Probability of Food Security (PFS) Analysis

• Probability of Food Security (PFS) is a family of measures that estimate the likelihood that households or regions meet defined food security criteria.
• Different formulations utilize household expenditure thresholds, IPC phase classifications, scenario simulations, and ensemble forecasts to derive probability estimates.
• Integrating varied data sources and modeling techniques, PFS offers actionable insights for policy evaluation, early warning systems, and dynamic risk assessment.

Probability of Food Security (PFS) is a probabilistic representation of whether a household, sub-national area, or country satisfies a specified food-security criterion at a given time. Across the recent literature, the term does not denote a single universally standardized quantity; rather, it is instantiated in several closely related ways. In household expenditure models, PFS is the probability that observed food spending is sufficient to afford a minimally adequate diet. In acute food insecurity early-warning systems, it is typically the probability that an area remains below an IPC crisis threshold, often expressed as the complement of the probability of IPC Phase 3+ conditions. In scenario and risk frameworks, it is the probability that a food security index, a vector of food-system indicators, or a set of adequacy constraints remains in a “secure” region under modeled uncertainty. This suggests that PFS is best understood as a family of formally comparable probability statements tied to explicit thresholds, outcome spaces, and forecasting horizons rather than as a single canonical scalar (Lee et al., 7 Sep 2025).

1. Conceptual definitions and threshold choices

The most explicit definition of PFS in the provided literature is household-level and expenditure-based. In the PSID-based formulation, PFS is the estimated probability that a household’s monthly per capita food expenditures are at least as large as the household-specific Thrifty Food Plan (TFP) cost:

$$\text{PFS}_{ist} = P\big(W_{ist} \ge W^{\text{TFP}}_{ist} \mid \Theta_{ist}\big),$$

with $W_{ist}$ denoting monthly per capita food expenditure and $W^{\text{TFP}}_{ist}$ the per capita TFP cost adjusted to household composition and survey month; in the SNAP application, the same object is defined with a local price adjustment using the grocery component of the Cost of Living Index (Lee et al., 7 Sep 2025). Under this formulation, PFS is a continuous measure on $[0,1]$, with larger values interpreted as a higher likelihood that the household can afford a minimally adequate diet (Lee, 27 Aug 2025).

A second major formulation is phase-based and area-level. In the FEWS NET–ACLED conflict-integration study, food security is operationalized through the FEWS NET Integrated Food Security Phase Classification (IPC), an ordinal scale with five classes: Minimal, Stressed, Crisis, Emergency, and Famine. That framework naturally induces a binary partition: $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$ and hence

$$\text{PFS}_{i,t}=P(\text{FoodSecure}_{i,t}=1\mid X_{i,t}).$$

Equivalent multiclass formulations define

$$\text{PFS}_{i,t}=P(Y_{i,t}\in\{1,2\}\mid X_{i,t})=\sum_{k=1}^{2}P(Y_{i,t}=k\mid X_{i,t}),$$

so that PFS becomes an aggregate probability over “non-crisis” IPC states (Bertetti et al., 2024).

A third formulation appears in explicitly probabilistic famine-warning systems. CERES issues 90-day-ahead probabilities of IPC Phase 3+, Phase 4+, and Phase 5 conditions. In that setting, a natural PFS is the complement of acute crisis risk: $\text{PFS}_{<3}=1-P(\text{IPC 3+}),$ that is, the probability that a region remains below Crisis over the forecast horizon. Because CERES also reports $P(\text{IPC 4+})$ and $P(\text{IPC 5})$, more severity-sensitive variants of PFS can be defined from nested tail probabilities (Pedersen, 10 Mar 2026).

A fourth formulation is prevalence-based rather than state-based. The Harmonized Food Insecurity Dataset (HFID) stores sub-national monthly prevalences of insufficient food consumption and crisis coping behavior. This supports a direct outcome-complement interpretation: $W_{ist}$0 where the underlying HFID indicators are the prevalence of households with poor or borderline Food Consumption Score and the prevalence with $W_{ist}$1, respectively. This suggests a household-probability interpretation at area level even in the absence of a fully specified structural probability model (Machefer et al., 10 Jan 2025).

Several other papers do not define PFS explicitly but provide constructions that are probabilistically adjacent. The access-to-finance study treats food security as a continuous latent variable in PLS-SEM rather than a binary or ordinal state; it then describes two ways to obtain a “probability-like” PFS, either by fitting a downstream logistic regression to a binary food security label or by mapping standardized latent scores to $W_{ist}$2 through a logistic transform. Because the paper itself does not estimate those probabilities, this is best treated as an inferred PFS construction rather than a directly reported estimand (Abolade et al., 23 Nov 2025).

2. Measurement architectures and data sources

PFS formulations differ principally by the observation system from which food security is inferred. Household expenditure-based PFS is grounded in longitudinal microdata. The PSID implementation uses 26 waves spanning 1979–2019 to construct a household-level food security panel, while the SNAP study uses nine PSID waves from 1997–2013 and combines monthly per capita food expenditure, SNAP benefits, household composition, demographic covariates, TFP costs, and state-year grocery price indices to estimate the expenditure distribution underlying PFS (Lee et al., 7 Sep 2025). In this architecture, the unit of analysis is the household or the individual assigned the household’s food expenditure process.

Acute food insecurity PFS relies on spatially explicit area classifications. The conflict-integration study uses FEWS NET “Current Situation” IPC classifications as the outcome variable and intersects livelihood-area polygons with FEWS NET administrative boundaries to obtain district-level labels. It then aggregates ACLED events to the same district boundaries, constructing three-month lagged conflict counts and fatalities as well as two-year cumulative sums. The resulting panel has, for each district and period, an IPC phase, historical food-security features, and conflict features aligned so that conflict temporally precedes the observed food security state (Bertetti et al., 2024).

Text-based early warning extends the information set beyond standard administrative monitoring. The news-streams study collects 11.2 million English-language articles from Factiva from June 1980 to July 2020, extracts 167 Granger-causal text features organized into 12 semantic clusters, and links them to district-level IPC trajectories across 15 fragile states. Its target remains IPC phase or crisis onset, but its predictors are high-frequency semantic proxies for conflict, weather, prices, pests, displacement, and other drivers of deterioration (Balashankar et al., 2021).

HFID provides a harmonized monthly backbone for multi-source PFS estimation. It consolidates IPC/Cadre Harmonisé phases, FEWS NET IPC-compatible phases, WFP Food Consumption Score prevalence, and WFP reduced Coping Strategy Index prevalence into a common ADMIN2-month reference system. The dataset spans 2007–present, contains 311,838 records across 80 countries, 1,264 ADMIN1 units, and 5,508 ADMIN2 units, and explicitly harmonizes spatial geometries through GADM intersections and temporal frequencies through monthly alignment rules (Machefer et al., 10 Jan 2025). This architecture is particularly suited to multi-output or hybrid PFS models because it co-locates ordinal phase outcomes and continuous prevalence outcomes.

Other architectures broaden PFS beyond current-state monitoring. The real-time hunger-monitoring forecasting study uses WFP Real-Time Monitoring data to model daily sub-national prevalence of insufficient food consumption and crisis coping behavior alongside conflict, weather, seasonal calendars, exchange rates, inflation, and price-spike indices (Herteux et al., 2023). Scenario studies, by contrast, use national or commodity-system time series. The VAR-based scenario framework combines FAOSTAT, World Bank, and USDA indicators on production, trade, consumption, prices, availability, access, and nutritional value, whereas the national probabilistic risk framework for Egypt and Ethiopia builds stochastic trajectories for population, climate, food-system capacity, and water stress under SSP–RCP combinations (Belmeskine et al., 2023).

3. Statistical formulations and model families

The household expenditure lineage estimates PFS by explicitly modeling the conditional distribution of food expenditure. In the PSID implementation, monthly per capita food expenditure is first modeled as

$W_{ist}$3

using Poisson quasi-maximum likelihood. A second regression on squared residuals estimates the conditional variance. Expenditure is then assumed to follow a Gamma distribution with shape and scale parameters set by the estimated conditional mean and variance, and PFS is computed as the right-tail probability above the TFP threshold: $W_{ist}$4 The SNAP study uses the same three-step structure, with the TFP threshold adjusted by the state-year grocery Cost of Living Index (Lee, 27 Aug 2025).

Phase-based early-warning models typically use classification machinery. In the conflict-integration study, baselines such as Previous Period’s IPC Score, Same Period Last Year, and Max-2PP encode persistence and seasonality, while the main models are class-weighted Logistic Regression and Random Forest. When formulated as binary crisis-versus-non-crisis prediction, logistic regression yields

$W_{ist}$5

so that

$W_{ist}$6

Under multiclass classification, PFS is obtained by summing class probabilities for IPC 1 and 2. Random Forest analogously returns class probabilities as the fraction of trees voting for each class (Bertetti et al., 2024).

The news-streams framework uses a panel autoregressive distributed lag model rather than a native probabilistic classifier. It predicts future IPC phase as a continuous score using lagged IPC, traditional risk indicators, and district/province/country-level news factors. Crisis outbreak predictions are then produced by thresholding the forecasted IPC trajectory with calibrated upper and lower thresholds. The paper explicitly notes that a probability of crisis could be obtained by calibrating the continuous score, for example through

$W_{ist}$7

and defining

$W_{ist}$8

This is again a derived PFS rather than a directly estimated one (Balashankar et al., 2021).

Scenario-based PFS models use predictive distributions rather than direct classification. In the VAR–Monte Carlo framework, scenario assumptions are encoded as exogenous shocks, a VAR is estimated over a vector of food-security indicators, and 5,000 simulations generate predictive distributions for prices, availability, access, and nutritional value. PFS then becomes the probability that a chosen index or constraint remains above a security threshold, for example

$W_{ist}$9

or, for joint constraints, the empirical probability that all specified adequacy conditions hold under scenario $W^{\text{TFP}}_{ist}$0 (Belmeskine et al., 2023).

The national SSP–RCP framework formalizes this more explicitly through a Food Security Risk Index,

$W^{\text{TFP}}_{ist}$1

where $W^{\text{TFP}}_{ist}$2 is minimum caloric requirement, $W^{\text{TFP}}_{ist}$3 food-system capacity, and $W^{\text{TFP}}_{ist}$4 water stress. A within-scenario PFS is then naturally

$W^{\text{TFP}}_{ist}$5

with across-scenario variants obtained by weighting scenario-specific probabilities or using a barycentric probability model over scenario measures (Koundouri et al., 2023).

CERES is the most explicitly operational probabilistic system. It uses logistic scoring models for $W^{\text{TFP}}_{ist}$6, $W^{\text{TFP}}_{ist}$7, and $W^{\text{TFP}}_{ist}$8, combining composite stress, IPC stress, conflict stress, drought stress, food-access stress, price stress, convergence score, and the number of independently flagged pillars. It enforces monotonicity constraints,

$W^{\text{TFP}}_{ist}$9

and reports 90% sensitivity intervals via 2,000 input perturbation draws. In this setting, PFS is directly interpretable as a complement probability over acute insecurity tails (Pedersen, 10 Mar 2026).

A distinct dynamic lineage links PFS to resilience. The non-equilibrium resilience framework models increments of a food security variable $[0,1]$0 through an ARMA$[0,1]$1 process,

$[0,1]$2

with resilience defined by $[0,1]$3 and $[0,1]$4, where

$[0,1]$5

This supports a threshold-based PFS such as $[0,1]$6, with anti-persistence interpreted as shortening the duration of food-insecurity episodes after shocks (Smerlak et al., 2016).

4. Determinants and empirical performance

A recurrent empirical result is that richer covariate sets improve food security prediction and therefore any derived PFS. The clearest example is conflict integration. Using ACLED-derived lagged conflict counts and fatalities in addition to food-security history raises Random Forest accuracy from 0.748 to 0.763 and F1 from 0.752 to 0.767, while Logistic Regression improves from 0.742 to 0.757 in accuracy. The same study reports that the four conflict-related variables rank among the top 10 most influential predictors in the logistic model, and Spearman correlations above 0.4 with $[0,1]$7 appear in multiple conflict-affected countries and regions. This indicates that conflict materially reshapes the estimated probability surface for food secure versus crisis conditions (Bertetti et al., 2024).

High-frequency textual signals yield another large predictive increment. The news-streams model reduces RMSE by 34.1% relative to a baseline based on traditional indicators, while the combined model reduces RMSE by 40%. At fixed precision of 80%, recall increases from 54% for the baseline to 66% for the news-based model and 86% for the combined model. The combined model predicts 1,543 of 1,797 observed crises, 581 more than the baseline, corresponding to the reported claim that it predicts 32% more food crises than existing models. Because those models are score-based rather than fully calibrated probabilities, the result is best interpreted as stronger crisis discrimination that could support a more informative PFS after calibration (Balashankar et al., 2021).

Food-consumption forecasting provides a related but outcome-prevalence route to PFS. In daily sub-national forecasting of insufficient food consumption for Mali, Nigeria, Syria, and Yemen, Reservoir Computing is identified as particularly well suited because of resistance to over-fitting and efficient training. The framework predicts 60 consecutive days ahead using WFP global hunger monitoring data and is evaluated by RMSE against ARIMA, XGBoost, LSTM, and CNN alternatives. This suggests that a threshold-based PFS defined as $[0,1]$8, where $[0,1]$9 is forecast insufficient food consumption prevalence, can be operationalized from ensemble forecast dispersion even though the paper itself reports point forecasts rather than calibrated probabilities (Herteux et al., 2023).

Price-driven risk models connect market stress to PFS through affordability. The Brexit expert-judgement study estimates a median CPI food basket price increase of $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$0 with a 90% credible interval $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$1 under a Deal scenario and $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$2 with $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$3 under No deal. Because household incomes are assumed largely static in the short term, the paper argues that the number and severity of food-insecure households are likely to increase. This supports a budget-feasibility PFS of the form $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$4, with the expert-elicited food-price distribution supplying the stochastic component (Barons et al., 2019).

Structural determinants can also be embedded into probability-like food security measures outside crisis classification. In the access-to-finance study, food security is a latent construct reflecting availability, access, utilisation, and stability, and the estimated structural path from access to finance to food security is $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$5 with $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$6, $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$7, while $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$8. The paper does not estimate PFS directly, but it explicitly proposes logistic mapping of standardized latent food-security scores to a $$\text{FoodSecure}_{i,t} = \begin{cases} 1 & \text{if } Y_{i,t}\in\{1,2\}\ 0 & \text{if } Y_{i,t}\in\{3,4,5\}, \end{cases}$$9 scale and interprets higher access-to-finance scores as shifting households toward higher food security probability-like values (Abolade et al., 23 Nov 2025).

Market-warning systems based on deep learning offer another probability-bearing representation. NourishNet combines price forecasting with a three-class warning classifier over “no warning”, “moderate warning”, and “high warning” states, with class probabilities obtained through softmax. Because “no warning” is the low-stress state, a price-based PFS can be identified with $$\text{PFS}_{i,t}=P(\text{FoodSecure}_{i,t}=1\mid X_{i,t}).$$0, or with $$\text{PFS}_{i,t}=P(\text{FoodSecure}_{i,t}=1\mid X_{i,t}).$$1 under a partial-risk interpretation. The reported classification F1 is 72.18%, and the best price-forecast MAE is approximately 0.054 for 30-day horizons (Balboni et al., 2024).

5. Longitudinal dynamics, decision support, and policy use

The strongest evidence on PFS as a dynamic welfare statistic comes from the PSID panel. Over 1979–2019, mean PFS is about 0.81, annual mean PFS ranges from 0.77 to 0.85, and estimated food insecurity prevalence based on PFS thresholds ranges from 8% in 1985 to 17% in 2009. Among individuals who ever experience a food insecurity spell, the average spell length is about 3.13 waves, about 52% of spells last one wave, and about 69% last at most two waves. Persistent insecurity is concentrated among non-White individuals, women, and those without a high school diploma, while college graduates have very low chronic insecurity rates. These results show that PFS is not only a cross-sectional score but also a tool for estimating spell lengths, transition matrices, and chronicity over multiple recessions and policy regimes (Lee et al., 7 Sep 2025).

The SNAP study uses PFS precisely for intensive-margin policy evaluation. In two-stage least squares models instrumenting SNAP participation with a state-level SNAP Policy Index, SNAP does not have significant effects on estimated food security on average in either the full sample or a low-income subsample defined as ever below 130% of the poverty line. The paper further reports that SNAP has stronger positive effects on those whose estimated food security status is in the middle of the distribution but no significant effects in the tails. This is a distinctive use of PFS: it permits policy heterogeneity analysis along the latent severity distribution rather than only at the extensive margin of food secure versus insecure (Lee, 27 Aug 2025).

Decision-support systems extend PFS from measurement to counterfactual policy comparison. The UK Dynamic Bayesian Network / Multiregression Dynamic Model treats health and education as observable consequences of food insecurity and combines them in a utility function,

$$\text{PFS}_{i,t}=P(\text{FoodSecure}_{i,t}=1\mid X_{i,t}).$$2

Although the paper evaluates policies via expected utility rather than an explicit PFS, it also states that any event of the form $$\text{PFS}_{i,t}=P(\text{FoodSecure}_{i,t}=1\mid X_{i,t}).$$3 can be assigned a model-based probability. This implies a policy-conditional PFS as the probability that modeled health and education outcomes remain in a satisfactory region under each intervention (Barons et al., 2020).

HFID and CERES illustrate operational deployment. HFID offers an updated monthly common reference system for sub-national food-insecurity signals, while CERES produces weekly 90-day-ahead probabilities for 43 high-risk countries, along with alert tiers and prospective public grading. In practical early warning, low PFS can therefore be mapped to action thresholds, either through explicit $$\text{PFS}_{i,t}=P(\text{FoodSecure}_{i,t}=1\mid X_{i,t}).$$4 complements in CERES or through phase, FCS, and rCSI harmonization in HFID-based modeling pipelines (Machefer et al., 10 Jan 2025).

At smaller scales, distribution and targeting systems can also be cast probabilistically. The food-bank policy study does not estimate PFS explicitly, but it proposes equitable allocation using an Atkinson-type resource welfare function and poverty headcount ratios, and evaluates outcomes through wastage reduction and the number of people served. This suggests a coverage-based PFS in which the probability of food security for an agency or region is proportional to the share of need met with adequate nutritional composition, although that probability mapping is not directly estimated in the paper (Sucharitha et al., 2019).

6. Limitations, calibration, and unresolved issues

A central limitation is definitional non-universality. In the expenditure literature, PFS is a household-level right-tail probability above a TFP threshold. In IPC-based early warning, it is the complement of crisis probability or the probability mass on IPC 1–2. In latent-construct and scenario literatures, it is often only a proposed transformation or thresholded event over a continuous score. This suggests that PFS values are only comparable when the underlying security criterion, unit of analysis, and horizon are explicitly aligned (Lee, 27 Aug 2025).

Calibration remains uneven. The conflict-integration study notes that Logistic Regression and Random Forest inherently produce probability estimates but does not report calibration metrics such as Brier score or cross-entropy, even though it states that such scoring rules would be natural for a PFS evaluation (Bertetti et al., 2024). The news-streams model explicitly lacks formal probabilistic calibration, treating forecast IPC as a risk score and suggesting Platt scaling or isotonic regression as extensions for crisis probabilities and PFS (Balashankar et al., 2021). Similar issues arise in food-consumption forecasting and price-warning models, where uncertainty is typically proxied by ensemble spread or classification confidence rather than fully validated predictive distributions (Herteux et al., 2023).

Expenditure-based PFS has a different limitation: it is an affordability proxy, not an experiential measure. The PSID papers emphasize that PFS is constructed from food expenditures relative to TFP and tracks USDA food security status sufficiently well to study long-run dynamics, but it is still a prediction rather than a direct HFSSM observation. The SNAP paper therefore treats PFS as a proxy that is powerful for panel analysis yet not identical to the official experiential measure (Lee et al., 7 Sep 2025).

Operational probabilistic systems also face uncertainty-quantification issues. CERES explicitly states that its historical back-validation uses four IPC Phase 4–5 events selected for data completeness and that those are in-sample sanity checks only, not prospective performance claims. It further states that its sensitivity intervals reflect parametric input perturbation, not full predictive uncertainty, and that prospective calibration requires 12–24 months and 2,500–5,000 prediction–outcome pairs. Until then, derived PFS values are decision-support probabilities rather than empirically settled calibrated risks (Pedersen, 10 Mar 2026).

Data integration can itself distort PFS estimates. HFID harmonizes heterogeneous sources through spatial intersection, name reconciliation, and temporal aggregation, but the paper notes substantial data gaps, variable-specific coverage differences, and source divergences such as systematically lower FEWS NET phases relative to IPC/Cadre Harmonisé in overlapping cases. Any HFID-based PFS therefore inherits uncertainty from spatial reconciliation, missingness, and source-specific measurement protocols (Machefer et al., 10 Jan 2025).

Finally, several frameworks highlight threshold and model dependence. Scenario-based national PFS depends on the selected food security threshold $$\text{PFS}_{i,t}=P(\text{FoodSecure}_{i,t}=1\mid X_{i,t}).$$5, the chosen scenario weights $$\text{PFS}_{i,t}=P(\text{FoodSecure}_{i,t}=1\mid X_{i,t}).$$6, and the structure of the Food Security Risk Index or VAR state vector (Koundouri et al., 2023). Resilience-based PFS depends on the threshold $$\text{PFS}_{i,t}=P(\text{FoodSecure}_{i,t}=1\mid X_{i,t}).$$7, the stationarity of increments, and the fitted ARMA dynamics (Smerlak et al., 2016). This suggests that future work on PFS will likely center not on finding a single universal formula, but on improving calibration, threshold transparency, uncertainty reporting, and cross-framework interoperability.