Agricultural decision analysis has long held that the probabilities relevant to a farm decision are the decision maker's own degrees of belief, informed by whatever data exist, and that sparse data are a reason to combine evidence with judgement and not a reason to abandon probabilistic reasoning (Anderson et al., 1977). Judgement has well-documented faults. People anchor on an initial value, give too much weight to vivid recent events and state ranges that are too narrow (Tversky and Kahneman, 1974). Structured elicitation methods have been developed to reduce these faults, and the guidance on them is detailed (O'Hagan et al., 2006).

Several technical results make simulation workable when data are thin. Richardson et al. (2000) set out a procedure for simulating correlated farm variables from short series using empirical distributions, without assuming normality. Their caution about distributional form is supported by Just and Weninger (1999), who showed that the evidence on the shape of crop yield distributions is sensitive to how trends are removed. Latin hypercube sampling covers the range of each input evenly with far fewer draws than simple random sampling (McKay et al., 1979), and the method of Iman and Conover (1982) imposes a chosen rank correlation on sampled inputs whatever their marginal distributions.

The starting point is an ordinary whole-farm budget for the coming year, laid out so that every enterprise gross margin is calculated from an explicit price, yield and area, and so that overheads, interest, lease payments and drawings appear as separate lines. The budget should be checked against the most recent actual accounts, however incomplete. A stochastic model can be no better than the accounting identities beneath it, and errors of structure, such as a forgotten cost or a double-counted by-product, are far more damaging than an imperfect distribution (Pannell, 1997).

Not every uncertain entry needs a distribution. A one-at-a-time sensitivity test on the deterministic budget, moving each entry between a low and a high value, shows which items move net income appreciably. On most farms these are the prices and yields of two or three main enterprises and the prices of one or two major inputs such as feed, fertiliser or fuel. Restricting the stochastic set to these five to eight variables keeps the elicitation manageable and the correlation structure small enough to specify with care. Everything else stays at its budgeted value.

Table 1 sets out the options for describing a single variable when records are short. For yields, the farmer's own experience is usually the best source, and a triangular distribution defined by the lowest, most likely and highest values is easy to elicit and to explain. The triangular form is a reasonable stand-in for smoother distributions in applications of this kind (Johnson, 1997). The extremes should be asked for before the most likely value, to limit anchoring, and the farmer should be asked to recall specific bad and good years and what caused them (O'Hagan et al., 2006).

Prices are a different matter, because long public series usually exist even when farm records do not. Agricultural prices show trends, seasonal patterns and cycles, and their short-run variation is better measured as deviation from these systematic movements than as raw dispersion (Tomek and Kaiser, 2014). The proposed approach is to take the current outlook price as the centre, to describe variability using percentage deviations of past market prices from their trend, and to adjust for the usual difference between the market quotation and the price the farm receives. Empirical deviations can be sampled directly, as in the approach of Richardson et al. (2000), which avoids choosing a functional form.

Treating the variables as independent is the most common error in simple risk models and usually understates risk. Prices of related commodities move together, feed costs follow grain prices, and yields of crops grown in the same season share the weather. Where a farm sells into a local market, yield and price may be negatively related, which dampens revenue variation. With few data, a full correlation matrix cannot be estimated. The procedure asks for a judgement on each important pair, expressed in broad classes such as strongly positive, moderately positive, unrelated or moderately negative, with a numerical rank correlation assigned to each class and checked against any market series available. The resulting matrix is imposed on the samples by the rank-based method of Iman and Conover (1982), after confirming that it is internally consistent (Vose, 2008).

Values are drawn by Latin hypercube sampling, and the budget is recalculated for each set of draws. A few thousand iterations are ample for a model of this size, and the adequacy of the number can be tested by repeating the run with a different random seed and confirming that the summary measures barely change. The work can be done in a spreadsheet with a simulation add-in or in a short script. Each run should be stored with its inputs, seed and date so that it can be reproduced when the budget is revisited.

The primary output is the cumulative distribution of net farm income. Three readings are useful to a farmer: the chance that income falls below zero, the chance that it falls below the amount needed to meet debt service and family drawings, and the income exceeded in nine years out of ten. Alternative plans, such as a change in enterprise mix or the forward sale of part of a crop, are compared by plotting their cumulative curves together. Where one curve lies wholly to the right of another the choice is clear (Hadar and Russell, 1969). Where curves cross, the ranking depends on risk attitude, and methods that rank plans over a range of risk aversion can be applied (Meyer, 1977; Hardaker et al., 2004).