A comparison of Bayesian hierarchical space-time models for earthquake data

Stochastic earthquake models are often based on a marked point process approach as for instance presented in Vere-Jones (1995). This gives a fine resolution both in space and time making it possible to represent each earthquake with corresponding foreshocks and aftershocks separately. However, it is not obvious that this microscopic approach is advantageous when aiming at earthquake predictions. In the present paper we take a macroscopic point of view considering grid cells of 0.5ʿx 0.5ʿ, or about 50 km x 50 km, and time periods of 4 months, which seems suitable for predictions. Hereby, also the effects of foreshocks and aftershocks are circumvented. More specifically, we will discuss different alternative Bayesian hierarchical space-time models in the spirit of Wikle et al. (1998). For each time period the observations are the magnitudes of the largest observed earthquake within each grid cell. In our models these largest observed earthquakes are represented by hidden system state variables called potentials. The potentials at each time period and grid point are decomposed into a time independent term and various alternative time dependent terms with spatial description ...repor

Air and water pollution over time and industries with stochastic dominance

We employ a stochastic dominance (SD) approach to analyze the components that contribute to environmental degradation over time. The variables include countries\u2019 greenhouse gas (GHG) emissions and water pollution. Our approach is based on pair-wise SD tests. First, we study the dynamic progress of each separate variable over time, from 1990 to 2005, within 5-year horizons. Then, pair-wise SD tests are used to study the major industry contributors to the overall GHG emissions and water pollution at any given time, to uncover the industry which contributes the most to total emissions and water pollution. While CO2 emissions increased in the first order SD sense over 15 years, water pollution increased in a second-order SD sense. Electricity and heat production were the major contributors to the CO2 emissions, while the food industry gradually became the major water polluting industry over time. SD sense over 15 years, water pollution increased in a second-order SD sense. Electricity and heat production were the major contributors to the CO2 emissions, while the food industry gradually

Obesity and osteoarthritis in knee, hip and/or hand: An epidemiological study in the general population with 10 years follow-up

<p>Abstract</p> <p>Background</p> <p>Obesity is one of the most important risk factors for osteoarthritis (OA) in knee(s). However, the relationship between obesity and OA in hand(s) and hip(s) remains controversial and needs further investigation. The purpose of this study was to investigate the impact of obesity on incident osteoarthritis (OA) in hip, knee, and hand in a general population followed in 10 years.</p> <p>Methods</p> <p>A total of 1854 people aged 24–76 years in 1994 participated in a Norwegian study on musculoskeletal pain in both 1994 and 2004. Participants with OA or rheumatoid arthritis in 1994 and those above 74 years in 1994 were excluded, leaving n = 1675 for the analyses. The main outcome measure was OA diagnosis at follow-up based on self-report. Obesity was defined by a body mass index (BMI) of 30 and above.</p> <p>Results</p> <p>At 10-years follow-up the incidence rates were 5.8% (CI 4.3–7.3) for hip OA, 7.3% (CI 5.7–9.0) for knee OA, and 5.6% (CI 4.2–7.1) for hand OA. When adjusting for age, gender, work status and leisure time activities, a high BMI (> 30) was significantly associated with knee OA (OR 2.81; 95%CI 1.32–5.96), and a dose-response relationship was found for this association. Obesity was also significantly associated with hand OA (OR 2.59; 1.08–6.19), but not with hip OA (OR 1.11; 0.41–2.97). There was no statistically significant interaction effect between BMI and gender, age or any of the other confounding variables.</p> <p>Conclusion</p> <p>A high BMI was significantly associated with knee OA and hand OA, but not with hip OA.</p