Dynamic Hierarchical Model Research Articles

Efficient and effective calibration of numerical model outputs using hierarchical dynamic models

Efficient and effective calibration of numerical model outputs using hierarchical dynamic models

A Bayesian spatio‐temporal model for short‐term forecasting of precipitation fields

AbstractWith extreme weather events becoming more common, the risk posed by surface water flooding is ever increasing. In this work we propose a model, and associated Bayesian inference scheme, for generating short‐term, probabilistic forecasts of localised precipitation on a spatial grid. Our generative hierarchical dynamic model is formulated in discrete space and time with a lattice‐Markov spatio‐temporal auto‐regressive structure, inspired by continuous models of advection and diffusion. Observations from both weather radar and ground based rain gauges provide information from which we can learn the precipitation field through a latent process in addition to unknown model parameters. Working in the Bayesian paradigm provides a coherent framework for capturing uncertainty, both in the underlying model parameters and in our forecasts. Further, appealing to simulation based sampling using MCMC yields a straightforward solution to handling zeros, treated as censored observations, via data augmentation. Both the underlying state and the observations are of moderately large dimension ( and respectively) and this renders standard inference approaches computationally infeasible. Our solution is to embed the ensemble Kalman smoother within a Gibbs sampling scheme to facilitate approximate Bayesian inference in reasonable time. Both the methodology and the effectiveness of our posterior sampling scheme are demonstrated via simulation studies and by a case study of real data from the Urban Observatory project based in Newcastle upon Tyne, UK.

The impact of international commodity price shocks on macroeconomic fundamentals: Evidence from the US and China

In light of the increased volatility in international commodity markets, we aim to investigate the effects of international commodity price shocks on the macroeconomic fundamentals of the United States and China. We expand upon existing literature by employing the Dynamic Hierarchical Factor Model (DHFM) to analyze commodities across different sectors. This approach allows us to uncover the heterogeneity and specific synergies among various commodity categories. Furthermore, we construct the Factor Augmented Vector Autoregression Model (FAVAR) and the Time-varying Parameter FAVAR model, utilizing the common factors extracted and monthly data on fundamental macroeconomic variables from the US and China. By conducting impulse response analysis, we empirically demonstrate the impact of international commodity price shocks on key macroeconomic indicators, including industrial production, CPI, interest rates, stock prices, and exchange rates. Moreover, we provide evidence that these impacts exhibit significant variations over time, particularly in response to major global events such as the 2008 Global Financial Crisis, the 2020 COVID-19 pandemic, and the 2022 Russia-Ukraine conflict crisis. Our findings yield valuable insights for investors, researchers, and policymakers seeking to understand the influence of international commodity prices on macroeconomic conditions.

Long‐term dynamics of wild primate populations across forests with contrasting protection in Tanzania

AbstractAnthropogenic activities driving tropical forests' loss imperil global biodiversity and provision of ecosystem services. In this context, systematic monitoring programs evaluating wildlife trends are essential. Non‐human primates are relevant conservation targets since they represent vital components of tropical forests by serving as pollinators and seed dispersers. Here, we present primate group counts data collected over 19 years in a primate hotspot in Tanzania. We analyzed data with a hierarchical dynamic model accounting for imperfect detection that estimates local group abundance and temporal rates of change, to assess whether habitat protection explained trends of the arboreal and diurnal Peters' Angola colobus (Colobus angolensis palliatus), Udzungwa red colobus (Piliocolobus gordonorum), and Tanzania Sykes' monkey (Cercopithecus mitis subsp. moloneyi). We targeted populations occurring in two forest blocks with contrasting protection regimes, with one block impacted by targeted poaching of the two Colobus species. We found that these latter species were much less abundant in the more human impacted forest, underwent a rapid decline, and subsequently remained at low abundance and without signs of recovery once this forest was granted greater protection. Instead, Sykes' abundance did not differ between forests, and improved protection was associated with a slight increase in abundance. Age class composition for social groups of both Colobus species differed between forests, indicating altered births and survivorship rates in the impacted forest. Results suggest that targeted hunting can prevent recovery for several years and even after increased habitat protection. Our approach appears valuable to monitor population dynamics over the long term, highlighting species‐specific variations in both vulnerability to anthropogenic disturbance and recovery patterns in primate populations.

Multivariate dynamic modeling for Bayesian forecasting of business revenue

AbstractForecasting enterprise‐wide revenue is critical to many companies and presents several challenges and opportunities for significant business impact. This case study is based on model developments to address these challenges for forecasting in a large‐scale retail company. Focused on multivariate revenue forecasting across collections of supermarkets and product categories, hierarchical dynamic models are natural: these are able to couple revenue streams in an integrated forecasting model, while allowing conditional decoupling to enable relevant and sensitive analysis together with scalable computation. Structured models exploit multi‐scale modeling to cascade information on price and promotion activities as predictors relevant across categories and groups of stores. With a context‐relevant focus on forecasting revenue 12 weeks ahead, the study highlights product categories that benefit from multi‐scale information, defines insights into when, how, and why multivariate models improve forecast accuracy, and shows how cross‐category dependencies can relate to promotion decisions in one category impacting others. Bayesian modeling developments underlying the case study are accessible in custom code for interested readers.

Globalization Versus Slowbalization: A Perspective on the Indian Economy

The crisis and ensuing recession have led the global leaders to focus inwards. While the trend had taken off with countries having to face rising inequality and a focus towards self-development, there is little evidence besides newspaper articles to support this hypothesis from the Indian perspective. The results, using dynamic hierarchical factor model analysis, over a subset of 21 economies which account for 66% of India’s trade, reveal that India’s globalization has been withering away over time. Using time-varying parameter regression estimation on the domestic and factors loading, it is observed that the portion of growth explained by domestic factors is increasing over time and that of foreign factors is degrading. The study provides evidence of slowbalization in Indian economy. As the government looks forward to an era of self-reliance and Make in India, the results hold significance for the future growth trajectory of the Indian economy.

Quantifying transmissibility of SARS-CoV-2 and impact of intervention within long-term healthcare facilities.

Estimates of the basic reproduction number (R0) for COVID-19 are particularly variable in the context of transmission within locations such as long-term healthcare (LTHC) facilities. We sought to characterize the heterogeneity of R0 across known outbreaks within these facilities. We used a unique comprehensive dataset of all outbreaks that occurred within LTHC facilities in British Columbia, Canada as of 21 September 2020. We estimated R0 in 18 LTHC outbreaks with a novel Bayesian hierarchical dynamic model of susceptible, exposed, infected and recovered individuals, incorporating heterogeneity of R0 between facilities. We further compared these estimates to those obtained with standard methods that use the exponential growth rate and maximum likelihood. The total size of outbreaks varied dramatically, with range of attack rates 2%–86%. The Bayesian analysis provided an overall estimate of R0 = 2.51 (90% credible interval 0.47–9.0), with individual facility estimates ranging between 0.56 and 9.17. Uncertainty in these estimates was more constrained than standard methods, particularly for smaller outbreaks informed by the population-level model. We further estimated that intervention led to 61% (52%–69%) of all potential cases being averted within the LTHC facilities, or 75% (68%–79%) when using a model with multi-level intervention effect. Understanding of transmission risks and impact of intervention are essential in planning during the ongoing global pandemic, particularly in high-risk environments such as LTHC facilities.

Monetary policy, hot money and housing price growth across Chinese cities

ABSTRACT We use a dynamic hierarchical factor model to identify the national, regional and local factors of the city-level housing price growth in China. During the zero-lower-bound (ZLB) episode in the U.S., local factors account for 78% of variations in the month-on-month city-level housing price growth. However, as the time horizon extends, the national factor gets a larger variance share, reaching 51% in a half-year horizon. This indicates that the city-level housing price growth in China is more of a national phenomenon in the long run. We then use a VAR model to investigate the driving forces of the national factor and find that monetary policy and hot money shocks affect the national housing price growth significantly. A tightening monetary policy shock has a significant negative impact on the national factor, which lasts for more than 2 years. An increase in hot money inflows causes a significant but transitory rise in the national factor. Moreover, we find that the quantitative easing measure adopted by the U.S. Fed is behind the surge of capital inflows into China.

Modelling asymmetric price responses of industrial energy demand with a dynamic hierarchical model

Accounting for asymmetric price responses while modelling industrial energy demand is required for a good understanding of the long-run properties of energy demand. This is to prevent formulating energy related policies on incomplete information resulting from masking the impacts of long-run impacts of different phases of energy price. Hence, this paper explores the asymmetric price responses of industrial energy demand for a panel of 54 sectors across 34 countries over the period 2000–2014 using a dynamic hierarchical model. The empirical results from both the regional and sectoral analysis indicate a considerable heterogeneity in the estimated long-run elasticities and preference for using hierarchical model. Further, the estimated elasticities in general indicate that producers are more responsive to price increases than price decreases. In addition, empirical findings reveal that industrial energy demand is characterised by endogenous factors embedded in the asymmetric price effects. From a policy perspective, these findings provide an evidence of marked long-run impacts of energy demand (that are not observable from a traditional symmetric energy consumption pattern) required in formulating dependable energy policies.

A hierarchical dynamic model used for investigating feed efficiency and its relationship with hepatic gene expression in APOE*3-Leiden.CETP mice.

BackgroundFeed efficiency (FE) is an important trait for livestock and humans. While the livestock industry focuses on increasing FE, in the current obesogenic society it is more of interest to decrease FE. Hence, understanding mechanisms involved in the regulation of FE and particularly how it can be decreased would help tremendously in counteracting the obesity pandemic. However, it is difficult to accurately measure or calculate FE in humans. In this study, we aimed to address this challenge by developing a hierarchical dynamic model based on humanized mouse data.MethodsWe analyzed existing experimental data derived from 105 APOE*3‐Leiden.CETP (E3L.CETP) mice fed a high‐fat high‐cholesterol (HFHC) diet for 1 (N = 20), 2 (N = 19), 3 (N = 20), and 6 (N = 46) month. We developed an ordinary differential equation (ODE) based model to estimate the FE based on the longitudinal data of body weight and food intake. Since the liver plays an important role in maintaining metabolic homeostasis, we evaluated associations between FE and hepatic gene expression levels. Depending on the feeding duration, we observed different relationships between FE and hepatic gene expression levels.ResultsAfter 1‐month feeding of HFHC diet, we observed that FE was associated with vitamin A metabolism, arachidonic acid metabolism, and the PPAR signaling pathway. After 3‐ and 6‐month feeding of HFHC diet, we observed that FE was associated most strongly with expression levels of Spink1 and H19, genes involved in cell proliferation and glucose metabolism, respectively.ConclusionsIn conclusion, our analysis suggests that various biological processes such as vitamin A metabolism, hepatic response to inflammation, and cell proliferation associate with FE at different stages of diet‐induced obesity.

Empirical estimates for heteroscedastic hierarchical dynamic normal models

The available heteroscedastic hierarchical models perform well for a wide range of real-world data, but for data sets that exhibit a dynamic structure they seem fit poorly. In this work, we develop a two-level dynamic heteroscedastic hierarchical model and suggest some empirical estimators for the association hyper-parameters. Moreover, we derive the risk properties of the estimators. Our proposed model has the feature that the dependence structure among observations is produced from the hidden variables in the second level and not through the observations themselves. The comparison between various empirical estimators is illustrated through a simulation study. Finally, we apply our methods to a baseball data.

The role of global relative price changes in international comovement of inflation

In this paper we investigate the impact of global relative price changes on domestic inflation. We use a dynamic hierarchical factor model (DHFM) to decompose consumer basket products’ inflation in a panel of countries into (i) a global factor, common to all price series and all countries, (ii) a price change shock at product group level, (iii) a price change shock at product subgroup level, and (iv) an idiosyncratic component. Using monthly data for 29 economies from 2003 to 2018 we find that product inflation rates demonstrate different sensitivity to common price shocks. For energy, some food and manufactured goods, global relative price changes may account for up to 49% of inflation variation which is quite high for this frequency and level of disaggregation. Moreover, common factors from the DHFM have significant explanatory power for overall CPI and its aggregate components across different countries.

Kalman Filter of Dynamic Hierarchical Model

In a specific way, the dynamic hierarchical model has been presented alongside with the derivation of the final formula of the Kalman filter. The filtering coefficient used along with the equations necessary for the filtering process has also been determined. Most of the related works were studied which gave rise to the problem statement of filtering problems placed under the case of st = . Most of the basic concepts of the dynamic hierarchical linear model were also displayed based on some previous works. A mathematical formula was also formulated and derived to calculate the dynamic hierarchical Kalman filter model, which results in a repetitive measure to estimate the model parameters. The proposed derived formula reduces the error associated with the model and achieves a successful optimal estimation of the parameters. This proves that the Kalman coefficient is the best filtering for any normal probability distribution and provides the least variance among the estimates. This study also provides an illustrative example of the model with the filtering process concerned. It was further illustrated that the findings can be used in practical applications, which reveals the fields that can be investigated in this area.

China’s business cycles at the provincial level: National synchronization, interregional coordination and provincial idiosyncrasy

To explain the emerging idiosyncrasy of China’s provincial business cycles, we apply a dynamic hierarchical factor model to decompose cyclical fluctuations in China’s provincial economy during 1988-2017 into a national factor, four regional factors, and several provincial factors besides idiosyncratic factors. We find that the national factor is key to the formation of most provincial business cycles, which hints that most provincial economic growth are featured by the “medium-high growth rate and low fluctuation” pattern in common. Additionally, regional business cycles display a ternary distribution in which the East leads, the Central and West follow, and the Northeast remains relatively independent. Moreover, there is a clear “club convergence” trend in provincial business cycles in all regions except the Northeast whose provincial business cycles are increasingly idiosyncratic. The government should be vigilant about the local idiosyncratic risk and strengthen the coordination mechanism of provincial economic growth to achieve a steady-state economy.

Understanding the Impact of Observation Data Uncertainty on Probabilistic Streamflow Forecasts Using a Dynamic Hierarchical Model

AbstractEarlier researches have proposed algorithms to quantify the measurement uncertainty in rating curves and found that the magnitude of the uncertainty can be significant enough to impact hydrologic modeling. Therefore, they suggested frameworks to include measurement uncertainty in the rating curve to make it robust. Despite their efforts, a robust rating curve is often ignored in traditional practices, considering the investment of time and money as well as the resulting benefit from it. In the current research, we are interested in understanding the role of the measurement error variance in real‐time streamflow forecasting. Our objectives are (i) to employ a state‐of‐the‐art statistical forecasting model that can handle measurement uncertainty in daily streamflow and (ii) to understand the trade‐off in forecasting performance when substantial knowledge regarding the measurement uncertainty is provided to the modeler. We apply the Bayesian dynamic hierarchical model (BDHM) on four gauging sites in the United States. Results show that the BDHM performs better than the daily climatology and local linear regression model. Also, the forecast variance changes proportionally with the change in the error variance as an input in the observation equation. Following this, we design a simulation‐based study, which assigns the measurement error in the reported streamflow to obtain multiple realizations of the true streamflow. The inclusion of substantial knowledge about the true error improves the BDHM's performance by lowering the CRPS (continuous rank probability score) values. However, the inclusion increases the forecast variance to bring the true streamflow within the sampling variability of the forecasted streamflow. Overall, an improved trade‐off between the success rate of forecasts and the forecast variance can be achieved by including the measurement error in the BDHM for rivers that witness less dispersed streamflow data.

Time-Varying Price Elasticity in a Service Market with Heterogeneous Customer Valuation

The demand for services such as self-storage varies across locations, over time, as well as across customer segments. Service providers try to leverage these variations and maximize profits by adopting dynamic pricing policies. Implementing dynamic pricing, however, requires accurate estimates of price elasticities at a granular level. Using data from a leading self-storage retailer in Europe, we estimate a Bayesian Dynamic Hierarchical Linear Model (DHLM) to obtain price elasticities across 67 stores, for 21 bi-weeks, and high-valuation vs. low-valuation customer segments. Our estimation procedure accounts for price endogeneity, which is essential when using the estimated price elasticities to set the dynamic pricing policy. We find evidence of different price elasticities between stores and over time, which supports the practice of local dynamic price setting, as well as strong differences between customer segments. Overall, high-valuation customers are more price-sensitive than low-valuation customers. In addition, while the price elasticity of high-valuation customers remains stable, low-valuation customers become less price sensitive over time. This implies that a markup policy should be followed for low-valuation customers, but a more stable pricing regime may suffice for high-valuation customers. Last, we show the benefits of our model compared to a benchmark model with time-invariant price elasticities in determining the pricing policy, and discuss how our model can be applied to other industries that practice revenue management.

A Dynamic Hierarchical Bayesian Model for the Estimation of day-to-day Origin-destination Flows in Transportation Networks

Estimation of origin-destination (OD) flows in transportation networks is a major step in transportation planning. We are interested in estimating OD flows given data on traffic link volumes over a sequence of days. We propose a dynamic hierarchical Bayesian model for the estimation of day-to-day OD flows. At the first level, we specify a dynamic Gaussian model which describes the evolution of OD flows over time. At the second level, we model the assignment of route flows given OD flows. Route choice probabilities are a function of user-predicted route costs, which depend on past user-experienced costs with a leaning parameter which controls the length of users memory. At the third level we model observed link volumes given route flows. Covariance matrices of OD flows and observed link volumes are modeled through variance functions. We develop a Metropolis-within-Gibbs algorithm to sample from the joint posterior distribution of OD flows, route flows, and parameters of the route choice model and the variance functions. Our model can be applied to both congested and uncongested networks and does not assume network equilibrium. We illustrate application of the model and sampling algorithm through numerical studies on two transportation networks from the literature. In a small test network, results indicate that OD flows and parameters may be identified given uninformative priors, while in a real-scale network OD flows and route choice parameters may be reasonably identified given prior knowledge on OD flows at the beginning of the planning horizon and their temporal variability.

The Measure of Population Aging in Different Welfare Regimes: A Bayesian Dynamic Modeling Approach.

Given a population at a specific time point, it is often of interest to identify the entry age into typical stages of life, such as being young, becoming adult and elderly. These age cutoffs are important because they influence the public opinion and have an impact on policy decisions. An issue of great social relevance is defining the threshold beyond which a person becomes elderly. Fixed cutoffs are debatable because of their conventional nature which disregards issues such as changing life expectancy and the evolving structure of the age distribution. The above shortcomings can be overcome if age cutoffs are defined endogenously, i.e., relative to the whole age distribution of each country at a specific time point. We pursue this line of research by presenting an analysis whose main features are: (1) establishing a relationship between a country's welfare regime and its age distribution and aging process, together with the identification of four clusters of countries corresponding to distinctive welfare models and (2) a Bayesian hierarchical dynamic model which accounts for the uncertainty in the time series of measurements of the endogenous cutoffs for the countries in the sample, as well as for their clustering structure. Our analysis leads to model-based estimates of country-specific endogenous age cutoffs and corresponding aging indicators. Additionally, we provide cluster-specific estimates, a novel contribution engendered by the use of hierarchical modeling, which widens the scope of our analysis beyond the countries which are present in the sample.

What drives fluctuations in exchange rate growth in emerging markets – A multi-level dynamic factor approach

Historically, exchange rates in many emerging economies have been volatile. We use a dynamic hierarchical factor model to investigate the driving forces behind these fluctuations in exchange rate growth and find that in recent years, especially since the Great Recession, the common (world) factor has become more important. We also find that, since 2009, US monetary policy and Chinese economic growth have had much greater effects on emerging market exchange rate growth fluctuations. The historical decomposition indicates that 18.8% and 23% of the variations in the world factor after 2009 can be explained by US monetary policy shock and Chinese industrial production shock, respectively.

Commodity price co-movement: heterogeneity and the time-varying impact of fundamentals

This paper extends the topical literature on the co-movement and determinants of primary commodity prices, by considering heterogeneity in commodities and time variation in the impact of fundamentals. We account for heterogeneity by employing a dynamic hierarchical factor model, which decomposes commodities into global and sectoral factors. Using a time varying parameter factor augmented VAR model, we shock global and sector-specific factors over time. We present plausible impulse responses to demand shocks, real interest rate shocks, and to elevated risks during the global financial crisis. We also identify that materials, food and metals respond heterogeneously to these shocks.