The present study was carried out at Department of Statistics, M.D. University, Rohtak and Department of Statistics, Sri Venkateswara College, University of Delhi during 2020-21. Let y_{jkr} (i, j, k, r = 1, 2……..m) denote the observation on the experimental unit of the ith genotype in the jth environment receiving two different treatments i.e. kth and rth. In this situation, general least square layout is most suitable one with m^{2} experimental units to be used in the experiment instead of m^{5 }possible experimental units needed in a complete layout. Therefore, the following model may be considered for such experiment.

Where,

µ is the general mean effect.

d_{i} is the additive effect of ith genotype.

e_{j} is the effect of jth environment.

t_{k }is the effect due to kth treatment on the ith genotype in the jth environment.

y_{r} is the effect due to rth treatment on the ith genotype in jth environment.

g_{ijkr} is the genotype environment interaction receiving kth and rth treatments.

e_{ijkr} is the random error term which is assumed to be NID (0, 𝛔^{2}).

If δ** **represent the set of m^{2} values, then (i, j, k, r)∈ δ; di is the possible pair (j, k, r) associated with a fixed value of i and similarly δ_{j}, δ_{k} and δ_{r}, then parameters involved in the above model may be obtained by minimizing the sum of square error.

and

If it is assumed that

then

on solving above equations simultaneously

Since the algebraic sum of deviation of a set of observation about their mean is zero and other product term also zero. Therefore, the analysis of variance may be given as:

Or may be portioned as:

Where,

The total sum of square (TSS) into its component parts, the sum of square for genotype (SSG), sum of square for environment (SSE_{n}), sum of square for treatment (SST_{1}), the sum of square for another treatment (SST_{2}), the sum of square for interaction (SSI) and the sum of square for error (SSE_{r}). The ANOVA for such layout may be framed as:

A stable genotype possesses an unchanged performance regardless of any variation of environmental conditions. The stability is termed as stability variance and can be estimated as:

By using the estimated values

or

is the stability variation for the ith genotype under experimental conditions. If it is assume that stability variance is equal to the within environment at variance 𝛔^{2} i.e. 𝛔_{i}^{2} = 0, then it can be a stable genotype. The variance of the estimated parameters for the proposed model may be given by

Similarly,

Maximal sata information prior (MDIP) for the conditions under consideration may be given by

It is well known that

then

is the data information averaged over the value (µ, si) with g(µ, si) prior this average may aso given by

The average information in the data density minus the information in the prior density therefore,

Lagrangian expression is

According to the Euler-Lagrange equation

Gives

Asymptotically locally invariant (ALI) prior for the conditions under consideration may be given by

Since the conditions of ALI prior are satisfied. Therefore, ALI prior for (µ, Zi) may be estimated by

Where,

Since the g(µ, Z_{i}) is a function of Z_{i} and independent of µ, therefore

or