A new method for conditioning stochastic groundwater flow models in fractured media

Many geological formations consist of crystalline rocks that have very low matrix permeability but allow flow through an interconnected network of fractures. Understanding the flow of groundwater through such rocks is important in considering disposal of radioactive waste in underground repositories. A specific area of interest is the conditioning of fracture transmissivities on measured values of pressure in these formations. This is the process where the values of fracture transmissivities in a model are adjusted to obtain a good fit of the calculated pressures to measured pressure values. While there are existing methods to condition transmissivity fields on transmissivity, pressure and flow measurements for a continuous porous medium there is little literature on conditioning fracture networks. Conditioning fracture transmissivities on pressure or flow values is a complex problem because the measurements are not linearly related to the fracture transmissivities and they are also dependent on all the fracture transmissivities in the network. We present a new method for conditioning fracture transmissivities on measured pressure values based on the calculation of certain basis vectors; each basis vector represents the change to the log transmissivity of the fractures in the network that results in a unit increase in the pressure at one measurement point whilst keeping the pressure at the remaining measurement points constant. The fracture transmissivities are updated by adding a linear combination of basis vectors and coefficients, where the coefficients are obtained by minimizing an error function. A mathematical summary of the method is given. This algorithm is implemented in the existing finite element code ConnectFlow developed and marketed by Serco Technical Services, which models groundwater flow in a fracture network. Results of the conditioning are shown for a number of simple test problems as well as for a realistic large scale test case.

Management interventions in dairy herds: exploring within herd uncertainty using an integrated Bayesian model

Knowledge of the efficacy of an intervention for disease control on an individual farm is essential to make good decisions on preventive healthcare, but the uncertainty in outcome associated with undertaking a specific control strategy has rarely been considered in veterinary medicine. The purpose of this research was to explore the uncertainty in change in disease incidence and financial benefit that could occur on different farms, when two effective farm management interventions are undertaken. Bovine mastitis was used as an example disease and the research was conducted using data from an intervention study as prior information within an integrated Bayesian simulation model. Predictions were made of the reduction in clinical mastitis within 30 days of calving on 52 farms, attributable to the application of two herd interventions previously reported as effective; rotation of dry cow pasture and differential dry cow therapy. Results indicated that there were important degrees of uncertainty in the predicted reduction in clinical mastitis for individual farms when either intervention was undertaken; the magnitude of the 95% credible intervals for reduced clinical mastitis incidence were substantial and of clinical relevance. The large uncertainty associated with the predicted reduction in clinical mastitis attributable to the interventions resulted in important variability in possible financial outcomes for each farm. The uncertainty in outcome associated with farm control measures illustrates the difficulty facing a veterinary clinician when making an on-farm decision and highlights the importance of iterative herd health procedures (continual evaluation, reassessment and adjusted interventions) to optimise health in an individual herd.

Bayesian analysis of a mastitis control plan to investigate the influence of veterinary prior beliefs on clinical interpretation

The fundamental objective for health research is to determine whether changes should be made to clinical decisions. Decisions made by veterinary surgeons in the light of new research evidence are known to be influenced by their prior beliefs, especially their initial opinions about the plausibility of possible results. In this paper, clinical trial results for a bovine mastitis control plan were evaluated within a Bayesian context, to incorporate a community of prior distributions that represented a spectrum of clinical prior beliefs. The aim was to quantify the effect of veterinary surgeons’ initial viewpoints on the interpretation of the trial results. A Bayesian analysis was conducted using Markov chain Monte Carlo procedures. Stochastic models included a financial cost attributed to a change in clinical mastitis following implementation of the control plan. Prior distributions were incorporated that covered a realistic range of possible clinical viewpoints, including scepticism, enthusiasm and uncertainty. Posterior distributions revealed important differences in the financial gain that clinicians with different starting viewpoints would anticipate from the mastitis control plan, given the actual research results. For example, a severe sceptic would ascribe a probability of 0.50 for a return of <£5 per cow in an average herd that implemented the plan, whereas an enthusiast would ascribe this probability for a return of >£20 per cow. Simulations using increased trial sizes indicated that if the original study was four times as large, an initial sceptic would be more convinced about the efficacy of the control plan but would still anticipate less financial return than an initial enthusiast would anticipate after the original study. In conclusion, it is possible to estimate how clinicians’ prior beliefs influence their interpretation of research evidence. Further research on the extent to which different interpretations of evidence result in changes to clinical practice would be worthwhile.

Cow, farm, and management factors during the dry period that determine the rate of clinical mastitis after calving

The purpose of the research was to investigate cow characteristics, farm facilities, and herd management strategies during the dry period to examine their joint influence on the rate of clinical mastitis after calving. Data were collected over a 2-yr period from 52 commercial dairy farms throughout England and Wales. Cows were separated for analysis into those housed for the dry period (8,710 cow-dry periods) and those at pasture (9,964 cow-dry periods). Multilevel models were used within a Bayesian framework with 2 response variables, the occurrence of a first case of clinical mastitis within the first 30 d of lactation and time to the first case of clinical mastitis during lactation. A variety of cow and herd management factors were identified as being associated with an increased rate of clinical mastitis and these were found to occur throughout the dry period. Significant cow factors were increased parity and at least one somatic cell count ≥200,000 cells/mL in the 90 d before drying off. A number of management factors related to hygiene were significantly associated with an increased rate of clinical mastitis. These included measures linked to the administration of dry-cow treatments and management of the early and late dry-period accommodation and calving areas. Other farm factors associated with a reduced rate of clinical mastitis were vaccination with a leptospirosis vaccine, selection of dry-cow treatments for individual cows within a herd rather than for the herd as a whole, routine body condition scoring of cows at drying off, and a pasture rotation policy of grazing dry cows for a maximum of 2 wk before allowing the pasture to remain nongrazed for a period of 4 wk. Models demonstrated a good ability to predict the farm incidence rate of clinical mastitis in a given year, with model predictions explaining over 85% of the variability in the observed data. The research indicates that specific dry-period management strategies have an important influence on the rate of clinical mastitis during the next lactation.

Cow, farm, and herd management factors in the dry period associated with raised somatic cell counts in early lactation

This study investigated cow characteristics, farm facilities, and herd management strategies during the dry period to examine their joint influence on somatic cell counts (SCC) in early lactation. Data from 52 commercial dairy farms throughout England and Wales were collected over a 2-yr period. For the purpose of analysis, cows were separated into those housed for the dry period (6,419 cow-dry periods) and those at pasture (7,425 cow-dry periods). Bayesian multilevel models were specified with 2 response variables: ln SCC (continuous) and SCC >199,000 cells/mL (binary), both within 30 d of calving. Cow factors associated with an increased SCC after calving were parity, an SCC >199,000 cells/mL in the 60 d before drying off, increasing milk yield 0 to 30 d before drying off, and reduced DIM after calving at the time of SCC estimation. Herd management factors associated with an increased SCC after calving included procedures at drying off, aspects of bedding management, stocking density, and method of pasture grazing. Posterior predictions were used for model assessment, and these indicated that model fit was generally good. The research demonstrated that specific dry-period management strategies have an important influence on SCC in early lactation.