differ much less from each other than both differed to the RMUT pathway. Therefore, there is also genetic evidence that adenocarcinoma fall into two main classes. The two pathways of the mechanistic model could be associated to the RMUT and RMUT+OWT pathways by their risk patterns in age and smoking. On the other hand, for squamous cell carcinoma one pathway was sufficient to describe the incidence data. Although effects of radiation appeared to be highly significant, they could be traced back to arise only from the first five years of follow up (33 cases therein). When the first five years were excluded, no significant radiation effect could be found. Interestingly, for lung squamous cell carcinoma the mechanistic models could fit the effects of cigarette smoking in initiation and promotion. This was different for lung adenocarcinoma, where the main effect of smoking was a promotion of already existing pre-cancerous clones. For both, lung adenocarcinoma and squamous cell carcinoma, no interaction between radiation and smoking could be fitted for the Life Span Study cohort. Results from analysis of the Eldorado cohort were in line with the results presented above. For lung adenocarcinoma both, the state-of-the-art statistical risk models and the generalised additive models, could find only a significant effect of radiation exposure. For lung squamous cell carcinoma, vice versa, both models could find only a significant effect of gamma radiation exposure. Concluding, we showed that lung cancer cannot be investigated as a single endpoint but the different subtypes have to be analysed separately. Different radiation qualities act differently to the different subtypes, indicating different biological processes. Analogously, although smoking is an important risk factor for all subtypes, its effects were different and with different magnitudes

Physics-guided machine learning approaches to predict stability properties of fusion plasmas

Disruption prediction and avoidance is a critical need for next-step tokamaks such as the International Thermonuclear Experimental Reactor (ITER). The Disruption Event Characterization and Forecasting Code (DECAF) is a framework used to fully determine chains of events, such as magnetohydrodynamic (MHD) instabilities, that can lead to disruptions. In this thesis, several interpretable and physics-guided machine learning techniques (ML) to forecast the onset of resistive wall modes (RWM) in spherical tokamaks have been developed and incorporated into DECAF. The new DECAF model operates in a multi-step fashion by analysing the ideal stability properties and then by including kinetic effects on RWM stability. First, a random forest regressor (RFR) and a neural network (NN) ensemble are employed to reproduce the change in plasma potential energy without wall effects, δWno-wall, computed by the DCON ideal stability code for a large database of equilibria from the National Spherical Torus Experiment (NSTX). Moreover, outputs from the ML models are reduced and manipulated to get an estimation of the no-wall β limit, βno-wall, (where β is the ratio of plasma pressure to magnetic confinement field pressure). This exercise shows that the ML models are able to improve previous DECAF characterisation of stable and unstable equilibria and achieve accuracies within 85-88%, depending on the chosen level of interpretability. The physics guidance imposed on the NN objective function allowed for transferability outside the training domain by testing the algorithm on discharges from the Mega Ampere Spherical Tokamak (MAST). The estimated βno-wall and other important plasma characteristics, such as rotation, collisionality and low frequency MHD activity, are used as input to a customised random forest (RF) classifier to predict RWM stability for a set of human-labeled NSTX discharges. The proposed approach is real-time compatible and outperforms classical cost-sensitive methods by achieving a true positive rate (TPR) up to 90%, while also resulting in a threefold reduction in the training time. Finally, a model-agnostic method based on counterfactual explanations is developed in order to further understand the model's predictions. Good agreement is found between the model's decision and the rules imposed by physics expectation. These results also motivate the usage of counterfactuals to simulate real-time control by generating the βN levels that would keep the RWM stable

Stochastic analysis of nonlinear dynamics and feedback control for gene regulatory networks with applications to synthetic biology

The focus of the thesis is the investigation of the generalized repressilator model (repressing genes ordered in a ring structure). Using nonlinear bifurcation analysis stable and quasi-stable periodic orbits in this genetic network are characterized and a design for a switchable and controllable genetic oscillator is proposed. The oscillator operates around a quasi-stable periodic orbit using the classical engineering idea of read-out based control. Previous genetic oscillators have been designed around stable periodic orbits, however we explore the possibility of quasi-stable periodic orbit expecting better controllability. The ring topology of the generalized repressilator model has spatio-temporal symmetries that can be understood as propagating perturbations in discrete lattices. Network topology is a universal cross-discipline transferable concept and based on it analytical conditions for the emergence of stable and quasi-stable periodic orbits are derived. Also the length and distribution of quasi-stable oscillations are obtained. The findings suggest that long-lived transient dynamics due to feedback loops can dominate gene network dynamics. Taking the stochastic nature of gene expression into account a master equation for the generalized repressilator is derived. The stochasticity is shown to influence the onset of bifurcations and quality of oscillations. Internal noise is shown to have an overall stabilizing effect on the oscillating transients emerging from the quasi-stable periodic orbits. The insights from the read-out based control scheme for the genetic oscillator lead us to the idea to implement an algorithmic controller, which would direct any genetic circuit to a desired state. The algorithm operates model-free, i.e. in principle it is applicable to any genetic network and the input information is a data matrix of measured time series from the network dynamics. The application areas for readout-based control in genetic networks range from classical tissue engineering to stem cells specification, whenever a quantitatively and temporarily targeted intervention is required